A Word from the Director..........................................................

CRM Annual Report 2001 - 2002 1

A Word from the Director................................................................................................................................ 2Presenting the CRM.......................................................................................................................................... 4Personnel 2001-2002.......................................................................................................................................... 5Scientific Personnel........................................................................................................................................... 6

Members 6Postdoctoral Fellows 8Visitors 10

Management..................................................................................................................................................... 12Bureau de direction 12Advisory Committee 12Computer Facilities 13

Homage to André Aisenstadt........................................................................................................................ 14Scientific Activities......................................................................................................................................... 16

Theme Year 2001-2002: Groups and Geometry 16Aisenstadt Chair 24General Program 2001-2002 26CRM Prizes 31National Program Committee 34Members’ Seminars and Special Events 38CRM-ISM Colloquium 44

Coming Activities ........................................................................................................................................... 45Theme Year 2002-2003: Math in Computer Science 45Theme Year 2003-2004: Geometric and Spectral Analysis 49Theme Year 2004-2005: Mathematics of Complex Multiple-Scale Systems 52Interdisciplinary and Industrial Program 54General Program 56

CRM Collaborative Network ....................................................................................................................... 58AARMS/ACSMA.............................................................................................................................................. 60Industrial Collaborations ............................................................................................................................. 61Awards, Distinctions and Landmarks........................................................................................................ 64Research Laboratories.................................................................................................................................... 65

CICMA 65CIRGET 67LACIM 69Mathematical Analysis Laboratory 71Applied Mathematics Laboratory 73Mathematical Physics Laboratory 74PhysNum 76Statistics Laboratory 78

Publications ..................................................................................................................................................... 80Recent Titles 80Previous Titles 81Research Reports 84

Financial Report at 31 May 2002 ................................................................................................................. 87Financial Statement 2001-2002 89

2 Annual Report 2000 - 2001 CRM

A Word from the DirectorScience first. It was anexceptionally rich year.The thematic program inGroups and Geometrybegan with a remarkablyvigorous three-weeksession in group theoryand low dimensionaltopology, with over onehundred participants foreach of the three weeks.

The workshops that followed were all greatsuccesses, and I hesitate to name just a few, forfear of offending those left out; I will howeverthank in passing our colleagues in Kingston,Eddy Campbell and David Wehlau, who puttogether a remarkable two-week session, with alarge number of students and visitors. Theholders of the Aisenstadt Chair this year werethree absolutely exceptional mathematicians:Edward Frenkel, Laurent Lafforgue and GeorgeLusztig. Lafforgue went on to receive a Fieldsmedal later in the year. Lafforgue and Frenkelgave their lectures in tandem, and wereaccompanied by Robert Langlands, who alsogave a series of talks. The year in all saw twentyor so lecture series, which had a considerableimpact (thanks once again to those who gavethem). If one adds to this the seminars of thevarious groups and laboratories attached to theCRM, the CRM-ISM Colloquium (my thanks tothe organizers, Dana Schlomiuk and TadashiTokieda), it all adds up to a rich scientificatmosphere, unthinkable even ten years ago.

The 2001-2002 program was not even over yetwhen we started on the 2002-2003 program onthe Mathematics of Computer Science. The CRMplayed host in May to two of the big conferencesin theoretical computer science, STOC and CCC.There were a number of small satellite activitiesorganized around this, and in June, a workshopon random number generators, organized instyle by Pierre L’Écuyer. The summer also saw aschool in quantum computing, directed by GillesBrassard, with over eighty participants.

As ever, the two industrial networks, MITACSand ncm 2, had their share of events anddevelopments. The main one was doubtless theofficial opening on December 6, 2001, of the newncm2 laboratory, the Laboratoire Universitaire

sur le Temps Extrême (LUTE). This laboratory,with an important infusion in cash, personneland computer time from Environment Canada,will work not only in the forecasting of extremeweather, but also on modelling its impacts, incollaboration with the various ncm2 partners. Afirst workshop is taking place in the fall of 2002on extreme values, and is co-organized with thefinance group. The year also saw the creation ofa second spin-off company, in data-miningapplied to insurance. The first, in imaging, wonthe Entrepreneurship prize of the École desHautes Études Commerciales de Montréal. TheCRM research group in imaging has continuedbuilding up a research network in brain-imaging. One of the group’s researchers, Jean-Marc Lina, is now sharing his time with theInstitut Universitaire de Gériatrie de Montréal,and is now an associate researcher at INSERM(France). This Montréal-Paris collaboration hasjust been awarded an important grant from theMinistère de la Recherche, de la Science et de laTechnologie.

The development of science does rely oncontinuous funding. This is an arduousconstraint and the year from this point of viewwas exceptionally full. The CRM submitted lastJanuary a request for renewal to NSERC, as partof a reallocations process that included fourinstitutes and twenty or so grant selectioncommittees. It was a heavy task: choosingpriorities, choosing programs, writing theproposal, organizing a site visit with over ahundred people to coordinate. Many of the CRMresearchers took part in the proceedings, and Ithank them. The whole process was a greatsuccess, with the CRM obtaining an 11% increasein funding, which puts it third in thereallocations exercise and gives it the samefunding as the Fields Institute and PIMS. Theadditional resources obtained will be usedmostly to increase funding of long-term visitorsand of postdoctoral fellows.

On the provincial front, as these words are beingwritten, the CRM has just submitted itsapplication to FQRNT, the provincial researchagency, for increased funding. The exercise, if itis crowned with success, will fund a certainnumber of laboratories associated to the CRM; ithas already allowed the CRM to obtain

A Word from the Director


significant financial support from all the majorQuébec universities, and this for the first time.

An additional satisfaction occurred in thewriting of the application, as I was listing the

large number of talented mathematicians thatare now in our universities, a large segment ofthem having just arrived. They will, I hope, havethe resources that they deserve.

Jacques Hurtubise


Presenting the CRMThe Centre de recherches mathématiques (CRM)was created in 1969 by the Université deMontréal through a special grant from theNational Research Council of Canada. It becamean NSERC national research centre in 1984. It iscurrently funded by NSERC (Natural Sciencesand Engineering Research Council), by theGovernment of Québec through the FQRNT(Fonds québécois de la recherche sur la nature etles technologies), by the Université de Montréal,and by private donations. The mission of theCRM is to do research in mathematics andclosely related disciplines and to provideleadership in the development of themathematical sciences in Canada.The CRM carries on its mission and nationalmandate in several ways:• it organizes a series of scientific events each

year, around a given theme (distinguishedlecture series, workshops, conferences,summer schools, visitor programs, etc.);

• its general program provides funding forconferences and special events at CRM andacross the country;

• each year it invites, through the AisenstadtChair, one or more distinguishedmathematicians, to give advanced courses aspart of its thematic program;

• it awards four prizes yearly: the CRM-FieldsInstitute Prize recognizing majorcontributions to mathematics, the AisenstadtPrize given for outstanding work done by ayoung Canadian mathematician, the CAP-CRM Prize for exceptional achievement intheoretical and mathematical physics, andthe CRM-SSC Prize for exceptionalcontributions to statistics in early career;

• it publishes some 150 technical reports andabout ten books per year. Some of itscollections are published jointly with theAMS and with Springer Verlag;

• it has an extensive postdoctoral fellowshipprogram, with 32 postdoctoral fellows inplace last year, funded either solely by theCRM or in partnership with otherorganizations;

• it informs the community of its activitiesthrough its web site at

www.CRM.UMontreal.CA;• it participates, with the other two Canadian

centres, in groundbreaking nationalinitiatives. One example is the MITACS

project (Mathematics of InformationTechnology and Complex Systems Another).example is the National ProgramCommittee, which provides funding for off-site research activities.

This national mandate is complemented by, andindeed supported by, a long-standing vocationof promoting research in the Montréal area. Forinstance,• the CRM supports, through partnership

agreements, a group of local researcherschosen mainly from departments ofmathematics and statistics, but alsocomputer science, physics, economics,engineering, etc.;

• it organizes series of regular seminars andlecture courses on different areas ofmathematical sciences;

• it sponsors joint activities with the ISM(Institut des sciences mathématiques)including the weekly CRM/ISM colloquium,graduate courses offered by distinguishedvisitors and a program of postdoctoralfellowships;

• it works actively at developing contacts withindustry. Its joint activities with liaison andresearch centres (CERCA, CIRANO andCRIM) and research centres doing appliedresearch (CRT, GERAD and INRS-Télécommunications) led to the creation ofthe Network for Computing andMathematical Modelling (ncm2). NSERC andabout twenty partners such as financialinstitutions, high-tech companies andgovernment agencies fund this network.

The CRM fulfils its national mission byinvolving the largest possible number ofCanadian mathematicians in its scientificprograms, both as participants and asorganizers. It also supports many events takingplace outside Montréal and the Province ofQuébec. It is recognized worldwide as one of themajor institutes in the mathematical sciences.The director of the CRM is assisted by twomanagerial structures: the Bureau de directionand the Advisory Committee. The AdvisoryCommittee is a group of internationallyrenowned mathematicians from Canada andabroad, who approve scientific programs andthematic years, choose recipients of the CRM-Fields and Aisenstadt prizes, and suggest newscientific ventures to explore.


Personnel 2001-2002The Director’s Office

Jacques Hurtubise DirectorJean LeTourneux Deputy Director, PublicationsYoshua Bengio Deputy Director, Industrial ProgramAnne Bourlioux Deputy Director, Scientific ProgramJohn Harnad Deputy Director, Scientific Program

(since January 2002)Niky Kamran Deputy Director, Scientific Program

(until December 2001)Diane Poulin Secretary

AdministrationBéatrice Kowaliczko Head of Administration (until April 2002)Vincent Masciotra Head of Administration (since April 2002); Financial and

Administrative OfficerMichèle Gilbert Administrative AssistantMuriel Pasqualetti Administrative AssistantJosée Simard Secretary

Scientific ActivitiesLouis Pelletier CoordinatorJosée Laferrière Assistant Coordinator

PublicationsAndré Montpetit TeX Expert (1/2 time)Louise Letendre TechnicianDiane Brulé-De-Filippis Secretary

Computer ServicesDaniel Ouimet Systems AdministratorAndré Montpetit Office systems manager (1/2 time)

CommunicationsSuzette Paradis Communications Officer & Webmaster (1/2 time)

MITACSNicole Huron Administrative Assistant


Scientific PersonnelSince its foundation in 1969, the CRM has been involved in a wide variety of research in mathematicsas reflected by the spectrum of the research interests of its members, including the CRM’s permanentresearch staff, members attached to the CRM through exchange agreements with neighboringuniversities and industries, and long-term visitors. The presence at CRM of such an active group ofresearchers has brought many benefits to the centre. In particular, the CRM’s national program isgreatly facilitated by having on hand a large reserve of willing organizers, who have even contributedfinancially to the organization of activities. The largest partnership is with the Université de Montréal,which gives the equivalent of five full-time teaching positions in release time to the CRM. Releaseagreements with the other Montréal area universities provide for the equivalent of two more full-timepositions. Facilities are also provided to researchers attached to junior colleges. Several members areattached to the CRM through industrial agreements such as those with Lockheed Martin Canada.

Members

Ali, Syed TwarequeMath. & stat.,Concordia Univ.

Angers, J.-F.Math. & stat.,Univ. de Montréal

Apostolov, VestislavMath., UQAM

Arminjon, PaulMath. & stat.,Univ. de Montréal

Bandrauk, AndréChimie,Univ. de Sherbrooke

Baribeau, LineMath. & stat.,Univ. Laval

Bartello, PeterMath. & stat.,McGill Univ.

Beaulieu, LilianeCégep du Vieux Montréal

Bédard, RobertMath., UQAM

Bélair, JacquesMath. & stat.,Univ. de Montréal

Benali, HabibINSERM, France

Bengio, YoshuaDIRO,Univ. de Montréal

Bergeron, AnneMath., UQAM

Bergeron, FrançoisMath., UQAM

Bergeron, NantelMath. & stat.,York Univ.

Bourlioux, AnneMath. & stat.,Univ. de Montréal

Boyer, StevenMath., UQAM

Brassard, GillesDIRO,Univ. de Montréal

Broer, AbrahamMath. & stat.,Univ. de Montréal

Brunet, RobertMath. & stat.,Univ. de Montréal

Bryant, DavidMath. & stat.,McGill Univ.

Clarke, FrancisUniv. de Lyon

Collin, OlivierMath., UQAM

Crépeau, ClaudeSchool of Computer ScienceMcGill Univ.

Csürös, MiklosDIRO,Univ. de Montréal

Cummins, Chris J.Math. & stat.,Concordia Univ.

Dafni, GaliaMath. & stat.,Concordia Univ.

Darmon, HenriMath. & stat.,McGill Univ.

David, ChantalMath. & stat.,Concordia Univ.

Delfour, MichelMath. & stat.,Univ. de Montréal

Durand, StéphaneCollège Édouard-Montpetit

Dssouli, RachidaComputer Science,Concordia Univ.

El-Mabrouk, NadiaDIRO,Univ. de Montréal

Fournier, RichardDawson College

Frigon, MarlèneMath. & stat.,Univ. de Montréal

Gagnon, LangisCRIM

Gander, MartinMath. & stat.,McGill Univ.

Gauthier, PaulMath. & stat.,Univ. de Montréal

Goren, EyalMath. & stat.,McGill Univ.

Goulard, BernardPhysique,Univ. de Montréal

Granville, AndrewMath. & stat.,Univ. de Montréal

Grundland, MichelMath., UQTR

Hall, Richard L.Math. & stat.,Concordia Univ.

Hallett, MichaelMath. & stat.,McGill Univ.

Harnad, JohnMath. & stat.,Concordia Univ.

Hurtubise, JacquesMath. & stat.,McGill Univ.

Hussin, VéroniqueMath. & stat.,Univ. de Montréal

Jakobson, DmitryMath. & stat.,McGill Univ.

Jaksic, VojkanMath. & stat.,McGill Univ.

Kamran, NikyMath. & stat.,McGill. Univ.

Kharlampovich, OlgaMath. & stat.,McGill Univ.

Kisilevsky, HershyMath. & stat.,Concordia Univ.

Klemes, IvoMath. & stat.,McGill Univ.

Scientific Personnel


Koosis, PaulMath. & stat.,McGill Univ.

Korotkin, DmitriMath. & stat.,Concordia Univ.

Labelle, GilbertMath., UQAM

Labelle, JacquesMath., UQAM

Lalonde, FrançoisMath. & stat.,Univ. de Montréal

Langlands, Robert P.Institute for AdvancedStudy, Princeton

Léger, ChristianMath. & stat.,Univ. de Montréal

Leroux, PierreMath., UQAM

Lesage, FrédéricCRM,Univ. de Montréal

Lessard, SabinMath. & stat.,Univ. de Montréal

LeTourneux, JeanPhysique,Univ. de Montréal

Lévesque, ClaudeMath. & stat.,Univ. Laval

Lina, Jean-MarcCRM,Univ. de Montréal

Major, FrançoisDIRO,Univ. de Montréal

Makkai, MichaelMath. & stat.,McGill Univ.

Mashreghi, JavadMath. & stat.,Univ. Laval

Maslowe, Sherwin A.Math. & stat.,McGill Univ.

Mathieu, PierrePhysique,Univ. Laval

McKay, JohnMath. & stat.,Concordia Univ.

Miasnikov, AlexeiMath. & stat.,McGill Univ.

Nekka, FahimaPharmacie,Univ. de Montréal

Nigam, NilimaMath. & stat.,McGill Univ.

Patera, JiriMath. & stat.,Univ. de Montréal

Perron, FrançoisMath. & stat.,Univ. de Montréal

Petridis, YiannisCRM,Univ. de Montréal

Polterovich, IosifMath. & stat.,Univ. de Montréal

Ramakrishna, RaviMath. & stat.,McGill Univ.

Ransford, ThomasMath. & stat.,Univ. Laval

Reutenauer, ChristopheMath., UQAM

Rosenberg, IvoMath. & stat.,Univ. de Montréal

Rousseau, ChristianeMath. & stat.,Univ. de Montréal

Roy, RochMath. & stat.,Univ. de Montréal

Russell, PeterMath. & stat.,McGill Univ.

Sabidussi, GertMath. & stat.,Univ. de Montréal

Saint-Aubin, YvanMath. & stat.,Univ. de Montréal

Sankoff, DavidMath. & stat.,Univ. de Montréal

Schlomiuk, DanaMath. & stat.,Univ. de Montréal

Schmidt, GeorgMath. & stat.,McGill Univ.

Shahbazian, ElisaLockheed Martin Canada

Stern, RonMath. & stat.,Concordia Univ.

Thaine, FranciscoMath. & stat.,Concordia Univ.

Toth, JohnMath. & stat.,McGill Univ.

Van Vliet, CarolynePhysics,Univ. of Miami

Valin, PierreLockheed Martin Canada

Vinet, LucMath. & Phys.,McGill Univ.

Winternitz, PavelMath. & stat.,Univ. de Montréal

Wise, DanielMath. & stat.,McGill Univ.

Worsley, KeithMath. & stat.,McGill Univ.

Zolésio, Jean-PaulINRIA, France



Postdoctoral FellowsEach year the CRM plays host to a number of postdoctoral fellows. The sources for their fundinginclude the NSERC postdoctoral program, the NATO international program administered by NSERC,the CRM (alone or with the ISM), and individual research grants from CRM’s members. The list belowincludes only postdoctoral fellows in residence at CRM or funded or co-funded by CRM, with theirfunding source given in brackets. Some of the fellows were in residence at CRM for only part of theyear – the affiliation is that where the doctoral degree was obtained.

Aguiar, MarceloTexas A&M Univ.(CRM-ISM)Allen, SteveUniv. de Sherbrooke(ncm2-Lockheed Martin)Bertola, MarcoS.I.S.S.A.(CRM-ISM)Brightwell, MarkUniv. of Glasgow(CRM-ISM)Buono, LucianoUniv. of Warwick(NSERC)Casesnoves, RaquelUniv. de Montréal(CRM)Chapoton, FrédéricParis VI(LACIM-CRM)Corteel, SylvieUniversité de Paris-Sud(CRM-ISM)Dai, JackIowa State Univ.(CRM-ISM)

Deteix, JeanUniv. de Montréal(CRM-GIREF)Guimond, Louis-SébastienUniv. de Montréal(CRSNG)Hagedorn, ThomasUniv. of Lethbridge(Sloan Fellowship)Langerman, StefanRutgers Univ.(CRM-McGill)Loutsenko, IgorUniv. de Montréal(ncm2)Maillot, SylvainUniv. Paul Sabatier(CRM)Masakova, SuzanaCzech Technical Univ.(NATO)Matessi, DiegoUniv. of Warwick(CRM-ISM)

Mei, MingKanazawa Univ.(CRM-McGill)Pal, AmbrusColombia Univ.(CRM-ISM)Penskoi, AlexeiUniv. de Montréal(CRM)Polterovich, IosifWeizmann Institute ofScience(CRM)Prasad, AmritanshuUniv. of Chicago(CRM-McGill-CICMA)Rasmussen, JorgenUniv. of Lethbridge(CRM-ISM)Saikia, AnupamTrinity College, Univ. ofCambridge(CRM-ISM)Savitt, DavidHarvard Univ.(NSERC)

Schiffler, RalfUQAM(FCAR)Sikora, S. AdamUniv. de Maryland(CRM-ISM)Tempesta, PiergiulioUniv. degli studi diLecce(CRM-ISM)Urquiza, José ManuelUniv. Pierre et MarieCurie(ncm2)Vénéreau, StéphaneInstitut Fourier(CRM-McGill)Vitse, PascaleUniv. de Bordeaux I(CRM-ISM)Wang, Sung HoDuke Univ.(CRM-ISM)



Next is a separate list for the postdoctoral fellows specifically involved with MITACS projects attachedto the CRM. The affiliation listed indicates where the research is being done.

Bao, WeishengInstitut de cardiologiede Montréal

Bub, GilMcGill Univ.

Caporossi, GillesUniv. de Montréal

Chavez, FranciscoUniv. of Toronto

Davidson, JoernUniv. of Toronto

Deerakhchan, KatayounInstitut de cardiologiede Montréal

Hadjar, AhmedÉcole Polytechnique deMontréal

Hong, GuUniv. of Waterloo

Kagabo, IssaÉcole Polytechnique deMontréal

Kanamori, TakafumiUniv. de Montréal

Mladenovic, NenadÉcole Polytechnique deMontréal

Shinagawa, KaoriInstitut de cardiologiede Montréal

Slimane, LeilaUniv. Laval

Stojkovic, GoranÉcole Polytechnique deMontréal

Stojkovic, MirelaÉcole Polytechnique deMontréal

Takeuchi, IchiroUniv. de Montréal

Tateno, KatsumiMcGill Univ.

Titcombe, MicheleMcGill Univ.

Villeneuve, DanielÉcole Polytechnique deMontréal

Wang, ShaojunUniv. of Waterloo

Ziarati, KoorushHEC Montréal

Zou, RenqiangInstitut de cardiologiede Montréal



VisitorsEach year the CRM hosts a large number of visitors. The majority comes to the centre to participate inscientific activities: in the year 2001-2002,!1667 such participants registered for workshops run solely bythe CRM. In addition, the CRM helped fund about twenty other scientific events. The following listincludes, only visitors who were in residence for long periods, ranging from a week to several months.

Akhperjanian, AshotYerevan Physics Inst.Aratyn, HenrikUniv. of IllinoisBen-Zvi, DavidUniv. of ChicagoBerest, YuriCornell Univ.Biswas, AtanuIndian Statistical Inst.Blouza, AdelUniv. Paris VIBridson, MartinPembroke CollegeBrinzanescu, VasileInst. of Mathematics SimonStoilowCasselman, William A.Univ. of British ColumbiaCojocaru, Alina CarmenQueen’s Univ.Cressie, Noel A.C.Ohio State Univ.Dawson, DonaldCarleton Univ.Deninger, ChristopherUniv. of MünsterDorodnitsyn, VladimirKeldysh Inst. of AppliedMathematicsDu Cloux, FokkoUniv. de Lyon I

Dumas, LaurentUniv. Paris VIFleischer, Isidore

Fleischmann, KlausWeiestrass Inst. for AppliedAnalysis & StochasticsFrenkel, EdwardUniv. of California, BerkeleyGazeau, Jean-PierreU. Paris VII Denis DiderotGeck, MeinolfUniv. Claude Bernard(Lyon I)Geiger, JochenJohann Wolfgang Goethe-Univ.Greven, AndreasUniv. Erlangen-NürnbergGrodzicky, RomanUniv. de MontréalGuillemin, VictorMITHavin, VictorMcGill Univ.Helmers, RoelofCWI AmsterdamHeusener, MichaelUniv. Blaise Pascal(Clermont-Ferrand II)Houzel, ChristianUPS, 2065 CNRSItskov, VladimirUniv. of MinnesotaJiang, YuUniv. AutonomaMetropolitana-IztapalapaKalnins, Ernest GüntherUniv. of Waikato

Karrakchou, JamilaÉcole Mohammadiad’ingénieurs

Khesin, BorisUniv. of TorontoKirillov, AlexandreUniv. of PennsylvaniaKlaassen, Chris A.Korteweg-de Vries Inst. forMathematics, UvAKnop, FriedrichRutgers Univ.Kokotov, A.Concordia Univ.Lafforgue, LaurentUniv. Paris-SudLedrappier, FrançoisÉcole Polytechnique(Palaiseau, France)Leitner, FrederickUniv. of ArizonaLevi, DecioUniv. di Roma TreLevy, JasonUniv. of OttawaLévy Véhel, JacquesINRIA, Projet FractalesLiben-Nowell, DavidMITLonghi, IgnazioUniv. of MünsterLusztig, GeorgeMITLysionok, IgorSteklov Mathematical Inst.Ma, LiTsinghua Univ.

Magri, FrancoUniv. di Milano

Mélard, GuyUniv. Libre de BruxellesMoody, Robert V.Univ. of AlbertaMurty, RamQueen’s Univ.Murty, V. KumarUniv. of TorontoNieto, Luis MiguelUniv. de ValladolidOnn, UriTechnion Inst.Orlov, AleksanderOceanology Inst.Osborn, TomUniv. of ManitobaOuansafi, AbdellatifUniv. de MontréalPatera, JanCzech Technical Univ.Pelantova, EditaCzech Technical Univ.Pogosyan, GeorgeBogoliubov Laboratory ofTheoretical PhysicsPolanco Ruig, Luis B.Univ. de ValenciaPopov, VladimirSteklov Mathematical Inst.Pouryayevali, MohamadRezaUniv. of IsfahanRacine, MichelUniv. of OttawaRaffinot, MathieuUniv. de Versailles



Raoult, AnnieUniv. Joseph-FourierRasmussen, ChristopherUniv. of ArizonaRoussarie, RobertUniv. de BourgogneSabin, MalcomeNumerical Geometry Ltd.Sahakyan, VardanYerevan Physics Inst.Scott, KeithAtlantic Nuclear ServicesLtd.Sengupta, JyotirmoyTata Inst. of FundamentalResearchSheftel, Mikhail B.Feza Gursey Inst.Sinha, KaneenikaQueen’s Univ.

Sorger, ChristophUniv. de NantesSpringer, Tonny A.Univ. of UtrechtStembridge, John R.Univ. of MichiganStrasburger, AleksanderUniv. of BialystokStrawdermann, William E.Rutgers Univ.Sujatha, R.Tata Inst. of FundamentalResearchSvobodova, MilenaCzech Technical Univ.Szmigielski, JacekUniv. of SaskatchewanThiriet, MarcINRIA Rocquencourt

Thomova, ZoraSUNY Inst. of TechnologyTouzi, NizarCRESTTyurin, AndreiSteklov Inst. of Mathematicsvan Diejen, Jan FelipeUniversidad de TalcaVarsaie, SaadInst. for Advanced Studiesin Basic SciencesVerger-Gaugry, Jean-LouisUniv. J. Fourier, GrenobleViolette, DonaldUniv. de MonctonVogan, David A. JrMIT

Vulpe, NicolaeAcademy of Sciences ofMoldovaWakolbinger, AntonJohann Wolfgang Goethe-Univ.Walton, MarkUniv. of LethbridgeZeron, Eduardo SantillanCinvestav-IPN (NationalPolytechnical Inst.)Zhang, YuanliUniv. de MontréalZich, JanCzech Technical Univ.Zuk, AndrzejUniv. of Chicago


ManagementBureau de direction

The Bureau consists of members from theUniversité de Montréal (8 to 11 members) andfrom the outside (2 to 5 members). The rector ofthe Université de Montréal and the dean of itsArts and Sciences faculty are represented onthe Bureau. The Bureau adopts the policies ofthe Centre, recommends the nomination andthe promotion of researchers and theappointment of regular members, advises thedirector on the preparation of the budget andthe Université de Montréal on the choice of thedirector.

Advisory CommitteeThe Advisory Committee is constituted ofdistinguished researchers from Canada andabroad. Its members are either mathematiciansor scientists with close ties to the mathematicalsciences. The rector of the Université deMontréal and the director of the CRM attendthe meetings of the Advisory Committee. TheAdvisory Committee is informed periodicallyof the activities of the Centre, through thedirector, and transmits any advice that it deemsrelevant to the Bureau de direction.

Bergeron, FrançoisUQAM

Brassard, GillesUniv. de Montréal

Caillé, AlainVice-rector, ResearchUniv. de Montréal

Cléroux, RobertUniv. de Montréal

Hubert, JosephAssociate Dean,Research, FASUniv. de Montréal

Hurtubise, JacquesDirector CRM,McGill Univ.

Hussin, VéroniqueUniv. de Montréal

Ransford, ThomasUniv. Laval

Rémillard, BrunoUQTR

Rousseau, ChristianeUniv. de Montréal

Saint-Aubin, YvanUniv. de Montréal

Craig, WalterMcMaster Univ.

Glynn, PeterStanford Univ.

Haiman, MarkUniv. of California

Hambleton, IanMcMaster Univ.

Hitchin, NigelOxford Univ.

Lawless, JerryUniv. of Waterloo

Luskin, MitchellUniv. of Minnesota

Murty, RamQueen’s Univ.

Odlyzko, AndrewUniv. of Minnesota

Rousseau, ChristianeUniv. de Montréal

Zelditch, StevenJohns Hopkins Univ.

Management


Computer FacilitiesThe CRM offers its members and visitors a Unixenvironment based on a Sun Enterprise-450equipped with four 400-MHz Ultra-Sparcprocessors and 2 Gb of memory as a mainserver,* and a secondary server Sun Sparc-1000with eight 40-MHz processors and 384 Mb ofmemory for lightweight tasks. A new Linuxserver (single processor PC at 1.4-MHz and 2 Gbof memory) was added at the beginning of 2002to offer a Linux environment to CRMresearchers. This computing power isdistributed through the offices and commonrooms via 30 Sun workstations (from Sparc-4 toUltra-10), several X-terminals, and four Linuxworkstations.

The software libraries include compilers (FORTEenvironment for C, C++ and Fortran, GNUcompilers, Java, etc.), programs for symbolicmanipulations and numerical computations(Mathematica, Maple, Macaulay, Matlab),several text editors, web browsers, mail tools,and most utilities common to the mathematicalworld (fftw-Discrete Fourier Transform, dstool-tool for dynamical systems, etc.). Upgrades toTeX and its dialects are uploaded whenever theyare released. Unix applications to communicatewith the PC and Mac world are also installed,such as SAMBA (PC file and printer server),OpenOffice (Office suite), and AUFS (file serverfor Macintosh). A Web server (Apache underUnix) with a secure SSL version and arecognized 128-bit Thawte certificate thatenables secure registration for participants toCRM activities hosts the CRM web pages. In2001, a new look was given to our web pages,including some Flash programming, and moreinformation.

For security, many programs for surveillanceand access control are in place, includingfrequent updates of the operating system. Mostof our computers are connected to an alarmsystem.

Since 1999, the CRM operates its own privatelocal area network (LAN): five BayNetworksBaystack-450 switches, providing 120 ports ontwisted-pair at 10/100 Mb/s and four optic fiberlinks supporting Gigabit Ethernet. This privatelocal network is linked to the network of theUniversité de Montréal that maintains the

connections with RISQ (Réseau interordinateursscientifique québécois) and CA*net (theCanadian Internet transit service). Members andguests can now connect their personal laptops(or computers) to the CRM private networkdirectly, or if they are outside CRM offices,through phone links to our PPP server and itsfour modems.

The support staff works on Sun stations or onMacintoshes tied to the Sun server for allservices, such as mail and backups. A three-yearplan for the replacement of all support staffcomputers started in 1999 and was completedthis year. Phase 1 of a new database wascompleted at the end of 2001. This databasehelps support staff to better manage the contacts,activities, registrations to activities, and offices ofCRM. Phase 2, which should be completed at theend of 2002, aims at enabling online printing ofadministrative forms and at standardizing theinformation needed at various stages of thepreparation of scientific activities (registrations,announcements, reports, etc.) A dynamicdirectory on the Web will also replace the CRMstatic directory with secure access to thedatabase.

Printing needs are served by two HP-8000DNworkgroup printers (1200-dpi double-sided), aswell as an ink-jet network printer Epson-900Nfor colour printing, and some small printers forsupport staff. The CRM established a printingquota system in 2001 in order to save paper.

The CRM’s servers are installed in a roomspecifically designed for computers, withindependent controlled environment and UPS(Uninterruptible Power Supply).

In 2002, a new room with five X-terminals andthree Mac computers was installed forconference participants at CRM to give themaccess to Telnet, FTP and SSH.

* The main server (Enterprise-450), 22 Sunworkstations Ultra-5 and Ultra-10 and the completeLocal Area Network installed in 1999 were all paid bya grant from the Canadian Foundation for Innovationtogether with the Government of the Province ofQuébec and a donation (20% of total value) from SunMicrosystems (for computers) and Anixter (for thenetwork).


Homage to André Aisenstadt

On 4 October 2001, André Aisenstadt, theCRM’s great benefactor, passed away. Hedeclared once, in a conversation: “Age iswithout importance. It’s what you do thatcounts.” An exceptionally long life permittedhim to demonstrate this assertion in strikingways.

The sciencesAfter leaving his native Russia, he beganengineering studies in Darmstadt, during whichhe discovered a deeper interest for mathematicsthan engineering. He thus decided to change hisstudies to mathematics, which he pursued at theuniversities of Würzburg and Jena, afterwardscompleting doctoral studies in mathematicalphysics in Zurich under the direction of ErwinSchrödinger. He counted among his teachersHermann Weyl and Andreas Speiser, and amonghis fellow students John von Neumann andEnrico Fermi. Even though Einstein had alreadyleft Zurich by then, he would return often and itis during one of these visits that AndréAisenstadt established a friendship that lasteduntil the end of the great physicist’s life.

Arrival in CanadaHaving obtained his PhD, André Aisenstadtfaced a dilemma: Herman Weyl began makingapproaches in England so that he could continuehis research at Oxford or Cambridge, but hisfather, a prosperous businessman, worrying thathis son would begin an academic career, invitedhim to join the family entreprise. The father won,but the son would always regret, it seems,having abandoned mathematics. In 1939, AndréAisenstadt immigrated to Canada and settled inMontréal for cultural reasons. Soon after hisarrival, Mackenzie King as hed him toparticipate in the creation of the CentralMortgage and Housing Agency and in theestablishment of a housing building program forveterans. While working on these projects inOttawa, he launched an enterprise in Montréal,the Parkdale Homes Development Corporation,which built large sectors of the city.

Charitable endeavoursAround 1967, his wealth established, AndréAisenstadt abandoned the construction industryin order to focus on charitable activities. Hiswife, Niussia Rosenstein, an accomplishedpianist, convinced him to actively participate inthe establishment of the Marlboro Festival andMusic School. All those who had the pleasure ofmeeting him know with what verve he wouldreminisce about Marlboro and more particularlyabout two of his friends, Rudolf Serkin andPablo Casals. In these same years began hisfinancial support of the CRM. A first donationled to the creation of the Aisenstadt Chair thatenabled the Centre to invite during those yearsthe most remarkable mathematicians of the time.Thanks to another financial gift, the AndréAisenstadt Prize, that recognizes the excellenceof young Canadian mathematicians, wasestablished in 1991. And the building thathouses the mathematical sciences at theUniversité de Montréal bears his name inrecognition of a major financial contribution forits construction.

Homage to André Aisenstadt

CRM Annual Report 2001-2002 15

Mathematics firstIt would be difficult to give an exhaustive list ofall the organizations that benefited from AndréAisenstadt’s generosity, but a short list wouldinclude the Montréal Jewish Hospital, theInstitut de recherches cliniques de Montréal andthe Montréal Symphony Orchestra. It wouldseem though that he drew particular satisfactionfrom having contributed to the development ofmathematics: “Thanks to my relationship withthe CRM,” he said in the same conversationquoted above, “I had a renaissance as amathematician.” It is therefore with alwaysrenewed pleasure that he would meet theholders of the Aisenstadt Chair and the winnersof the Prize.

A love of artThe Aisenstadt university building, the Chairand the Prize will help future generationsremember the debt they have towards theperson who gave them their name. It isnonetheless important not to forget the valuesthat underlay the charitable activities of thisremarkable man. Didn’t he say in that sameconversation — For me, art — and by art I meanmathematics as much as music, literature andpainting — is neither an hors d’oeuvre nor a dessert,it is the main course of life.

Jean LeTourneuxDeputy Director

An afternoon in memory of André Aisenstadt

On January 18th, 2002 the CRM hosted a small celebration of André Aisenstadt’s role in the Montréalmathematical community, with three special speakers. The first, Niky Kamran, was the first recipient ofthe André-Aisenstadt prize (1991). The title of his talk was L’opérateur de Dirac en géométrie de Kerr. FrancisClarke, of the Institut Universitaire de France and the Université de Lyon, director of the CRM from 1984to 1993, spoke on La théorie du retour d’état (feedback) en théorie du contrôle: une introduction, The last speaker,Jingyi Chen, the 2001 winner of the André-Aisenstadt prize, gave his prize lecture on Quaternionicmappings between hyperkähler manifolds. Reminiscences followed the scientific part of the afternoon: AnatoleJoffe and Francis Clarke, who were successive directors of the CRM, spoke with some emotion of theirassociation with André Aisenstadt, and Robert Lacroix, the Rector of the Université de Montréal, spoke ofAndré Aisenstadt’s role within the University. The afternoon’s events were closed off with a reception,which recalled the memory of a man who not only loved science but who also had an unfailing sense ofhospitality.


Scientific ActivitiesThe core of each year’s scientific program at the CRM is its thematic program. The AdvisoryCommittee chooses the topic for its scientific importance, its timeliness, and its impact on theCanadian scientific community. Preceding years’ topics include: Probability and Stochastic Control(1992-93); Dynamical Systems (1993-94); Geometry and Topology (1994-95); Applied and NumericalAnalysis (1995-96); Combinatorics and Group Theory (1996-97), Statistics (1997-98), Number Theoryand Arithmetic Geometry (1998-99), Mathematical Physics (1999-00), Mathematical Methods in Biologyand Medicine (2000-01). A year’s activities can combine a good number of workshops and conferences,one or two Aisenstadt Chairs, a number of visiting scientists in residence, and some postdoctoralfellowships. Typically, there is some coordination with Montréal universities to offer appropriategraduate courses in order to help graduate students participate in the activities. The reports arepresented in the language in which they were submitted.

Theme Year 2001-2002:Groups and Geometry

The role of group actions and groups in generalis ubiquitous in geometry, and the year’sprogram concentrated on some areas in whichthere has been important recent progress. Theyear consisted of two segments, the first moredifferential-geometric in flavour, and the otherone concentrating specifically on the linksb e t w e e n a l g e b r a i cgeometry, group theoryand representat iontheory. There was aspecial focus on training,with intensive mini-courses, introductoryseries, and CRM-ISMg r a d u a t e c l a s s e sspecially organized inconjunction with thethematic year. Therewere ten postdoctoralfellows with researchinterest connected to thetheme year. For the firstt ime, a grant ofUS$50,000 was receivedfrom the NationalScience Foundation withthe specific purpose offunding US students andpostdoctoral researchersinterested in participating in CRM’s theme yearactivities. There were a total of 1305 registeredparticipants for the activities.

GROUPS, TOPOLOGY ANDDIFFERENTIAL GEOMETRYJune-December 2001

Groups and Low-DimensionalTopologyJune-July 2001Org.: Steven Boyer (UQAM), Dani Wise (Brandeis &McGill)

The two workshops andfive mini-courses were atremendous success byany measure. Eachweek had more than100 participants, manyof whom were involvedin all three weeks. Oneof the most satisfyingaspec ts was theattendance of a greatnumber of graduatestudents who wered r a w n f r o m s i xdifferent continents.T h e f o r m a t o fsandwiching the mini-courses between theworkshops meant that agreat many studentstook part in weeks 1and 3 as well, much to

the delight of the more senior participants.Throughout the scientific level of the talks aswell as their exposition qualities were of a veryhigh order. The general feeling was that the

Scientific Activities


research areas covered were in a healthy statewith a promising future.The topics covered during the workshop ongroups and 3-manifolds included geo-metrization of 3-dimensional orbifolds, non-hyperbolic Dehn fillings of hyperbolic 3-manifolds, the weak Lopez conjecture, the word-hyperbolicity of the fundamental groups oflaminar 3-manifolds, the virtual Hakenconjecture, the generalized Smale conjecture,Heegard splittings, representations of the braidgroup, and geometric cobordisms of manifolds.The mini-course lecturers put a tremendouseffort into the preparation and presentation oftheir subjects with the result that each did a trulyexceptional job of presenting what was at timesquite technical and demanding material. It ishard to imagine better or more accessibleintroductions to these areas.The topics covered during the workshop ongeometric group theory included: Word-hyperbolic groups, decision problems, theboundary of a group, CAT(0) geometry,representation varieties, mapping class group,proof of the Tarski conjecture on the elementarytheory of free groups, splittings of groups,isoperimetric functions, torsion groups,quasiconvex subgroups, group theoreticalapproaches to the geometrization conjecture.

WORKSHOP ON GROUPS AND 3-MANIFOLDSJune 25-29, 2001Org.: Steven Boyer (UQAM), Dani Wise (Brandeis &McGill)

This workshop focused on recent progress onvarious open topological and geometricclassification problems as well as some of thenewer research directions.Invited speakers: S. Bigelow (Univ. of Melbourne), M.Boileau, (Univ. Paul Sabatier), D. Calegari (Harvard Univ.),D. Cooper (Univ. of California, Santa Barbara), M. Culler(Univ. of Illinois at Chicago), N. Dunfield (Harvard Univ.),C. Gordon (Univ. of Texas at Austin), S. Kerckhoff (StanfordUniv.), M. Lackenby (Univ. of Oxford), D. Long (Univ. ofCalifornia, Santa Barbara), J. Luecke (Univ. of Texas atAustin), Y. Moriah (Technion – Israel Institute ofTechnology), J. Porti (Univ. Autonoma de Barcelona), A.Reid (Univ. of Texas at Austin), Y. Rieck (Nara Women’sUniv.), H. Rubinstein (Univ. of Melbourne), P. Shalen (Univ.of Illinois at Chicago), Y.-Q. Wu (Univ. of Iowa), X. Zhang(SUNY Buffalo).

MINI-COURSESJuly 2-6, 2001

Michel Boileau (Univ. Paul Sabatier)Geometrization of 3-dimensional orbifolds

Martin Bridson (Univ. of Oxford)Non-positively curved spaces and hyperbolic groupsRuth Charney (Ohio State Univ.)The geometry of Coxeter and Artin groupsBenson Farb (Univ. of Chicago)A crash course on the geometry of groupsPeter Shalen (Univ. of Illinois at Chicago)Representations of 3-manifold groups

WORKSHOP ON GEOMETRIC GROUP THEORYJuly 9-13, 2001Org.: Steven Boyer (UQAM), Dani Wise (Brandeis &McGill)

The theory of infinite groups was revolutionizedby an infusion of ideas from geometry andtopology. This has led to the resolution of manyold problems and the formulation of newproblems and methods that have broadened thescope of the field. This workshop focused onthese new developments in geometric grouptheory.Invited speakers: Iain Aitcheson (Univ. of Melbourne), M.Bestvina (Univ. of Utah), B. Bowditch (Univ. ofSouthampton), Noel Brady (Univ. of Oklahoma), M. Bridson(Univ. of Oxford), S. Gersten (Univ. of Utah), I. Kapovich(Univ. of Illinois at Urbana-Champaign), M. Kapovich (Univ.of Utah), O. Kharlampovich (McGill Univ.), Bruce Kleiner(Univ. of Michigan at Ann Arbor), Igor Lysionok (SteklovInstitute), J. McCammond (Texas A & M Univ.), John Meier(Lafayette), Lee Mosher (Rutgers), A. Miasnikov (CCNY),Graham Niblo (Southampton), P. Papazoglou (Univ. Paris-Sud), Michah Sageev (Technion), John Stallings (Berkeley),Paul Schupp (UIC), Zlil Sela (Hebrew Univ.). There was alsoan additional panel of nine contributed talks featuring:Patrick Dehornoy (U. Caen), Murray Elder (Texas A&M),Max Forester (Warwick), Daniel Groves (Oxford), DanGuralnick (Technion), Chris Hruska (Cornell), Jan-MarkIniotakis (Warwick), Tim Riley (Oxford), Eric Swenson(BYU).

Topology of Manifolds and GroupActionsAugust 20-24, 2001Org.!: Ian Hambleton (McMaster), Ronnie Lee (Yale)

Recently there have been importantbreakthroughs in the study of the topology ofmanifolds and related topics on group actions,especially in the area of 3-and 4-dimensionalmanifolds with new input from the Seiberg-Witten theory and symplectic topology. Thisworkshop provided an ideal setting to presentthese new advances and related developments inother areas of topology.The workshop had 38 participants, including anice mixture of mathematicians from differentareas of geometric and algebraic topology. Theaim of the conference to bring about formal and



informal discussion between differentperspectives, was certainly realized in therelaxed and convivial setting of the CRM. Theorganizational support from the CRM wasoutstanding, as usual.The program was interesting and varied, with alarge number of talks by recent Ph.D.’s andpostdoctoral fellows.Invited speakers: J. Morgan (Columbia Univ.), R. Gompf(Univ. of Texas at Austin), T.-J. Li (Princeton Univ.), D.Ruberman (Brandeis Univ.), S. Vidussi (Univ. of California),F. Quinn (St. Francis Xavier Univ.), S. Krushkal (Yale Univ.),B. Williams (Univ. of Notre Dame), A. Edmonds (IndianaUniv.), M. McCooey (McMaster Univ.), M. Marcolli (Max-Planck-Institute für Mathematik), H. Boden (McMasterUniv.), R. Fintushel (Michigan State Univ.), P. Feehan(Rutgers Univ.), S. Strle (McMaster Univ.), S. Cappell(Courant Institute), P. Ozsvath (Princeton Univ.), J. Davis(Univ. of Toronto), H. Johnston (Vassar College), R. Schultz(Univ. of California), E. Miller (Polytechnic Univ.), G.Friedman (Yale Univ.), B. Owens (Trinity College), E.Pedersen (State Univ. of New York at Binghamton).

Infinite-Dimensional Lie GroupsOctober 29 to November 6, 2001Org.: Niky Kamran (McGill), Boris Khesin (Toronto)From a differential-geometric point-of-view,infinite-dimensional Lie groups arise asautomorphism groups of various geometricstructures on the manifolds, such as a volumeform, a foliation, a contact structure or asymplectic structure. The study of these infinite-dimensional Lie groups becomes a fundamentalproblem in areas of mathematics as diverse ashydrodynamics and symplectic topology.Another wide class of infinite-dimensional Liegroups is formed by loop groups, Kac-Moodygroups, and more generally, by gauge groups onmanifolds of arbitrary dimension. The successesin the study of these groups have beenimmensely fruitful both in low-dimensionalgeometry and topology and in quantum fieldtheory.Infinite-dimensional Lie groups are alsofundamental in the theory of integrable systemsand their hierarchies. In this context, their actionbecomes quite explicit on spaces of pseudo-differential and Fourier integral operators. Thistwo-week session started out two very beautifulseries of four conferences given by VictorGuillemin (MIT) and A. Kirillov (Penn.). Thefollowing week was occupied by a workshopthat reviewed a good sample of the topicsmentioned above. Altogether, there were manyvery interesting discussions between peopleworking on various aspects of the problem andthe interactions were very fruitful.

Introductory LecturesOctober 29-November 1, 2001V. Guillemin (MIT)The convexity theorem and moment polytopesA.A. Kirillov (Pennsylvania)The Virasoro group and related complex geometryWorkshop on the Geometry of Infinite-Dimensional Lie GroupsNovember 2-6, 2001Invited speakers: O. Bogoyavlenskij (Queen’s), V. Guillemin(MIT), J. Harnad (CRM & Concordia), L. Jeffrey (Toronto),M. Kapranov (Toronto), A. Kirillov (Pennsylvania), F.Lalonde (UdeM), J. Leslie (Howard), E. Meinrenken(Toronto), G. Misiolek (Notre Dame), P. Olver (Minnesota),H. Omori (Tokyo), V. Ovsienko (CNRS-Luminy), A. Pianzola(Alberta), M. Pinsonnault (UQAM), T. Ratiu (EPFL,Lausanne), T. Robart (Howard), C. Roger (Lyon I), P.Slodowy (Hamburg), R. Wendt (Fields Institute), P.Winternitz (CRM), C. Woodward (Rutgers Univ.), I.Zakharevich (Ohio State).

GROUPS AND ALGEBRAIC GEOMETRYJanuary-June 2002The importance of algebraic geometry inrepresentation theory has grown enormouslyduring the past decades with the arrival of suchtechniques as D-modules and perverse sheaves.Geometry intervenes in a crucial fashion in theproof of such results as the Kazhdan-Lusztigconjecture, the construction of canonical basesfor representations, and the work of Beilinson-Drinfeld on the Geometric Langlands program.A number of deep connections have arisenbetween the algebraic geometry and algebraiccombinatorics, whose ramifications extend allthe way to mathematical physics and topology.A special emphasis of the program will be ingraduate training, and a variety of short courseswill be organized, as well as graduate courses ofa more introductory nature. Funding is availablefor graduate students wishing to attend.

Graduate coursesJanuary-April 2002The semester included several graduate coursesrun by ISM to prepare local students to thethematic year activities.Abrahamm Broer (Montréal)Hilbert schemes of points and their applicationsHenri Darmon (McGill)Automorphic formsEyal Goren (McGill)Curves, vector bundles on curves and their moduliFrédéric Lesage (Montréal)Algèbres de Kac-Moody



WORKSHOP ON HILBERT MODULAR VARIETIESAND FORMSJanuary 3-6, 2002, Far Hills Inn, QuébecOrg.: E. Z. Goren and H. Darmon (McGill)

The Workshop was dedicated to surveyingrecent developments in the study of Hilbertmodular varieties and forms, such as: (i)stratification and classification of Hilbertmodular varieties, special loci and cycles; (ii)Hilbert modular forms: congruences, andassociated Galois representations; (iii) rationalpoints on Hilbert modular varieties. Applicationto the Langlands program and the Fontaine-Mazur conjecture; (iv) periods of Hilbertmodular forms. Application to the constructionof rational points on elliptic curves and modularabelian varieties.The workshop has been a tremendous success. Itbrought together experts and junior researchersin the area of Hilbert modular varieties andforms. We had an intensive program, consistingof 15 lectures in three days, given by some of the28 participants. The ambient atmosphere, in asecluded cozy Laurentian resort, with theopportunity of walks in the woods, cross-country skiing and other activities, was a majorfactor in the success of the workshop in the senseof interaction between researchers in the field,and helped to establish the informal anddynamic atmosphere we were aspiring toachieve.The scientific level of the workshop was veryhigh. Much of the results reported were verynew, not yet published, and helped bring theparticipants up to date with current research.The mathematical discussion was continued,during the joint meals, and well into the night inthe lounge. Particular topics, such as the Serreconjecture for Hilbert modular forms, were in theair. It is clear that several participants of theworkshop, who work on aspects of thatconjecture, will use some of the results reportedby the other participants.

Invited speakers: J. Achter (Columbia), F. Andreatta (Padua),N. Archinard (CICMA), S. Baba (CICMA), A. Brown (Tata),H. Darmon (McGill), L. Dembele (McGill), F. Diamond(Brandeis), J. Ellenberg (Princeton), A. Ghitza (MIT), E.Goren (McGill), P. Green (Harvard), F. Jarvis (Sheffield), E.Kani (Queen’s), A. Logan (Berkeley), E. Nevens (ImperialCollege), M.-H. Nicole (McGill), U. Onn (Technion), A. Pal(CRM), A. Prasad (CRM), R. Pries (Columbia), R.Ramakrishna (Cornell), A. Saikia (CICMA), D. Savitt(CICMA), R. Sreekantan (Tata), M. Thillainatesan(Columbia), A. Tupan (CICMA), Chia-Fu Yu (Columbia).

Winter School on Computations inCoxeter GroupsJanuary 21-28, 2002Org. : W. Casselman (UBC), R. Bédard (UQAM), F. duCloux (Lyon I), M. Geck (Lyon I)

Each lecturer gave five lectures. Bill Casselmangave the introductory lectures on Coxetergroups, Fokko du Cloux lectured on details ofmachine computations in Coxeter groups,Meinholf Geck lectured on character tables andHecke algebras of finite Coxeter groups, andRobert Bédard summarized the state of currentknowledge about Kazhdan-Lusztig cells in affineCoxeter groups. Evenings were spent in worksessions at computers, involving both lecturersand students. These were something of anexperiment, and only partially successful, butthe idea was basically a fruitful one. If this is tobe repeated in the future, they should probablybe made more formal.It is intended that the entire series will beeventually available on the Internet. Stillphotographs were made of every blackboardwritten, and very soon the overheadtransparencies will be scanned, also. These arec u r r e n t l y a v a i l a b l e a thttp://www.math.ubc.ca/people/faculty/cass/coxeter/farhills/lectures.html along with arewritten version of about half of the lectures byCasselman, currently being expanded.The material covered in the courses is not at allcurrently available publicly in a digestible form,and the long-term benefit of the workshop willlikely be the Internet notes.

Group Actions on Rational VarietiesFebruary 27 to March 3, 2002Org.: P. Russell (McGill)

The workshop had an international composition,with participants from Canada, Japan,Singapore, Taiwan, the USA, the Netherlands,France, Germany, Chile, Russia, Sweden,Switzerland and Poland. A special effort to bringgraduate students and posdoctoral fellows to the



workshop paid off, ten attended and of these sixgave talks.Recent developments in group actions on affinespaces and related varieties with simpletopology made up, as planned, the main themeof the workshop. Algebraic, complex analyticand topological aspects were covered.Interestingly, the workshop brought into sharpfocus the important role played by Danielewskisurfaces both in the study of surfaces with trivialMakar-Limanov invariant and the study ofadditive actions on affine 3-space. Thissurprising connection had only very recentlybecome apparent.An excursion to Mt. St. Hilaire was highlyappreciated by all participants in the workshop.The excursion ended with a lively session onopen problems at the Gault Estate. These arenow in the process of being collected and will bemade publicly available as part of the CICMApreprint series.Invited speakers: A. Broer (Université de Montréal), P.Cassou-Noguès (Université Bordeaux I), D. Daigle(Université d’Ottawa), K. Fieseler (Uppsala University), G.Freudenburg (University of Southern Indiana), R. Ganong(York University), M. Gizatullin (Universidad TecnicaFederico Santa Maria), A. Hundemer (McGill University), Z.Jelonek (Polish Academy of Sciences), S. Kaliman (Universityof Miami), M. Kang (Taiwan National University), H. Kraft(Universität Basel), F. Kutzschebauch (Uppsala University),S. Marcello (Universität Regensburg), K. Masuda (HimejiInst. of Tech.), M. Miyanishi (Osaka University), L. Moser-Jauslin (Université de Bourgogne), V. Popov (SteklovMathematical Institute), M. Roczen (Humboldt-Universitätzu Berlin), A. Sathaye (University of Kentucky), V. Shpilrain(The City College of New York), S. Vénéreau (CRM), D.Wright (Washington University), D. Zhang (NationalUniversity of Singapore).

Classical Invariant Theory WorkshopApril 8-19, 2002, Queen’s University, KingstonOrg.: H.E.A. Eddy Campbell (Queen’s), & David Wehlau(Royal Military College, Kingston)

Week OneThe first week of the workshop was devoted tointroductory lectures aimed at graduatestudents, younger mathematicians and for thosewho wished to acquire a breadth of knowledgeacross invariant theory. The workshop was partof the theme year on Groups and Geometry beingheld under the auspices of the Centre derecherches mathématiques.During the first week, four distinguishedmathematicians gave a series of lectures. Theywere Professors P. Fleischmann (Kent),Hanspeter Kraft (Basel), G. W. Schwarz(Brandeis), and Harm Derksen (Michigan).

Week TwoThe second week was devoted to a workshop onInvariant Theory, for which many of theyounger mathematicians stayed to listen. Theexperts listed below gave talks of 50 minutesduration, bearing in mind the audience. In thissecond week, the focus was on current problemsin keeping with the workshop nature. Thespeakers included Loek Helminck, JuliaHartmann, Marcus Hunziker, NondasKechagias, Gregor Kemper, Frederich Knop,Alexander Kuehn, Lucy Moser-Jauslin, VladimirPopov, Yasmine Sanderson, Mufit Sezer, JoelSegal, R. James Shank, Nicolas Thiery, andWilberd van der Kallen.ProceedingsA volume of proceedings of the Workshop isplanned in the CRM Proceedings and LectureNotes Series, published by the AmericanMathematical Society. The four main lecturershave submitted expository articles summarizingtheir lectures, and we expect to have 14additional papers, all of which are beingrefereed at the time of this report. As well, therewill be an article describing current problemswith contributions from many of theparticipants.Invited speakers: Jaydeep Chipalkatti, Jianjun Chuai, HarmDerksen, Peter Fleischmann, Julia Hartmann, LoekHelminck, Markus Hunziker, Wilberd van der Kallen,Dikran Karagueuzian, Kiumars Kaveh, Nondas Kechagias,Gregor Kemper, Friedrich Knop, Hanspeter Kraft, AlexanderKuehn, Lucy Moser-Jauslin, Mara Neusel, Vladimir Popov,Leonid Rybnikov, Yasmine Sanderson, Gerald Schwarz, JoelSegal, Mufit Sezer, R. James Shank, Alexander Smirnov,Nicolas Thiery, Oxana Yakimova.

Concentration Period on the LanglandsProgram for Function FieldsApril 29 to May 17, 2002Org.: H. Darmon (McGill), J. Hurtubise (CRM)

On a vu ces dernières années des percéesspectaculaires dans le programme de Langlandssur des corps de fonctions tant en caractéristiquezéro qu’en caractéristique p. Le but de cettepériode de concentration était de fournir auxparticipants un survol de quelques-unes destechniques essentielles du domaine ainsi que desnouveaux résultats. Le résultat fut une des sériesde conférences les plus spectaculaires qu’a vuesle CRM depuis plusieurs années.April 8-26, 2002!La première partie du programme fut occupéepar des cycles de conférences de trois ou quatreheures donnés par des gens de la région deMontréal, pour étudiants de 2e et 3e cycles et



post-doctorants sur la matière nécessaire à unecompréhension du programme de Langlands. Laliste des conférenciers et de leurs sujetscomprend!:Abraham Broer (Montréal)D-modulesJacques Hurtubise (CRM & McGill)The Hitchin systemsJason Levy (Ottawa)Trace formulaeRam Murty (Queen’s)A Survey of the Langlands Program in number fieldsAmbrus Pal (CRM)Introduction to shtukasAmritanshu Prasad (CRM)Automorphic representationsDavid Savitt (McGill)Étale cohomology30 April to 16 May 2002

Cette période comprenait deux phases. Lapremière a porté sur les multiples ingrédientsdes preuves des conjectures de Langlands; lesconférences de la Chaire Aisenstadt de E.Frenkel et de L. Lafforgue ont constitué ladeuxième. À travers ces deux parties, lespersonnes assistant à l’atelier eurent aussi lachance d’entendre sept conférences de R.Langlands les entretenant de ses idées récentessur l’endoscopie.The speakers were (with abstracts):David Ben-Zvi (Chicago)OpersOpers are a remarkable class of connections onalgebraic curves, arising in integrable systems,conformal field theory and representationtheory, which play a central role in the work ofBeilinson-Drinfeld on the geometric Langlandscorrespondence. A tour of some of the differentplaces opers appear was offered, visiting theHitchin system, Hamiltonian reduction of Kac-Moody algebras, differential operators and theKdV equations, projective structures and theVirasoro algebra, and vertex algebras.

David Goss (Ohio State)Recent advances in characteristic p arithmeticWe will discuss recent advances in the theory ofthe finite characteristic arithmetic associated toDrinfeld modules. Included will be some recentideas related to a possible Riemann hypothesis

for the L-series of such objects. Also discussedwere advances in the associated theory ofmodular forms associated to Drinfeld modules.In particular, we will discuss Boeckle’sassociation of Galois representations to cuspforms.

Edward Frenkel (UC Berkeley)Aisenstadt Chair 2001-2002Recent developments in the geometric LanglandsProgramIn recent years it was realized that the Langlandsconjectures (in the function field case) might beformulated geometrically and hence over anarbitrary ground field, for instance, the field ofcomplex numbers. In that case the role of therepresentation theory of groups over local non-Archimedean fields is played by therepresentation theory of affine Kac-Moodyalgebras, as can be seen from the recent work ofA. Beilinson and V. Drinfeld. These lecturesreviewed the geometric Langlands conjecturesand various approaches to proving them. Alsodiscussed were the intriguing parallels betweenthe finite field and the complex field settings.

Laurent Lafforgue (IHES)Aisenstadt Chair 2001-2002Chtoucas de Drinfeld et correspondance de LanglandsLa présentation a porté sur les grandes lignes dela démonstration de la correspondance deLanglands pour GL(r) sur les corps de fonctions,généralisant la preuve de Drinfeld dans le cas durang r = 2. Plus particulièrement on s’est attachéà montrer le rôle des principaux ingrédients dela démonstration!: la géométrie des chtoucas deDrinfeld et de leurs compactifications!; laformule des traces d’Arthur-Selberg!; la formuledes points fixes de Grothendieck-Lefschetz!; lespropriétés connues des fonctions L de paires tantdu côté automorphe que galoisien.

Robert Langlands (IAS)Au-delà de l‘endoscopieGrâce aux travaux récents d’Arthur surl’endoscopie et la formule des traces et à d’autrestravaux pas moins importants de grand nombrede mathématiciens sur le lemme fondamental,nous commençons à mieux comprendre non passeulement comment utiliser la formule des tracespour établir le transfert des formes automorphesd’un groupe à un autre, mais aussi quelle est lavraie portée, en particulier le contenu



géométrique ou topologique, des problèmes àpremière vue techniques qu’il faut surmonter.Il n’en reste pas moins que les méthodes utiliséessont toujours d’un pouvoir limité et ne suffisentpas à la résolution générale des problèmes poséspar la fonctorialité, en particulier ceux quiinterviennent dans les conjectures d’Artin oude Ramanujan-Selberg. Elles nous inspirenttoutefois une grande confiance dans la formuledes traces telles que développée dans lesdernières années et, emporté par cette confiance,l’objectif dans ce cours fut de chercher une voiequi puisse nous permettre de dépasser ce qu’ona fait jusqu’à présent.Le cours s ’adressa i t aux j eunesmathématicien(ne)s spécialist(e)s de la théorieanalytique ou de la théorie algébrique desnombres ou des formes automorphes voulanttravailler dans la théorie moderne des formesautomorphes, un sujet ou toutes ces théories sebrassent. Quelques connaissances préalables desformes automorphes sur GL(2) étaient exigéeaussi bien qu’une absence d’idées fixes. Le coursfut en grande partie axé sur un examen d’unpoint de vue inhabituelle de la formule destraces telles que décritent dans le livre deJacquet-Langlands.

Alexander Polishchuk (Boston)Introduction to perverse sheavesThese lectures focussed on the definition andpresentation of some examples of perversesheaves in two contexts: (1) complex geometry,(2) algebraic geometry in positive characteristic.Also discussed were the Riemann-Hilbertcorrespondence in case (1) and faisceaux-fonctionsdictionary in case (2).

Christophe Sorger (Nantes)Moduli stacks of G-bundlesAfter collecting preliminary material onalgebraic stacks useful for moduli problems,moduli of G-bundles were introduced and someof the (by now) basic theorems as theuniformization theorem were proved.

Workshop in honour of Robert LanglandsMay 17, 2002

Un atelier en l’honneur de R. Langlands fut tenule 17 mai pour souligner son 65e anniversaire.Les conférenciers comprenaient quelques-uns deses collaborateurs en théorie des nombres et en

mécanique statistique, ainsi que deux de sesétudiants. L’atelier visait tout particulièrement àsouligner ses contributions au développementdes mathématiques à Montréal.Invited speakers:James Arthur (Toronto)Développements en germes pour les groupes réelsLaurent Clozel (Paris-Sud & Caltech)Rigidité et équipartition!: résultats et conjecturesDennis Gaitsgory (Chicago)On the geometric Langlands conjecture for GLnPhilippe Pouliot (Texas)Finite number of states, de Sitter space, and quantumgroups at rootsYvan Saint-Aubin (Montréal)Deux exemples simples de transition de phase!: lapercolation et le modèle d’Ising

Computational Lie TheoryMay 27 to June 7, 2002Org.: W. Casselman (UBC), F. Knop (Rutgers)

There were two series of lectures by MeinholfGeck on applications of GAP in doing researchinvolving Coxeter and algebraic groups, and byJohn Stembridge mostly on tensor productdecomposition, with examples using Maple. Theworkshop complemented the Aisenstadt lecturesgiven concurrently by George Lusztig.The most surprising lecture was by GregWarrington, who exhibited several counter-examples to what many people had earlierthought – that the m coefficients for thesymmetric groups were always 1. Reallysurprising was that this had been known forseveral years by Tim McLarnahan, but that hisdiscoveries had not been published. Warringtonhad written his own programs to explore thephenomenon further.Invited speakers: R. Bédard (UQAM), R. Bezrukavnikov(Chicago), M. Brion (Joseph Fourier), F. du Cloux (Lyon I),M. J. Dyer (Notre Dame), W. Fulton (Michigan), M. Geck(Lyon), G. J. Heckman (Nijmegen), A. G. Helminck (NorthCarolina State), F. Knop (Rutgers), J. McKay (Concordia), M.Noumi (Kobe), E. M. Opdam (Amsterdam), A. Ram(Wisconsin), Y. B. Sanderson (William Paterson) T. A.Springer (Utrecht), J. R. Stembridge (Michigan), B. Sturmfels(Berkeley), P. Trapa (Harvard), J. F. van Diejen (Chile), M.van Leeuwen (Poitiers), D. A. Vogan Jr (MIT), N. R. Wallach(California, San Diego), G. Saunders Warrington (Harvard),A. Zelevinski (Northeastern).



Algebraic Transformation GroupsJune 10-14, 2002Org.: A. Broer (Montréal), J. Carrell (UBC)

The purpose of the workshop was to bringtogether experts in algebraic groups, algebraicgeometry, representation theory and relatedareas, especially those touching on: geometricmethods in representation theory using toolslike equivariant cohomology and perversesheaves; the Hilbert scheme of points on asurface and its connection with the n!-conjecturein algebraic combinatorics; equivariant versions

of cohomology and Chow groups related to flagmanifolds and Schubert varieties; quantumcohomology and Schubert calculus.Invited speakers: K. Behrend (UBC), A. Bertram (Utah), T.Braden (Massachusetts), M. Brion (Grenoble), W. A.Casselman (British Columbia), V. Ginzburg (Chicago), M.Haiman (UCSD), G. Heckman (Nijmegen), R. B. Howlett(Sydney), F. Knop (Rutgers), A. Knutson (Berkeley), B.Kostant (MIT), S. Kumar (North Carolina), L. Manivel(Grenoble), E. Meinrenken (Toronto), I. Mirkovic(Massachusetts), H. Nakajima (Kyoto), D. Peterson (UBC), Y.B. Sanderson (William Paterson), T. A. Springer (Utrecht), D.E. Taylor (Sydney), E. Vasserot (Cergy-Pontoise), C.Woodward (Rutgers).


24 Annual Report 2000-2001 CRM

Aisenstadt ChairThe Aisenstadt Chair was endowed by Montréal philanthropist Dr. André Aisenstadt. Under itsauspices, one or more distinguished mathematicians are invited each year for a period of at least oneweek, ideally one or two months. During their stay the lecturers present a series of courses on aspecialized subject. They are also invited to prepare a monograph. At the request of Dr. Aisenstadt, thefirst of their lectures should be accessible to a wide audience. Previous holders of the Aisenstadt Chairare: Marc Kac, Eduardo Zarantonello, Robert Hermann, Marcos Moshinsky, Sybren de Groot, DonaldKnuth, Jacques-Louis Lions, R. Tyrell Rockafellar, Yuval Ne’eman, Gian-Carlo Rota, Laurent Schwartz,Gérard Debreu, Philip Holmes, Ronald Graham, Robert Langlands, Yuri Manin, Jerrold Marsden, DanVoiculescu, James Arthur, Eugene B. Dynkin, David P. Ruelle, Robert Bryant, Blaine Lawson, YvesMeyer, Ioannis Karatzas, László Babai, Efim I. Zelmanov, Peter Hall, David Cox, Frans Oort, Joel S.Feldman, Roman Jackiw, Duong H. Phong, Michael S. Waterman and Arthur T. Winfree.The CRM was honoured to have as Aisenstadt chairholders, during the 2001-2002 theme year inGroups and Geometry, Professors Edward Frenkel of the University of California at Berkeley, ProfessorLaurent Lafforgue of the Institut des Hautes Études Scientifiques and Professor George Lusztig of MIT.

Professor Edward FrenkelUniversity of California at Berkeley

On the week of May6-14, 2002, ProfessorEdward Frenkel gavea series of eightconferences titled“Recent developmentsin the geometricLanglands Program”as part of the series oflectures on the

Langlands program for function fields. Frenkel’slectures were greatly enjoyed by everyone inattendance for their remarkable clarity, theywere one of the high points, along with those ofLaurent Lafforgue, of the theme year. Here is thesummary of the talks:

In recent years it was realized that theLanglands conjectures (in the functionfield case) might be formulatedgeometrically and hence over an arbitraryground field, for instance, the field ofcomplex numbers. In that case the role ofthe representation theory of groups overlocal non-Archimedean fields is played bythe representation theory of affine Kac-Moody algebras, as can be seen from therecent work of A. Beilinson and V.Drinfeld. In these lectures we will reviewthe geometric Langlands conjectures andvarious approaches to proving them. Wewill also discuss the intriguing parallelsbetween the finite field and the complexfield settings.

Professor Frenkel obtained his undergraduatedegree from Moscow in 1989 and his Ph.D. fromHarvard in 1991 under the supervision ofB.!Feigin. He was then appointed at the HarvardSociety of Fellows and became in 1997 fullprofessor at Berkeley. His mathematical interestscover a remarkably wide range of topics,including fields, quantum theory, integrablesystems, representation theory and algebraicgeometry.

Professor Laurent LafforgueInstitut des Hautes Études Scientifiques

A s p a r t o f t h econcentration period onthe Langlands program forfunction fields, ProfessorLaurent Lafforgue gave aseries of five conferencesMay 6-14, 2002, with thetitle Chtoucas de Drinfeld etcorrespondance de Langlands.Here is the summary of thetalks:

On se propose de présenter les grandes lignesde la démonstration de la correspondance deLanglands pour GL(r) sur les corps defonctions, généralisant la preuve de Drinfelddans le cas du rang r=2. On s’attachera enparticulier à montrer le rôle des principauxingrédients de la démonstration:• la géométrie des chtoucas de Drinfeld

et de leurs compactifications;• la formule des traces d'Arthur-Selberg;• la formule des points fixes de

Grothendieck-Lefschetz;



• les propriétés connues des fonctions Lde paires tant du côté automorphe quegaloisien.

The following week, he gave us an additionalseries of three talks on several variations ofGrassmannians and their compactification; somespecific cases constitute a key ingredient of hisproof for the Langlands conjecture for GL(r) overfunction fields; he has since greatly generalizedthe theory. The material of those three talks aswell as those from the previous series will bepublished as a CRM monograph.After graduating from the École NormaleSupérieure, Laurent Lafforgue entered the CNRSas a research fellow in 1990. In 1994, hepresented his thesis D-Chtoukas de Drinfeld,under the guidance of Gérard Laumon. Firstappointed as a professor at Orsay, he acceptedan appointment as permanent professor at IHÉSin 2000. He was awarded the Cours Peccot at theCollège de France in 1996 and was an invitedspeaker at the International Congress ofMathematicians in Berlin in 1998. In 2002, hereceived the Fields Medal for this proof of theLanglands conjecture on the correspondenceconnecting arithmetic properties to analyticproperties of automorphic representations.

Professor George LusztigMIT

On May 27, 2002, ProfessorGeorge Lusztig gave a publicconference entitled “Homo-morphisms of the icosahedralgroup into reductive groups,”in which he exploredhomomorphisms of finitegroups, in particular theicosahedral group, into

reductive groups. Those homomorphisms arestrongly constrained and Professor Lusztigpresented one classification. This conference wasfollowed by a more specialized series, titled“Hecke algebras with unequal parameters,”given as part of the workshop on computationalLie theory. Those talks were very well receivedand will be the object of an AMS-CRMmonograph.Holder of the Norbert Wiener Chair at MIT,Professor Lusztig is one of the greatestcontemporary mathematicians and has had animpact during his very successful career on awide range of mathematical problems. Amongothers, he has produced fundamental results onthe representations of finite groups of the Lietype; a construction for canonical bases ofrepresentations based on quantum algebras; aswell as results at the core of the cohomologymethods in representation theory.



General Program 2001-2002The CRM’s general program funds a wide variety of scientific events, both on-site, elsewhere inCanada and around the world. Whether it be for specialized workshops for a small number ofresearchers, large meetings for hundreds of participants or activities for high school or undergraduatestudents, the general program promotes research in mathematical sciences at all levels. The program isquite flexible, to allow for opportunities as they arise.

Second public lecture of the CanadianJournal of StatisticsJune 14, 2001, Simon Fraser UniversityOrg.: Christian Genest (Laval), Richard Lockhart (SimonFraser)

Dans le cadre du 29e congrès annuel de la Sociétéstatistique du Canada, tenu à l’Université SimonFraser (Burnaby, Colombie-Britannique) du 10au 14 juin 2001, le professeur Peter M. Hooper del’Université de l’Alberta a présenté ses travauxde recherche concernant un modèle derégression flexible défini à partir d’une base defonctions logistiques adaptatives.L’article du professeur Hooper a ensuite faitl’objet d’un débat public, animé par le rédacteuren chef de La revue canadienne de statistique (RCS),le professeur Richard A. Lockhart. Plusieursspécialistes du domaine ont commentépubliquement les travaux du professeur Hooper,soit Mary J. Lindstrom (University of Wisconsinat Madison), James O. Ramsay (McGillUniversity), Nancy E. Heckman (University ofBritish Columbia), ainsi que Hugh A. Chipmanet Hong Gu (University of Waterloo). Lescongressistes, présents en grand nombre à cedébat, ont également été invités à poser desquestions ou à formuler des suggestions.Les commentaires retenus, ainsi que les réponsesdu professeur Hooper, ont été publiés avecl’article dans le numéro de septembre 2001 de Larevue canadienne de statistique (Vol. 29, No 3, 2001,pp. 343-378). Une version pdf de l’article estaccessible en permanence sur la vitrine Internetde la RCS, à l’adresse http://www.mat.ulaval.ca/rcs

Étant donné le franc succès remporté par cetteactivité, la RCS et le CRM ont décidé depoursuivre leur collaboration en organisant, àMontréal cette fois, un 3e débat public. Celui-ci aeu lieu le 22 mars 2002.

Eighth Canadian conference ofmathematics studentsJune 12-17, 2001, Université LavalOrg.: Pier-André Bouchard St-Amant (Laval), Jean-PhilippeBoulet (Laval), Sylvain Hallé (Laval), Jean-François Plante(Laval)

Cette conférence annuelle s’adresse auxétudiants canadiens de premier cycle dont leprogramme d’é tudes cont ient desmathématiques avancées. Les étudiants inscritssont invités à présenter un exposé de 20 ou 50minutes sur un sujet mathématique de leurchoix. Aux exposés d’étudiants s’ajoutent cinqconférences données par des professeursd’universités canadiennes. Ainsi, Nelly Simoesnous a fait un exposé très intéressant sur lathéorie des files d’attente.Évidemment, les étudiants ont également profitéde l’occasion pour découvrir la ville de Québec.Ils avaient la possibilité d’aller visiter la citadellede Québec ou simplement d’aller se promenerdans le Vieux Québec, ce qui fût grandementapprécié.

Séminaire de mathématiquessupérieures: Modern Methods inScientific Computation & ApplicationsJuly 9-20, 2001, Université de MontréalOrg.: G. Sabidussi (Montréal), K. Mikula (Slovak TechnicalUniversity), A. Bourlioux (Montréal), M. Gander (McGill),S. Lessard (Montréal), G. C. Papanicolaou (Stanford), A.Stuart (Warwick)

The 40th session of the Séminaire demathématiques supérieures (9-20 July 2001) wasdevoted to Modern Methods in ScientificComputation and Applications. No session of theSMS during the last 25 years having dealt withnumerical mathematics, the program for 2001was specifically designed to show how wide theinfluence of scientific computing had becomeduring that period. The main themes were imageprocessing, mathematical finance, electricalengineering, thin films, moving interfaces, andturbulent combustion, the common threadrunning through these subjects being thenumerical solution and analysis of theasymptotic behavior of the partial differentialequations involved in these problems. The



following 8 mini-courses were given: Domaindecomposition methods (L. Halpern, Paris XIII,and F. Nataf, École Polytechnique); Multigridmethods (G. Haase and U. Langer, Linz);Numerical aspects of deterministic and randomdynamical systems (T. Humphries, Sussex, andA. Stuart, Warwick); Matrix analysis ofextremely large systems (Z. Bai, UC Davis, andG. Golub, Stanford); Stochastic differentialequations and volatility analysis (G.Papanicolaou, Stanford, and R. Sircar,Princeton); Applications of PDEs in imageprocessing (K. Mikula, STU Bratislava, and J.Sethian, Berkeley); Asymptotic analysis ofrupturing and fingering in thin films (A.Bertozzi and T. Witelski, Duke); Numericalcombustion (P. Souganidis, Texas at Austin, andA. Bourlioux, Montréal).In addition to the 16 speakers, 59 participantscoming from 20 different countries attended thesession. Besides the support by the CRM, theSMS benefited from support by NATO (throughits Advanced Study Institutes Program), theUniversité de Montréal, and McGill University.Martin Gander (McGill) and Anne Bourlioux(Montréal) were the scientific organizers of thesession.The proceedings have been published by KluwerAcademic Publishers in the NATO Science SeriesII, Vol. 75.

Statistics 2001 Canada: The FourthCanadian Conference in AppliedStatisticsJuly 6-8, 2001, Université ConcordiaOrg.: Y. Chaubey (Concordia), F. Nebebe (Concordia)

The conference was a success. It attractedapproximately 250 participants representinggovernment, education and industry from allover the globe. Important problems associatedwith current issues in genomics, environment,health, networking and data management, alongwith theoretical developments in statistics werediscussed. The conference featured 144 speakersin seven plenary sessions and 42 invited andcontributed papers sessions. On overwhelmingdemand from the contributors, the organizersdecided to publish refereed proceedings of theconference in a volume entitled Recent Advancesin Statistical Methods, edited by Yogendra P.Chaubey and published by World ScientificPublishing (UK) Ltd.

FUSION 2001: 4th InternationalConference on Information FusionAugust 7-10, 2001, Montréal261 participantsOrg.: E. Shahbazian (Lockheed Martin Canada & CRM), D.Blair (Georgia Tech.), P. Willett (U. Conn.), P. Valin(Lockheed Martin Canada & CRM).Fusion 2001 provided a forum for fusionresearch, applications, and technologicaladvances by scientists and engineers working inall aspects of information and data fusiontechniques and systems. This fourth incarnationof the International Conferences on InformationFusion was held on behalf of the InternationalSociety on Information Fusion (ISIF) in Montréalfrom August 7-10, 2001, during a record-breaking heat wave (35 days without rain!). Theorganization and sponsorship were sharedbetween Lockheed Martin Canada, the Networkfor Computing and Mathematical Modeling(ncm2), the Centre de Recherches Mathématiques(CRM) of the Université de Montréal, DefenseResearch Establishment Valcartier (DREV), theCanadian Space Agency (CSA), Mathematics ofInformation Technology and Complex Systems(MITACS), and was under the technical co-sponsorship of the IEEE AES Society.Conference topics covered theoretical andtechnical advances for fusion algorithms andsystems, and provided real-world applications.There were 146 technical contributions from 304authors representing 19 countries. There werealso seven organized sessions onComputationally Intensive Distributed SensorNetworks, Formal Methods, Image Fusion &Exploitation, Distributed Tracking, SituationAnalysis and Situational Awareness, KnowledgeBase Role in Information Fusion, Non-linearFiltering and Probabilistic Multi-HypothesisTracking. For a more detailed report, see

www.crm.umontreal.ca/fusion.

Seconde conférence à la mémoire deGilles FournierAugust 13-15, 2001, Université de SherbrookeOrg.: Marlène Frigon (Montréal), Andrzej Granas(Montréal), Tomasz Kaczynski (Sherbrooke)

Les thèmes principaux de cette secondeconférence dédiée à la mémoire de GillesFournier ont été la théorie des points fixes et lathéorie de points critiques ainsi que leursapplications aux équations différentielles et auxsystèmes dynamiques. À cette occasion, desdéveloppements récents de ces domaines ont étéprésentés par des experts conduisant à deséchanges stimulants entre eux et les participants.Des conférences de nature historique ont aussi



été présentées notamment sur la contribution deGilles Fournier.La participation à cette conférence a étéexcellente. Cette conférence était suivie par unatelier sur l’indice de Conley. Ainsi, plusieurspersonnes ont prolongé ou devancé leur séjour àSherbrooke (selon le cas) pour participer auxdeux conférences. Aussi, il y a eu une bonneparticipation d’étudiants de cycles supérieursd’ici et de l’étranger.

Invited speakers: M. Allili (Lennoxville), F. Collin(Sherbrooke), P. Deguire (Moncton), Z. Dzedzej (Gdansk), N.El Khattabi (Maroc), A. Felshtyn (Greifwald), K. Geba(Gdansk), A. Granas (Montréal), A. Marino (Pise), M.Martelli (Cal St. Fullerton), J. Mawhin (Université Catholiquede Louvain), K. Saadi Drissi (Maroc), N. Schlomiuk(Montréal), H. Steinlein (Munich), A. Szulkin (Stockholm).

Spectral Statistics and High EnergyEigenstatesAugust 25 to September 2, 2001, CRMOrg.: Dmitry Jakobson, John Toth, Yiannis Petridis(McGill).

The workshop brought together mathematiciansand physicists working in the areas of RandomMatrix Theory, Riemann-Hilbert Problems,Toeplitz Quantization, Analytic Number Theory(Automorphic Forms and L-functions),Semiclassical Theory and Partial DifferentialEquations, focusing on spectral statistics andasymptotic properties of high energyEigenstates, and resulting in lively interactionamong the participants. For many conferenceparticipants, this was their first visit to Montréal,and several of them mentioned to organizerstheir very positive impressions of the conference,the CRM and the city, and indicated their desireto come again.Four very successful introductory courses werepresented by: P. Bleher, Semiclassical Asymptoticsin Random Matrix Models 1,2,3; Z. Rudnick,Quantum Maps: Semiclassics and Number Theory1,2,3; A.!Uribe, Berezin-Toeplitz Operators 1,2,3;and S. Zelditch, 1. Highly Excited QuantumEigenstates, 2. Riemannian Manifolds with ExtremeEigenfunction Growth, and 3. Random SphericalHarmonics.Building on the success of the conference, and onthe success of two sectional meetings of the AMSat CRM in May 2002 (on Random Matrices, andon Spectral Geometry and Analytic Aspects ofAutomorphic Forms), the organizers areplanning three workshops related to the

conference theme during the year in Analysis atCRM and Fields Institute in 2003/2004.Invited speakers: A. Gamburd (Stanford), I. Vardi (IHES), P.Bleher (Indiana, Purdue), Z. Rudnick (Tel Aviv), R. Speicher(Queen’s), I. Dumitriu (MIT), E. Duenez (Johns Hopkins), A.Bourget (McGill), H. Widom (Santa Cruz), K. Soundararajan(IAS), H. Donnelly (Purdue), P. Sarnak (Princeton), U.Smilansky (Weizmann), B. Eynard (CRM), T. Tate (Keio), A.Uribe (Michigan), M. Min-Oo (McMaster), V. Jaksic (JohnsHopkins), J. Harnad (CRM), W. Craig (McMaster), I. Rivin(Temple), M. Bertola (CRM).

Histoires de catégoriesSeptembre 13-14, 2001, CRMOrg.: Luc Bélair (UQAM), Liliane Beaulieu (CRM)Cet atelier des 13 et 14 septembre, auquel ontparticipé des mathématiciens, des historiens etdes philosophes des mathématiques, avait pourobjectif principal de faire le point sur l’histoirede la théorie des catégories. La parole étaitlargement donnée aux protagonistes de cettehistoire. Les événements du 11 septembre 2001ont chambardé l’horaire prévu, en empêchant C.Houzel et C. McLarty de faire le voyage. C.McLarty a pu reporter sa participation au 21septembre. Les organisateurs tiennent àremercier les participants, et en particulier lesconférenciers, pour avoir rendu ces journéesfructueuses, dans un contexte international peupropice aux souvenirs du temps passé. Lescomptes-rendus de ces journées seront publiéssous la direction de Liliane Beaulieu.Invited speakers: L. Beaulieu (CRM), C. Houzel (Paris), J.Lambek (McGill), W. Lawvere (Buffalo), M. Makkai (McGill),C. McLarty (Case Western), G. Reyes (Montréal).

Journée statistique du CRM et 3e

conférence publique de la Revuestatistique du CanadaMarch 22, 2002, CRMOrg.: Christian Genest (Laval), Christian Léger (CRM,Montréal).

Le Centre de recherches mathématiques (CRM)et la Revue canadienne de statistique (RCS) sesont à nouveau associés afin de présenter la 3e

Conférence publique de la RCS dans le cadre dela Journée statistique du CRM. Suite au succèsobtenu lors de la présentation des deuxpremières conférences publiques tenues lors desdeux derniers congrès annuels de la SSC, la RCSa innové en présentant sa troisième Conférencepublique au CRM le 22 mars 2002.La Conférence publique portait sur l’articleintitulé Box-Cox transformations in linear models:Large sample theory and tests of normality, desauteurs Gemai Chen de l’Université de Calgary,ainsi que Richard A. Lockhart et Michael A.Stephens de l’Université Simon Fraser. En



étudiant la théorie asymptotique des estimateursdans le modèle de transformation de Box et Cox,les auteurs ont constaté que la distribution del’estimateur de régression dépend fortement duparamètre de transformation alors que si onnormalise par le paramètre de dispersion deserreurs, la dépendance par rapport au paramètrede transformation est grandement diminuée. Deplus, l’hypothèse de la normalité des erreurs esttrès importante et ils démontrent comment onpeut tester cette hypothèse dans ce contexte detransformation. L’article a été commenté parKjell Doksum de l’Université de la Californie àBerkeley et Richard A. Johnson de l’Universitéde Wisconsin-Madison, par Peter M. Hooper del’Université de l’Alberta et par Peter J.McCullagh de l’Université de Chicago. Uneréplique de la part des auteurs a conclu lasession. La contribution des divers intervenantsa permis de mieux comprendre ce problèmeimportant de la théorie de la régression.La Journée statistique du CRM a débuté le matinavec des conférences sur les travaux récents dequatre des conférenciers commentant l’article dela Conférence publique. Deux des présentationsportaient sur le thème des transformations enrégression. Richard A. Johnson a introduit A newfamily of power transformations to improve normalityalors que Kjell Doksum a parlé de Robustness andstability of parameters and estimates. Peter Hoopera présenté Relating patterns of fetal growth to healthoutcomes at birth.Finalement, Peter McCullagh a discuté deStatistical models for Monte-Carlo integration. Laparticipation des étudiants et des boursierspostdoctoraux a été particulièrement importante.L’expérience consistant à présenter uneconférence publique de la RCS en dehors ducongrès annuel de la Société statistique duCanada a donc été couronnée de succès.Invited speakers: G. Chen (Calgary), K. Doksum (Berkeley),P. Hooper (Alberta), R. Johnson (Wisconsin at Madison),R.!Lockhart (Simon Fraser), P. McCullagh (Chicago),M.!Stephens (Simon Fraser).

CNTA VII Meeting of the CanadianNumber Theory AssociationMay 19-25, 2002, CRM, Université de Montréal.Org.: H. Kisilevsky (Concordia) & E. Goren (McGill)The Canadian Number Theory Association(CNTA) was founded in 1987 at the InternationalNumber Theory Conference at Laval University.The purpose of the CNTA is to enhance andpromote learning and research in Number

Theory, particularly in Canada. To advancethese goals the CNTA organizes majorinternational conferences, with the aim ofexposing Canadian students and researchers tothe latest developments in number theory worldwide. This year, the CNTA VII conference wasimmediately preceded by a three-weekworkshop on the Langlands Program forfunction fields at the CRM. Sessions coveredtopics in algebraic number theory,computational number theory, analytic numbertheory, diophantine analysis and approximation,and arithmetic algebraic geometry. There were187 participants.Invited Speakers: M.!Bennett (Urbana-Champaign), A.!Besser(Ben-Gurion), M.!Bhargava (Princeton), J.!Borwein (SimonFraser), D.!Boyd (UBC), D.!Brownawell (Penn. State),Y.!Bugeaud (Strasbourg!I), D.!Burns (King’s College), I.!Chen(Simon Fraser), H.!Cohen (Bordeaux), B.!Conrad (Michigan),C.!Consani (Toronto), J.!Cremona (Nottingham), H.!Darmon(McGill), C.!Deninger (Munster), W.!Duke (UCLA),R.!Dvornicich (Pisa), S.!Edixhoven (Rennes), J.!Friedlander(Toronto), D.!Goss (Ohio State), A.!Granville (Georgia),A.!Iovita (Washington), C.!Khare (Utah), H.!Kim (Toronto),J.!Lagarias (AT&T Labs), M.!Laurent (Luminy, CNRS),G.!Martin (UBC), W.!McCallum (Arizona), D.!McKinnon(Waterloo), K.!Murty (Toronto), R.!Murty (Queen's), K.!Ono(Wisconsin), G.!Pappas (Michigan State), C.!Pomerance (BellLabs), B.!Poonen (Berkeley), C.!Popescu (Johns Hopkins),R.!Ramakrishna (Cornell), M.!Rapoport (Köln), Z.!Rudnick(Tel-Aviv), K.!Soundararajan (Michigan), W.!Stein (Harvard),C.!Stewart (Waterloo), V.!Vatsal (UBC), D.!Wan (UC Irvine),A.!Weiss (Alberta), T.!Wooley (Michigan).

Conférence Constance van Eeden!:Statistique mathématique 2002May 24-25, 2002, CRMOrg.!: Marc Moore (École Polytechnique), Sorana Froda(UQAM), Christian Léger (CRM)

Les 24 et 25 mai dernier, le CRM a été l’hôted’une conférence soulignant le 75e anniversairede naissance de Mme Constance van Eeden ainsique sa longue et remarquable carrière enrecherche et en direction d’étudiants. Mme vanEeden est Professeur émérite à l’Université deMontréal ainsi que Professeur honoraire del’Université de la Colombie Britannique.Ancien étudiant à la maîtrise de Mme vanEeden, Louis-Paul Rivest de l’Université Laval adébuté la Conférence en présentant Un modèle destatistique directionnelle pour la détection et lacorrection du «!crosstalk!» en cinématique humaine.Puis Roelof Helmers, compatriote du CWIAmsterdam, a présenté ses travaux sur Statisticalestimation of Poisson intensity functions. DenisLarocque des HEC, son dernier étudiant audoctorat à l’Université de Montréal, a fait unsurvol des plus récentes méthodes en statistiquenon paramétrique dans A review of modern



methods based on signs and ranks formultidimensional data. Bill Strawderman, del’Université Rutgers et statisticien en résidencedu Fonds Constance van Eeden à UBC en 1999,nous a entretenus de Bayes minimax estimation ofa normal mean vector for general quadratic loss. Unautre compatriote de l’Université d’Amsterdam,Chris Klaassen, a présenté ses travaux surAsymptotic most accurate confidence intervals in thesemiparametric symmetric location model. JimZidek, un de ses plus fidèles collaborateurs deUBC, a présenté une très bonne conférence autitre fort intriguant de Uncertainty.De plus, Yves Lepage de l’Université deMontréal et second étudiant au doctorat de Mmevan Eeden a fait un survol de sa contributionexceptionnelle à la statistique non paramétriqueainsi qu’à la direction d’étudiants (plus de 13 audoctorat et 18 à la maîtrise). Finalement, François

Perron de l’Université de Montréal a présenté unsurvol de ses plus importantes contributions,dont plusieurs sont récentes, à l’estimation dansdes espaces paramétriques contraints.Plus d’une cinquantaine de chercheurs,étudiants, ex-étudiants ou ex-collègues de Mmevan Eeden ont pu bénéficier de cet excellentprogramme scientifique. Finalement un livreintitulé Mathematical Statistics and Applications:Festschrift for Constance van Eeden estprésentement en préparation. Édité par MarcMoore de l’École Polytechnique et Sorana Frodade l’Université du Québec à Montréal, deuxanciens étudiants au doctorat de Mme vanEeden, ainsi que par Christian Léger du CRM etde l’Université de Montréal, ce livre sera publiéen 2003 conjointement par le CRM et l’IMS(Institute of Mathematical Statistics).



CRM PrizesCRM-Fields Institute PrizeIn 1994, the Centre de recherchesmathématiques (CRM) and the Fields Instituteannounced the creation of a new prize to beawarded for exceptional contributions to themathematical sciences. The recipient of theprize is chosen by the Advisory Committee ofthe CRM and the Scientific AdvisoryCommittee of the Fields Institute according tothe criterion of excellence in research. Theprize consists of both a $5,000 award and amedal, and the winner is required to give alecture at the CRM and the Fields Institute. Thepast recipients are: H.S.M. Coxeter (1995), G.A.Elliot (1996), J. Arthur (1997), R.V. Moody(1998), Stephen A. Cook (1999), Israel MichaelSigal (2000), and William T. Tutte (2001). TheCRM-Fields Institute 2002 Prize is awarded toProfessor John B. Friedlander.

Professor Friedlanderis one of the world’sforemost analyticnumber theorists,and is a recognizedleader in the theoryof prime numbersand L-functions. Hereceived his B.Sc.from the Universityof Toronto in 1965, a

M.A. from the University of Waterloo in 1966,and a Ph.D. from Penn State in 1972. He was alecturer at M.I.T. in 1974-76, and has been on thefaculty of the University of Toronto since 1977,where he served as Chair during 1987-91. He hasalso spent several years at the Institute forAdvanced Study where he has collaborated withE. Bombieri and many others. John Friedlanderis a Fellow of the Royal Society of Canada (1988),was an invited lecturer at the 1994 ICM in Zurichand delivered the CMS Jeffery-Williams Lecturein 1999. He has contributed significantly tomathematics in other ways, especially inCanada, through his role at NSERC(Mathematics GSC, 1991-94), as MathematicsConvenor of the Royal Society of Canada (1990-93), and as a Council member (1989-95) andScientific Advisory Panel member (1996-2000) ofthe Fields Institute. He has also served on theEditorial Board of the Canadian Journal ofMathematics and the Canadian MathematicsBulletin for the past four years.

André-Aisenstadt PrizeCreated in 1991, the André-AisenstadtMathematics Prize is intended to recognize andreward ta lented young Canadianmathematicians. The Prize, which is given forresearch achievement in pure and appliedmathematics, consists of a $3000 award. Therecipient is chosen by the CRM AdvisoryCommittee. At the time of nomination,candidates must be Canadian citizens orpermanent residents of Canada, and no morethan seven years from their Ph.D. The previouswinners of the André-Aisenstadt Prize were:Niky Kamran (1991), Ian Putnam (1992),Michael Ward and Nigel Higson (1994), AdrianS. Lewis (1995), Henri Darmon and Lisa Jeffrey(1996), Boris Khesin (1997), John Toth (1998),Changgeng Gui (1999), and Dr. EckhardMeinrenken (2000). CRM was delighted toaward the 2001 André-Aisenstadt Prize toProfessor Jingyi Chen of t h e University ofBritish Columbia

Mr. Chen obtained aPh.D. from StanfordUniversity in 1992. He hassince been a professor att h e M a s s a c h u s s e t t sInstitute of Technology, atNorthwestern Universityand the University ofCalifornia. His works ingeometric analysis havebeen recognized. He wasawarded the Alfred P.

Sloan Research Fellowship from the NationalScience Foundation (USA) PostdoctoralFellowship. He has published over twentyarticles and is an invited speaker all over theworld. Professor Chen delivered a lecture onJanuary 18, 2002. Here is the summary:Quaternionic mappings between hyperkahlermanifoldsQuaternionic maps (Q-maps) betweenhyperkahler manifolds are quaternionicanalogues of Cauchy-Riemann equations ofmaps between Kahler manifolds and they arisenaturally in higher dimensional gauge theory.Q-maps between quaternion numbers are justsolutions to Cauchy-Riemann-Fueter equations.The Q-maps are energy minimizers in theirhomotopy classes, hence harmonic. We willdiscuss a necessary and sufficient condition on



when a Q-map becomes holomorphic withrespect to some complex structures, and giveexamples of Q-maps that cannot beholomorphic. When the domain of Q-maps isreal 4-dimensional, we will analyze the structureof the blow-up set of a sequence of Q-maps, andshow that the singular set of a stationary Q-mapis at most a 1-dimensional Hausdorff rectifiableset. We will also indicate possible applications ofthis compactness result.

CAP-CRM PrizeAwarded for the first time in 1995, theCAP-CRM Prize is given for outstandingcontributions to theoretical and mathematicalphysics. It consists of a $2000 award and amedal. Previous winners were Werner Israel(1995), William G. Unruh (1996), Ian Affleck(1997), J. Richard Bond (1998), David J. Rowe(1999), Gordon W. Semenoff (2000), and André-Marie Tremblay (2001). The 2002 CAP-CRMprize has been awarded to Professor PavelWinternitz of the Université de Montréal.

The Canadian Associationof Phycisists (CAP) andthe Centre de recherchesmathématiques (CRM)are happy to announcethat the 2002 CAP-CRMPrize in Theoretical andMathematical Physics hasbeen given to PavelWinternitz, professor atthe Département de

mathématiques et de statistiques of theUniversité de Montréal for his work onsymmetry methods in physics. In approximately250 articles, he has made fundamentalcontributions to, amongst others, the followingsubjects: classification of Lie groups andalgebras, their applications to the study ofdifferential equations and difference equations,separation of variables in Hamilton-Jacobi andSchrödinger type equations, quantum groupsand their applications. Born in Prague in 1936,Pavel Winternitz studied in the Soviet Union.After his bachelor and master’s degree at theUniversity of Leningrad, he obtained a Ph.D. inTheoretical Physics from Dubna’s JINR (1966). In1972, he joined the Université de Montréal. Aninternational symposium was held at the CRMin 1997 to celebrate his sixtieth birthday as well

as that of his colleague and compatriot JiriPatera.

CRM-SSC PrizeIn 1999, the Centre de recherchesmathématiques (CRM) and the StatisticalSociety of Canada created the CRM-SSC Prizein statistics in recognition of outstandingcontributions to the Statistical Sciences duringthe recipient’s first 15 years after earning adoctorate. The CRM-SSC Prize in Statisticsconsists of a $3000 award and a medal. Therecipient is chosen by a joint CRM/SSCadvisory committee, consisting of threemembers named by the SSC and two,including a president, by the CRM. Previouswinners were Christian Genest (1999), RobertTibshirani (2000) and Colleen Cutler (2001).This year, the Centre de recherchesmathématiques and the Statistical Society ofCanada have awarded the CRM-SSC 2002 Prizein Statistics to Professor Larry A. Wasserman ofCarnegie Mellon University, in Pittsburgh.

The 2002 CRM-SSC Prizein Statistics has beenawarded to Dr Larry A.Wasserman of CarnegieM e l l o n U n i v e r s i t y ,Pittsburgh, for thebreadth and originality ofhis contributions tostatistical theory and hisi n f l u e n c e i n t h ed e v e l o p m e n t a n dapplication of Bayesian

methodology. The announcement was made atthe Annual Meeting of the Statistical Society ofCanada (SSC), held in Hamilton, Ontario, May26-29, 2002.Larry Wasserman was born in Windsor, Ontario,where he grew up. He studied mathematics andstatistics at the University of Toronto (B.Sc.,1983; M.Sc., 1985; Ph.D., 1988). He has since beenaffiliated with Carnegie Mellon University,where he is now Professor of Statistics. Theauthor or co-author of more than 60 scientificarticles, he is widely recognized as one of thecurrent leaders in Bayesian inference. He hasbrought his expertise to bear on the foundationsof statistics and on numerous aspects of modernstatistical theory, including sampling, mixturemodels, multiple testing, goodness-of-fit androbustness issues, and both nonparametric andcausal inference. In addition, he maintains active



collaborations with astrophysicists and statisticalgeneticists.Larry Wasserman’s pathbreaking work hasalready earned him several distinctions. Winnerof the SSC’s Pierre Robillard Award for the bestthesis in probability or statistics defended at aCanadian university in 1988, he was made aFellow of the American Statistical Associationand of the Institute of Mathematical Statistics in1996.

He is also the 1999 winner of the Presidents’Award, given each year by the Committee ofPresidents of Statistical Societies to anoutstanding researcher under the age of 40. Hehas been an Associate Editor for The CanadianJournal of Statistics and the Journal of StatisticalPlanning and Inference. He continues to serve inthat capacity for The Annals of Statistics and theJournal of the American Statistical Association.Larry is married to an Italian statistician, IsabellaVerdinelli. In his spare time, he enjoys readingnovels, drinking fine wine, and hanging out inRome.



National Program CommitteeThe three Canadian institutes in themathematical sciences, CRM, Fields and PIMS,have initiated a program for the support of jointactivities of a national stature in themathematical sciences. A National ProgramCommittee of members from the three institutesadministers this program, funded to the tune of$100,000 per year. This committee makesrecommendations to the three directors. Theprogram has many mandates, the first being tofund conferences and workshops in themathematical sciences across Canada. Thesefunds are essentially allocated to activities thatfall outside the main purview of the threeinstitutes, or that would benefit from jointinstitute funding. The program also aims tosupport activities that are held at the meetings ofthe three mathematical sciences societies: CMS,CAIMS, and SSC, as well as to support theparticipation of graduate students at thesescientific meetings. Finally, it coordinatesinternational programs and other ventureswhere it is advantageous for the three institutesto act as a whole.

The International Workshop onDynamical Systems and theirApplication to BiologyAugust 2-6, 2001, Cape Breton, Nova ScotiaOrg.: Shigui Ruan (Dalhousie), Gail Wolkowicz(McMaster), Jianhong Wu (York)

The 45 participants came from Austria, Canada,China, Japan, Singapore, Spain, Taiwan, the UK,and the USA. Among them there were 14 PDFsand graduate students. On top of the 38 half-hour talks, there were two panel discussions onepidemiological models (chaired by Fred Brauerand Pauline van der Driessche) and populationdynamics (chaired by Jim Cushing, HerbFreedman and Hal Smith). The workshopfocused on (1) communication of currentresearch results, ideas, and problems indynamical systems and their applications inbiology, (2) future research directions indynamical systems and mathematical biology,and (3) initiating possible collaborations. It alsoprovided a wonderful opportunity for youngCanadian researchers and graduate students tocommunicate with the leading researchers andto present their research work. The proceedingsof the workshop will be published as a volumein the Fields Institute Communications.

13th Canadian Conference onComputational GeometryAugust 13-15, 2001University of Waterloo, OntarioOrg.: T. Biedl, E. Demaine, M. Demaine, A. Lubiw (Univ. ofWaterloo)Supported by the NPC (CRM, Fields, PIMS), Univ. ofWaterloo

The Canadian Conference on ComputationalGeometry (CCCG) focuses on the mathematicsof discrete geometry from a computational pointof view. Abstracting and studying the geometryproblems that underlie important applications ofcomputing (such as geographic informationsystems, computer-aided design, simulation,robotics, solid modeling, databases, andgraphics) leads not only to new mathematicalresults, but also to improvements in theseapplications. Despite its international following,CCCG maintains the informality of a smallerworkshop (70-85 attendees) and attracts a largenumber of students.

Second Workshop on the Conley Indexand Related TopicsAugust 15-18, 2001, Univ. de Sherbrooke, QuébecOrg.: Tomasz Kaczynski (Sherbrooke), Octav Cornea(Lille), Michael Dellnitz (Paderborn), KontantinMichaikow (Georgia Tech), Marian Mrozek (Kraków), andHiroe Oka (Ryukoku)Supported by the NPC (CRM, Fields, PIMS) and theFaculté des sciences de l’Université de Sherbrooke

The workshop is a continuation of the firstConley Index Workshop held in the BanachCenter (Warsaw, Poland) in June 1997. Theobjective of the workshop is to stimulate anexchange and collaboration on various problemsrelated to extensions and applications of theConley index theory as well as to thecomputation of the index. A particular place wasgiven to infinite dimensional Conley index,computational topology and computationaldynamics, and applications.There were 63 participants from 14 countries.The principal speakers were Norman Dancer(Sydney), Marek Izydorek (Gdansk), WilliamKalies (Florida Atlantic U), Christopher McCord(Cincinnati), James Reineck (Buffalo), RomanSrzednicki (Kraków), James Yorke (Maryland),and Piotr Zgliczynski (Kraków). O. Cornea, K.Mischaikow, and M. Dellnitz also gave tutoriallectures.



UNB Workshop on Modelling &Scientific ComputationSeptember 29-30, 2001, University of New BrunswickOrg.: V. Husain, J. Stockie and J. WatmoughInvited speakers!: Claudio Albanese (Toronto), MattChoptuik (UBC), Leah Keshet (UBC), Brian Wetton (UBC)

The workshop was considered to be highlysuccessful by the participants and organizers.Forty-two researchers from diversemathematical disciplines participated. The fourplenary speakers (Claudio Albanese, MattChoptuik, Leah Keshet, and Brian Wetton) gaveoverviews of the problems and computationalmethods in their respective fields, mathematicalfinance, numerical relativity, computationalbiology, and fluid mechanics. Severalcontributed talks covered a broad range of topicsin these fields, as well as in numerical analysisand physics.The success of the workshop inspired discussionof establishing an annual or bi-annual series ofsuch meetings in the Atlantic region.

CMS Winter MeetingDecember 8-10, 2001Toronto Colony Hotel, Toronto, OntarioOrg.: Tom Salisbury (president), Juris Steprans (localcommittee predident), Stan Kochman, Nantel Bergeron,Monique Bouchard (CMS)Supported by the NPC Canadian Mathematical SocietyNPC (Fields/CRM/PIMS), Dean of Arts, York UniversityDepartment of Mathematics and Statistics, York UniversityNumber of participants: 269

In 2001, the CMS’s annual winter meetingincluded eight special sessions and nine plenarylectures (including one public lecture and twoprize lectures). Four satellite conferences wereplanned in conjunction with the meeting. Agrant from the National Program Committeeprovided the funding for two of the specialsessions Industrial Mathematics, organized byHuaxiong Huang; Moonshine, organized by ChrisCummins). NPC funds were also used for thesupport of graduate students attending themeeting.Invited speakers: Kai Behrend (UBC), Martin Golubitsky(University of Houston), Katherine Heinrich (University ofRegina), Nathan Ng (University of Georgia), John Ockendon(Oxford University), Arturo Pianzola (University of Alberta),David Pimm (University of Alberta), Richard Schoen(Stanford University), Dan Voiculescu (Berkeley).

Western Canada Linear AlgebraMeetingMay 10-11, 2002, University of ReginaOrg.: Steve KirklandSupported by the NPC (CRM, Fields, PIMS), University ofRegina Conference Fund, and the Faculty of Science of theUniversity of Regina.

Held over two days, WCLAM 2002 featured 18talks by speakers from Canada, the United Statesand Germany. The lectures covered a range ofresearch areas associated with linear algebra,including matrix theory, operating theory, graphtheory, applied mathematics, numerical analysisand combinatorics. The list of speakers includedtwo winners of the Hans Schneider prize, whichis given out every three years by theInternational Linear Algebra Society foroutstanding contributions to research in linearalgebra. As with previous WCLAM’s, studentand postdoctoral participation is encouraged,and WCLAM 2002 had ten such participants.Indeed two students were given financialsupport towards their travel expenses in orderthat they could speak at the meeting.The meeting’s atmosphere is informal, with noparallel sessions, and with plenty of time forone-on-one discussion. As a result, WCLAM2002 is not only a forum for disseminatingresearch results, but also a venue for establishingnew research contacts and for makingconnections across a broad array of researchinterests.Invited speakers: Jane Day (San Jose State Univ.), LudwigElsner (Univ. Bielefeld), Chris Godsil (Univ. of Waterloo)

The 30th Canadian Annual Symposiumon Operator Algebras and OperatorTheoryMay 13-17, 2002, Lakehead UniversityOrg.: Andrew J. Dean

The 30th Canadian Annual Symposium onOperator Algebras and Operator Theory tookplace at Lakehead University in Thunder Bay,Ontario. Our main speaker was Professor AdrianOcneanu of Pennsylvania State University, whogave a series of three lectures on thegeometrization of quantum subgroups andsubfactors.The conference was opened by Professor K.Davidson of the University of Waterloo and theFields Institute, who spoke about his joint workwith Laurent Marcoux on spans of unitary andsimilarity orbits. This bit of scheduling may havebeen a mistake on the part of the organizer, as



they continued to improve their result as theconference went on!Also on the list of invited speakers were suchregulars of Canadian Operator Symposia past asGeorge Elliott, Man-Duen Choi, and PeterRosenthal of the University of Toronto, andHeydar Radjavi of Dalhousie University.Other invited speakers from abroad includedProfessor D. Hadwin of the University of NewHampshire, who spoke on an approach toVoiculescu’s free entropy using coveringnumbers, and Professor Marius Dadarlat ofPurdue University, whose topic was the problemof uniformly embedding a group into a Hilbertspace.In addition to the established researchers, theconference also provided a forum for severalgraduate students and postdocs from Canadianuniversities to present their work.Invited speakers!: Adrian Ocneanu (Penn State U.), Man-Duen Choi (U. of Toronto), Marius Dadarlat (Purdue U.),Ken Davidson (U. of Waterloo), George Elliott (U ofToronto), Don Hadith (U. of New Hampshire), HeydarRadjavi (Dalhousie U.), Peter Rosenthal (U. of Toronto).

CMS Summer MeetingJune 2-4, 2001, University of SaskatchewanOrg.: K.Taylor, C. Soteros, M. Bremner, Y. Cuttle and F.-V.Kuhlmann (Saskatchewan)Supported by the NPC (CRM, Fields, PIMS), and theUniversity of Saskatchewan

The 2001 Summer Meeting of the CanadianMathematical Society was both a scientific andan organizational success. There are relativelyfew mathematicians who live within easytraveling distance of Saskatoon, so the total of279 registered participants exceeded mostexpectations and seems to be a record for aregular summer meeting.David Boyd, University of British Columbia,gave the CMS Jeffery-Williams Lecture and LisaJeffrey, University of Toronto, gave the CMSKrieger-Nelson Lecture. The plenary lecturerswere Georgia Benkart, Wisconsin-Madison; ZoeChatzidakis, Paris; Geoffrey Grimmett,Cambridge; and Barry Simon, CalTech.There were also ten well-attended specialsessions in Abstract Harmonic Analysis,Geometric Topology, Graph Theory, InfiniteDimensional Lie Theory and RepresentationTheory, Mathematical Education: Cognition inMathematics, Matrix Analysis, Model TheoreticAlgebra, Number Theory - in Honor of DavidBoyd, Rigorous Studies in the Statistical

Mechanics of Lattice Models, and ScatteringTheory and Integrable Systems.

CAIMS8-10 June 2002University of CalgaryOrg.: P. Binding, T. Ware (University of Calgary)

The 23th Annual Meeting of CAIMS/SCMAI washosted by the University of Calgary andattended by over ninety academics, postdoctoralfellows and graduate students from acrossCanada, but also from the United States and asfar afield as Israel and the EuropeanCommunity. Despite the unusually wet weather,the atmosphere at the meeting was very positive.There was a lively interaction amongst theparticipants, whose interests included fluiddynamics, environmental mathematics,Hamiltonian dynamics, mathematical modelling,computational finance and computer graphics.There were five plenary talks, each of which wasfollowed by three parallel sessions eachfocussing on one of the above areas. Thepresentations were of a consistently highstandard, and the meeting provided an excellentshowcase for the activities of Canadian appliedand industrial mathematicians.Invited speakers: J. Marsden (Caltech), A. Gargett (OldDominion), G. Swaters (Alberta), N. Dyn (Tel Aviv), andH.!Ockendon (Oxford).

30th Annual Meeting of the StatisticalSociety of Canada (SSC)May 26-29, 2002, McMaster University, HamiltonSupported the NPC (CRM, Fields, PIMS) and McMasterUniversity.

This meeting was an unequivocal success, with379 registered participants. Three workshopswere held:• Design and Analysis of Cluster

Randomization Trials by A. Donner,University of Western Ontario, and N. Klar,Cancer Care Ontario.

• Design and Analysis of ComputerExperiments for Engineering by J. Sachs,Duke University, and W. Welch, Universityof Waterloo.

• Handling Missing Data by K. Nobrega andD. Haziza, Statistics Canada.

There were 46 scientific sessions in total, plus aposter session. Topics ranged from theoreticalprobability, inference, and stochastic processesto applied sessions on environmental issues,



statistical genetics, and statistics andgovernmental policy.Thanks in no small part to the funding from theNPC, the meeting included a large number ofinternationally known speakers. The particularspeakers whose funding was wholly or partiallycovered by the grant from NPC, by session,were:• Probability (Ilie Grigorescu, University of

Miami),• Statistical Inference (Chris Klaassen,

University of Amsterdam and WilliamStrawderman, Rutgers University)

• Statistics for Microarray Data Analysis(Michael Newton, University of Wisconsin atMadison and Terry Speed, University ofCalifornia at Berkeley)

• Statistics and Brain Mapping (Pedro Valdes-Sosa, Cuban Neuroscience Center and MooChung, University of Wisconsin at Madison)

• Statistics and Public Policy (Miron Straf,National Academy of Sciences)

• Split Plot Experiments in Industry (RobertMcLeod, PhD student at University ofManitoba)

• New Research Findings in Analysis Methodsfor Survey Data (Christian Boudreau, PhDstudent at University of Waterloo).



Members’ Seminars and Special EventsThe members of the CRM are encouraged to organize seminars and other scientific activities duringtheir stay at the CRM. These activities take the form of courses, workshops and research seminars

Analysis Seminar CRM-ISMOrg.: Paul Gauthier(CRM & Univ. de Montréal)June 1, 2001Paul Gauthier, Univ. de MontéalLa fonction zêta de Riemann et les cercles deremplissageJune 8, 2001Jie Xiao, Concordia Univ.Isoperimetric inequalities via Hausdorff contentJune 15, 2001Alexandre Girouard, Univ. de MontéalRétraction de boule en dimension infinieJune 21, 2001Pierre-Olivier Rathé, Univ. de MontéalProduits de BlaschkeJune 28, 2001Jean-Phlippe Samson, Univ. de MontéalSurconvergenceJuly 19, 2001Sébastien Manka, Univ. de MontéalUn théorème de sélection pour les relationsAugust 2, 2001Victor Havin, Saint PetersburgSur la séparation des singularités de fonctionsanalytiques bornéesAugust 6, 2001Abel Schroeder, ORT Braude College, IsraelEquations for linear fractional maps of operator ballsFebruary 5, 2002Paul Gauthier, Univ. de MontéalThéorème de Bloch conforme-faux pourquasiconformeFebruary 12, 2002Jie Xiao, Concordia Univ.Corona theorem for conformal deformationsFebruary 19, 2002Nabil AyoubLa constante de BlochFebruary 26, 2002André Boivin, Western Ontario Univ.Théorèmes d'approximation et applications

March 12, 2002Olivier Rousseau, Univ. de MontéalThéorie du degré topologique de Brouwer et théorèmede JordanMarch 19, 2002Richard Fournier, Dawson College & Univ. deMontréalInégalités différentielles et univalenceMarch 26, 2002Rasul Shafikov, SUNY at Stony BrookEquivalence of domains in Cn

April 2, 2002Richard Fournier, Dawson College & Univ. deMontréalLa suite universelle de Maurice Heins et autrespathologiesApril 9, 2002Sébastien Manka, Univ. de MontréalLe théorème d'approximation de CarlemanApril 16, 2002Nabil AyoubThéorème de Bloch et théorème de LandauApril 30, 2002Paul Gauthier, Univ. de MontréalPropriété d'universalité de la fonction zêta deRiemannMay 7, 2002Richard Fournier, Dawson College & Univ. deMontréalSur un homeomorphisme de l'ensemble des fonctionsanalytiques bornéesMay 14, 2002Jean-Philippe Samson, Univ. de MontréalUne introduction aux séries de DirichletMay 21, 2002Todor FabianUne interprétation probabiliste de la fonction Zêta deRiemann, sa représentation spectrale et applications

Seminar in Non-linear AnalysisOrg.: Marlène Frigon (CRM & UdeM)September 19 and 26, 2001Isidore Fleischer, CRMSur les fonctions à variations bornées à valeurs dansles espaces métriques



October 3, 2001Nicolas Beauchemin, Univ. de MontréalIntroduction à la catégorie de Lusternik-SchirelmanOctober 24 and 31, 2001Nicolas Beauchemin, Univ. de MontréalLa catégorie relativeNovember 14, 2001Nicolas Beauchemin, Univ. de MontréalThéorie des points critiques pour des fonctionnellesmultivoquesNovember 28 and December 5, 2001Alexandre Girouard, Univ. de MontréalEnlacement homologiqueDecember 11, 2001Donal O'Regan, National Univ. of IrelandIntegral EquationsJanuary 11, 2002Donald Violette, Univ. de MonctonDifférentiabilité de type univoque pour une certaineclasse d'applications multivoquesJanuary 30, 2002Alexandre Girouard, Univ. de MontréalAxiomatisation des inégalités de MorseFebruary 6-13 and 20, 2002Nicolas Beauchemin, Univ. de MontréalIntroduction à la f-catégorieMarch 13, 2002Ron Stern, Concordia Univ.A necessary condition for state constrainedstabilizationMarch 27, 2002Nicolas Beauchemin, Univ. de MontréalLa catégorie relative au sens de SzulkinApril 25 and May 2, 2002Nicolas Beauchemin, Univ. de MontréalApplication de la catégorie relative aux équationsdifférentielles

Special LecturesOrg.: N. Kamran & J. Hurtubise (CRM &McGill)September 10, 13, 14 and 17, 2001Li Ma, Tsinghua Univ.Mean Curvature Flow for Lagrangian Submanifolds, I

Special LectureOrg.: Adam Sikora (CRM)July 13, 2001Louis Kauffman, Univ. of Illinois at ChicagoVirtual Knot Theory

Special LecturesOrg.: Jean-Marc Lina (CRM)October 3, 2001Noel Cressie, Ohio State Univ.Fast spatial prediction via multi-resolution tree-structured modelsOctober 4, 2001Noel Cressie, Ohio State Univ.Fast spatial prediction via multi-resolution tree-structured models II

March 13, 2002Bradley J. Lucier, Purdue Univ.Wavelet Methods for Medical Tomography

Special LecturesOrg.: J. Harnad (Concordia & CRM)September 26, 2001A. N. Tyurin, Steklov Mathematical InstituteQuantization and theta-functionsOctober 3, 2001A. N. Tyurin, Steklov Mathematical InstituteSymplectic geometry of moduli spaces of vectorbundlesOctober 10, 2001A. N. Tyurin, Steklov Mathematical InstituteNon-abelian theta-functions

Special LecturesOrg.: John Taylor (McGill)September 28 and October 5, 2001Francois Ledrappier, École Polytechnique(Palaiseau, France)Brownian motion and negatively curved manifolds

October 12, 2001Francois Ledrappier, École Polytechnique(Palaiseau, France)Ergodic properties of some linear actionsOctober 19 and 26, 2001Francois Ledrappier, Ecole Polytechnique(Palaiseau, France)Aspects de la rigidité pour les variétés à courburenégative



Special Lecture CRM-ISMOrg.: Dana Schlomiuk (UdeM)October 4, 2001Jean-Paul Pier, Centre universitaire duLuxembourgL'analyse fonctionnelle, une théorie omniprésentedans les mathématiques du 20e siècle

Special LecturesOrg.: Peter Russell (McGill)March 8, 2002Vladimir Popov, Steklov InstituteColloque CRM-ISMModern developments in invariant theoryMarch 13, 2002Vladimir Popov, Steklov InstituteSelf-dual algebraic varieties and nilpotent orbitsMarch 13, 2002Vladimir Popov, Steklov InstituteAutomorphism groups of finite dimensional simplealgebrasMarch 20, 2002Vladimir Popov, Steklov InstituteGenerators and relations of affine coordinate rings ofsemisimple groupsMarch 20, 2002Vladimir Popov, Steklov InstituteDiscrete complex reflection groups

Special LecturesOrg.: Jacques HurtubiseMarch 19, 21, 26, 28 & April 2, 2002Nizar Touzi, Univ. de Paris I Panthéon-SorbonneContrôle stochastique et applications à la financeApril 22, 2002Jonathan Borwein, Simon Fraser Univ.Why Math is (Still) Hard: Challenges inMathematical Computing

Special Lecture (CCC 2002)Org.: Jacques HurtubiseH. Cohen, Univ. de BordeauxCourbes elliptiques!: de la théorie à la pratique

CRM-CERCAOrg.: José Urquiza (CRM), Josée Manseau(École Polytechnique), Donatien N’dri (ÉcolePolytechnique)October 18, 2001Jean Deteix

Modélisation et design de pièces en composite:optimisationNovember 8, 2001Marc Thiriet, CNRS & Univ. Pierre et MarieCurie & INRIA, FranceTraitements endovasculaires. Des modèlesnumériques aux outils médicauxNovember 29, 2001Patrick Terriault, École de TechnologieSupérieure, Univ. du Québec à MontréalConception de dispositifs médicaux en alliages àmémoire de formeDecember 13, 2001Gérard Plante, Univ. de SherbrookePrésentation des activités du à l'Université deSherbrookeFebruary 7, 2002Dominique Pelletier, École Polytechnique deMontréalAnalyse de sensibilité et d'incertitude par la méthodede l'équation des sensibilitésFebruary 21, 2002Adel Blouza, Univ. de Rouen & Univ. Paris VIUne version du lemme de Friedrichs et applicationsau modèle de coque de KoiterFebruary 21, 2002Laurent Dumas, École Normale Supérieure deParis & Univ. Paris VIOptimisation de formes aérodynamiques dansl'industrie automobileFebruary 28, 2002Laurent Dumas, École Normale Supérieure deParis & Univ. Paris VIModèles de billard’étude asymptotiqueFebruary 28, 2002Adel Blouza, Univ. de Rouen & Univ. Paris VIRéduction algorithmique des systèmes cinétiquesraidesMarch 21 and 28, 2002Michel Delfour, CRM & Univ. de MontréalModèles de coques minces et de coques asymptotiques

April 4, 2002Annie Raoult, LMC & TIMC, IMAG, Univ.Joseph Fourier, GrenobleNouveautés en modélisation hiérarchique de plaquesApril 11, 2002Annie Raoult, LMC & TIMC, IMAG, Univ.Joseph Fourier, GrenobleModélisation de l'orientation des fibres cardiaques



Seminar in Mathematical PhysicsOrg.: J. Harnad (CRM & Concordia) & PavelWinternitz (CRM)September 18, 2001Ahmed Sebbar, Univ. de BordeauxCapacities, Jacobi Matrices, & Jacobi FormsSeptember 25, 2001Misha B. Sheftel, St. Petersburg & IstanbulMethod of group foliation, non-invariant solutions ofthe heavenly equationand heavenly metricsSeptember 26, 2001A.N. Tyurin, Steklov Mathematical Institute,Russian Academy of Sciences, MoscowNon-abelian theta-functions and spin networks IOctober 2, 2001E.G. Kalnins, University of Waikato, NewZealandPerturbations of Black holes and special functionsOctober 3, 2001A.N. Tyurin, Steklov Mathematical Institute,Russian Academy of Sciences, MoscowNon-abelian theta-functions and spin networks IIOctober 9, 2001Michel Grundland, UQTR & CRMSur certains aspects géométriques des applications dumodèle sigma CP2October 10, 2001A.N. Tyurin, Steklov Mathematical Institute,Russian Academy of Sciences, MoscowNon-abelian theta-functions and spin networks IIIOctober 16, 2001Aleksander Strasburger, Univ. de BialystokOn the ordering problem in QM and its connectionwith certain classes of Orthogonal PolynomialsOctober 23, 2001David Calderbank, Univ. of EdinburghIntegrable background geometries in dimensions oneto fourNovember 1, 2001Henrik Aratyn, Univ. of IllinoisSymmetries of Integrable Models and Applications tothe Witten-Dijkgraaf-Verlinde EquationsNovember 13, 2001Decio Levi, Univ. Roma TreMultiscale Reduction for Differential Differenceequations and IntegrabilityNovember 20 and 22, 2001Aleksander Orlov, Institute of Oceanology,Moscow & CRMHypergeometrical tau-functions

November 27, 2001Eyal Markman, Univ. of Massachusetts(Amherst)Elliptic Sklyanin systemsDecember 4, 2001Ray McLenaghan, Univ. of WaterlooGroup invariant classification of separableHamiltonian systems in the Euclidean planeDecember 11, 2001Zuzana Masakova, CRMCombinatorial properties of cut and project sequencesJanuary 15, 2002Pavel Winternitz, CRM & DMSSystèmes intégrables et superintégrables dans lesespaces avec courbureJanuary 22, 2002Dmitri Korotkin, Concordia Univ. & CRMSome integrable systems on Hurwitz spacesJanuary 29, 2002Simon Gravel, CRM & Univ. de MontréalSystèmes superintégrables avec symétries dutroisième ordreFebruary 5, 2002Luis-Miguel Nieto, Univ. ValladolidHigher order supersymmetric periodic potentialFebruary 12, 2002Mikhail Babich, Concordia Univ. & SteklovMathematical Institute, St.Petersburg, RussiaSchlesinger system with 4 points, its symmetries,connections with Painlevé VI system and thealgebraic surface theoryFebruary 19 and 21, 2002Fréderic Lesage, CRMThéorie des champs intégrables et dualitéFebruary 26, 2002Jean-Louis Verger-Gaugry, Institut Fourier,Saint-Martin d’Hères, FranceUn théorème de compacité pour l'ensemble desensembles uniformément discrets de Rn et ses sous-ensembles : réseaux, ensembles modèles, ensembles deDelaunay, clusters.March 12, 2002Charles P. Boyer, Univ. of New MexicoSasakian-Einstein GeometryMarch 19, 2002John Harnad, CRM & Concordia Univ.Matrix models, integrable systems, duality, and allthat



March 26, 2002Maria Cristina Ciocci, Univ. of GentKAM for reversible systemsApril 2, 2002Michel Racine, Univ. d’OttawaSuperalgèbres simplesApril 4, 2002Jan Zich, Technical Univ., Prague & CRMVoronoi and Delone tiling of quasicrystalsApril 9, 2002G. Pogosyan, UNAM, Mexico & JINR, Dubna,RussiaSuperintegrable potentials in N-dimensionalEuclidean spaceApril 16, 2002Marco Bertola, CRMFundamental systems of solutions for infiniterecurrence relations arising in two-matrix models;applications to the Riemann-Hilbert problemApril 23, 2002Jacek Szmigielski, Univ. of SaskatchewanAn Ansatz for the large n asymptotics of bi-orthogonal polynomials. The genus zero caseApril 25, 2002Miroslav Englis, Mathematics Institute,Academy of Sciences, PragueA review of (Berezin and other) quantization methodsApril 30, 2002Bertrand Eynard, Saclay (France) & CRMDiscrete classical strings, Weyl functions, andintegrable systemsMay 7, 2002T. A. Osborn, Univ. du ManitobaMagnetic Curvature of Quantum Phase SpaceMay 14, 2002Franco Magri, Univ. Milano-BococcaA geometrical characterization of separable systemsaccording to Levi Civita: classical roots and modernperspectives

Special Days in Dynamical SystemsOrg.: Dana Schlomiuk (UdeM & CRM) &Christiane Rousseau (UdeM & CRM)November 29, 2001

Dana Schlomiuk, UdeM & CRMÉquations différentielles algébriques dans le planprojectif complexeRobert Roussarie, Univ. de DijonIntégrales abéliennes et cycles limites

Nicolae Vulpe, Académie des sciences deMoldavieDifferential operators and multiplicity of singularpoints for polynomial differential systemsChristiane Rousseau, UdeM & CRMPoints de selle normalisables et intégrables dans lesystème de Lotka-Volterra

CRM Postdoctoral Fellows SeminarOrg.: Pietro-Luciano Buono (CRM)January 16, 2002Marco Bertola, CRMThe (Bi)-Orthogonal Polynomial Approach toRandom (Two)-Matrix ModelsJanuary 23, 2002Diego Matessi, CRMMirror Symmetry according to the SYZ-conjectureJanuary 30, 2002José Urquiza, CRMContrôle d'équations des ondesFebruary 16, 2002Luciano Buono, CRMBifurcations, G-Transversality and StratificationsFebruary 20, 2002Piergiulio Tempesta, CRMSuperintegrability, Classical Lie theory and ExactSolvability in Quantum Mechanics

Statistics SeminarsOrg.: Jean-François Angers (UdeM) & RochRoy (UdeM)July 4, 2001Guy Mélard, Univ. Libre de BruxellesProblèmes numériques relatifs aux processusVARMAJuly 11, 2001Atanu Biswas, Indian Statistical Institute,CalcuttaAdaptive designs for normal responses withprognostic factorsDecember 13, 2001Kilani Ghoudi, UQTREstimateurs non-paramétriques des distributions devaleurs extrêmes multivariéesDecember 21, 2001Christian Robert, Univ. Paris Dauphine &CRESTEstimation de mélanges de distributions!: Résultatsrécents et perspectives



January 11, 2002Jacques Carrière, Univ. of AlbertaA Gaussian Process of yield rates calibrated withstripsFebruary 6, 2002Jean-François Angers, Univ. de MontréalTests pour vérifier l'égalite de deux fonctionsFebruary 13, 2002Luc Perreault, Hydro-QuébecAnalyse bayésienne multisite d'une rupture dans desséquences de variables aléatoireshydrométéorologiquesFebruary 20, 2002Racula Balan, Univ. de SherbrookeStatistique bayésienne non-paramétrique dans le casmarkovien

February 27, 2002Denise A. Lievesley, Directrice de l’Institut destatistique, UnescoLe mandat et les activités de l'Institut de statistiquede l'UNESCOMarch 27, 2002Alain Latour, UQAMProcessus GARCH à valeurs entièresApril 3, 2002Alain Vandal, McGill Univ.Utilisation des ondelettes pour élaborer des tests dansles modèles autorégressifs dans les duréesconditionnellesApril 10, 2002Pierre Duchene, HECDeux applications de la théorie des graphes àl'analyse de survie



CRM-ISM ColloquiumThe CRM, together with the Institut des sciences mathématiques (the Québec university graduatemathematics consortium), runs the Montréal mathematics colloquium, which, during the universityyear, organizes survey talks by distinguished mathematicians on topics of current interest.

Fall 2001Organizers: D. Schlomiuk (CRM & UdeM) &T. Tokieda (UQAM & UdeM)Friday September 21Henri Darmon, McGill UnivElliptic curves and Hilbert's twelfth problem

Wednesday September 26Louis Nirenberg, Courant Institute of Math. SciencesA problem on differential forms coming from economics

Friday October 5Carolyn S. Gordon, Dartmouth CollegeCan you hear the shape of a manifold

Friday October 12Andrei N. Tyurin, Steklov InstituteThree mathematical facets of SU(2) spin networks

Friday October 19Paul Gauduchon, École Polytechnique (France)Variétés kählériennes ortho-toriques

Friday October 26Chris Sogge, Johns Hopkins Univ.Riemannian manifolds with maximal eigenfunction growth

Friday November 2David Ruelle, IHESNonequilibrium Statistical Mechanics: Entropy Productionfor Quantum Spin Systems

Friday November 9 (CRM-Fields Prize 2001William T. Tutte, Univ. of WaterlooSome adventures in Graph Theory

Friday November 16Claude LeBrun, SUNY Stony BrookPromotional Materials for Infinite-Dimensional Lie Groups

Friday November 23Juan Maldacena, Harvard Univ.QCD, strings and black holes

Friday November 30Dorian Goldfeld, Columbia Univ.Multiple Dirichlet series and moments of zeta and L-functions

Winter 2002Friday December 7Andrzej Zuk, The Univ. of ChicagoGroups with property (T)

Friday January 25Izabella Laba, Univ. of British ColumbiaA review of some tiling problems

Friday February 1Martin J. Gander, McGill Univ.The Jungle of Domain Decomposition Methods: Schwarz,Schur, Feti, Neumann-Neumann and More

Friday February 22Boris Khesin, Univ. of TorontoTrinity of Euler equations on the Virasoro group

Friday March 1Hanspeter Kfrat, Univ. BaselSeparation of Orbits in Varieties

Friday March 8Vladimir Popov, Steklov Institute, MoscowModern developments in invariant theory

Friday March 15Askold Khovanskii, Univ. of TorontoNewton polyhedra

Friday March 22Ed Spiegel, Columbia Univ.Continuum Equations for Rarefied Gases

Friday April 5Yakov Eliashberg, Stanford Univ./IASGeometry of contact domains and transformations

Friday April 12Goro Shimura, Princeton Univ.The arithmeticity of Euler products and Eisenstein series ona unitary group

Friday April 19Bernard Malgrange, Institut Joseph Fourier, Univ. deGrenoble 1Théorie de Galois différentielle non-linéaire

Friday April 26Kumar Murty, Univ. de TorontoElliptic curves and Sieve methods

Friday May 2Hassan Aref, Univ. of Illinois at Urbana-ChampaignVortex crystals


Coming Activities

Theme Year 2002-2003:Math in Computer Science

Organizing CommitteeDavid Avis (McGill), Yoshua Bengio (Montréal),Gilles Brassard (Montréal), Luc Devroye(McGill), Pierre L’Écuyer (Montréal), PierreMcKenzie (Montréal), Prakash Panangaden(McGill), Bruce Reed (McGill), and DenisThérien (McGill).

OverviewThe field of computation, formally born only lastcentury but with roots that stretch back toEuclid, is now a mathematical discipline in itsown right, with solid theoretical foundations onwhich are based its spectacular development.The CRM special year in the mathematics ofcomputer science proposes to explore in depth asignificant spectrum of the many sub-areas thatare core foundational material for moderncomputer science, that exhibit significant andnew mathematical content, and that have indeedinfluenced the development of mathematics.Mathematically, the areas with the earliestinfluence on computer science were logic anddiscrete mathematics. Since then, the theoreticalfoundations of computer science haveblossomed, and ideas from the area (likeeffectiveness, complexity and tractability) havegrown to occupy an ever more important role in

mathematics. More recently, a recurrent themein many of the domains examined areprobabilistic methods; these have permeated thewhole of computer science, and so particularemphasis will be placed on the utilisation ofthese techniques, both in theoretical areas and inmore applied ones such as simulation andmachine learning.

Summer School on QuantumInformation ProcessingJuly 16-20, 2002Org.: Gilles Brassard (Montréal)

Classical information theory is firmly rooted inthe classical physics of Newton and Einstein.But the world is quantum mechanical. This hasprevented us from tapping the full potential ofphysical reality for information processingpurposes. For instance, quantum mechanicsallows for unbreakable cryptographic codes andsuch a high level of parallelism in computationthat a classical computer the size of the universewould be left behind. The goal of this school is tomake the field of quantum informationprocessing accessible to a general audience ofmathematicians and computer scientists whohave little or no familiarity with quantummechanics.Invited speakers: A. Ambainis, C.H. Bennett, G. Brassard,H. Buhrman, R. Cleve, C. Crépeau, D. Gottesman, N. Gisin,

Coming Activities


P. Hoyer, R. Laflamme, A. Tapp, J. Watrous.

Aisenstadt Chair lecture seriesThere will be three series of conferencesassociated with the Aisenstadt Chairs by ManuelBlum (Carnegie Mellon), Laszlo Lovasz (MicrosoftResearch), and Endre Szemeredi (RutgersUniversity).

CONCENTRATION PERIOD IComplexity Theory, Analysis ofAlgorithmsMay-June 2002Org.: Pierre McKenzie (Montréal), Denis Thérien (McGill)

In May 2002, the CRM will host two of the mostimportant international conferences intheoretical Computer Science, namely the ACMSymposium on Theory of Computing and theIEEE Conference on Computational Complexity.In addition, there will be several one-weekworkshops on topics that lie at the core of thetheory of computing. Each workshop will bringtogether a number of leading scientists who willpresent both expository lectures and state-of-the-art research.

Lecture series on branching programsMay 13-17, 2002Org.: Ingo Wegener (Dortmund)

ACM Symposium on Theory of Computing(STOC)May 19-21, 2002

IEEE Conference on ComputationalComplexityMay 21-24, 2002

Randomness in Branching programMay 27-31, 2002

Random techniques play an important role incomputer science, through algorithms, whichgive an efficient solution to problems for whichno good deterministic solution is known, orthrough the probabilistic study of complexity. Aweek will be devoted to this theme, starting withthe links between probabilistic methods andbranching programs.

Verification and model-checkingJune 3-7, 2002

In the past ten years, theoretical work in the areaof verification has started to bear fruit. Theworkshop will cover the major areas of thisdevelopment, in particular those linked tomodel-checking.

Descriptive complexityJune 10-14, 2002

An area that has come to the fore in recent years,descriptive complexity gives a tool thatcomplements more classical approaches tocomplexity theory. After a survey of the area, theworkshop will concentrate on links betweenbranching programs and algebraic structures.Invited speakers: D. Barrington, P. Beame, P.L. Crescenzi, R.Gavalda, N. Immerman, K.J. Lange, P. Pudlak, A. Razborov,M. Sachs, R. Raz, P. Schnoebelen.

CONCENTRATION PERIOD IIQuantum Foundations in the Light ofQuantum InformationOctober 14 to November 2, 2002Org.: Gilles Brassard (Montréal), Christopher A. Fuchs(Bell Labs, Lucent Technologies)

Rolf Landauer’s best-known aphorism isinformation is physical. This workshop is centredon the belief that physics is informational! Ourlong-term purpose is to reformulate thefoundations of quantum mechanics in the lightof quantum information theory. Rather thanbeing counterintuitive, could it be that quantummechanics was inevitable for information tobehave as we understand it now? For instance,what can we derive from the fact thatunconditionally secure cryptographic keydistribution is possible but bit commitment isnot?Invited speakers: M. Appleby, H. Barnum, C.H. Bennet, G.Brassard, H. Briegel, J. Bub, A. Cabello, C. Caves, R.Floreanini, C. Fuchs, N. Gisin, L. Hardy, P. Hayden, F.Markopoulou, D. Mayers, D. Mermin, D. Poulin, R. Schack,B. Schumacher, J. Smolin, R. Spekkens, C. Timpson.

CONCENTRATION PERIOD IIICombinatorics, probability andalgorithmsMay 2003Org.: David Avis (McGill), Luc Devroye (McGill), Bruce A.Reed (Waterloo)

Leave nothing to chance. This cliché embodiesthe common belief that randomness has no placein well-planned methodologies, every i shouldbe dotted and every t should be crossed. Indiscrete mathematics, at least, nothing could befurther from the truth. Introducing randomchoices into algorithms can improve theirperformance. The application of probabilistictools has led to the resolution of combinatorialproblems which have resisted attack for decades.A month-long concentration period will takeplace around this general theme. Lecturers at the

Coming Activities


school will introduce participants to a number ofweapons, mostly from the probabilistic arsenal,and their applications in combinatorics and inthe study of algorithms. We anticipate asignificant amount of collaboration betweenparticipants at the school during the month.There will be five-hour mini-courses given by: V. Chvatal(Rutgers), A. Frieze (Carnegie-Mellon), L. Lovasz,(Microsoft), C. McDiarmid (Oxford), M. Molloy (Toronto), J.Pach (City College New York et Hungarian Academy ofSciences), E. Szemeredi (Rutgers).

INTERNATIONAL ANNUAL MEETINGSACM Symposium on Theory ofComputing (STOC)May 19-21, 2002

IEEE Conference on ComputationalComplexityMay 21-24, 2002Org.: Pierre McKenzie (Montréal), Denis Thérien (McGill)These two conferences are part of theconcentration period on Complexity theory,analysis of algorithms.

Mathematical Foundations ofProgramming Semantics (MFPS)March 19-22, 2003Org.: Prakash Panangaden (McGill)

Conferences and workshops in this series, heldannually since 1985, aim to provide a forum forresearchers in all areas surrounding semantics topresent their latest research results, and toimprove communication and interactionsbetween mathematicians and computer scientistswho work in these areas. The areas of relevanceinclude category theory, domain theory, logicand topology on the mathematics side, and typetheory, semantics, and the design andimplementation of programming languages onthe computer science side.

IEEE Symposium on Logic inComputer Science (LICS)June 20-26, 2003Org.: Amy P. Felty (Ottawa), Philip Scott (Ottawa)

To be held at the University of Ottawa, the IEEESymposium on Logic in Computer Science(LICS) is an annual international forum ontheoretical and practical topics in computerscience that relate to logic in a broad sense. TheCRM will be sponsoring four satellite workshopsfor this conference.

WORKSHOPSRandom Number Generation andHighly Uniform Point SetsJune 17-28, 2002Org.: Pierre L’Écuyer (Montréal)

This workshop will bring together the worldleaders in the theoretical and practical aspects ofrandom number generation by computer and thedesign of highly uniform point sets for quasi-Monte Carlo integration. The general theme isthe development of practical random numbergeneration software for various classes ofapplications, such as simulation, statistics,numerical analysis, computer games, lotteries,cryptology, etc. In simulation, highly uniform (orlow-discrepancy) point sets can oftenadvantageously replace the traditional randomnumbers. Their construction and analysis can bebased on ideas and tools that are very similar tothose used for random number generators andwe want to strengthen this connection.Invited speakers: P. Boyle, G.J. Chaitin, C. Crépeau, L.Y.Deng, M. Evans, H. Faure, M. Fushimi, J. Gentle, M. Goresky,S. Heinrich, A. Keller, A. Klapper, C. Lemieux, G. LeobacherM. Mascagni, M. Matsumoto, H. Morohoshi, S. Ninomiya, T.Nishimura, A.B. Owen, W. Schmid, I. Sloan, H.Wozniakowski.

Mathematical Models and Techniquesfor Analysing SystemsSeptember 30 to October 4, 2002Org.: Prakash Panangaden (McGill)

The analysis of systems has both diversified anddeepened tremendously in the last few years. Interms of diversification, systems of interest nowinclude stochastic systems, real-time systemsand hybrid systems, that is, systems where thestate space is partly discrete and partlycontinuous. Applications include flightmanagement systems for aircraft, process controlsystems, telecommunication systems and battlemanagement systems. In all of these one has todeal with continuous time evolution and usuallywith probabilistic aspects as well. Perhaps themost successful mathematical technique fordealing with these problems – now almosttwenty years old – is model checking. This isnow being extended to probabilistic systems andthe theory has advanced to the point where toolshave been designed and built. In terms of thegeneral mathematical theory co-inductivetechniques, like bisimulation, have proved theirvalue repeatedly.The workshop would have two main speakers,who will each give five lectures: Prof. Marta

Coming Activities


Kwiatkowska, U. Birmingham, ProbabilisticModel Checking, and Dr. Jan Rutten, CWIAmsterdam, Coinductive Calculus.Additional invited speakers: R. Alur, P. Caines,R. Jagadeesan, and D. Precup.

Finite Model TheoryMarch 2-9, 2003Org.: Denis Thérien (McGill)

This workshop will focus on the expressivepower of logics and on the deep relationshipbetween logic and computational complexity.The principal speaker will be Phokion Kolaitis(U.C. Santa Cruz). The workshop will be held atthe Bellairs Research Institute of McGillUniversity.

Semigroups and AutomataMarch 9-16, 2003Org.: Denis Thérien (McGill)

This workshop will discuss recent developmentsin the theory of automata and semigroups, inparticular some dealing with long-standing openproblems such as decidability of the dot-depthhierarchy and decidability of Rhodescomplexity.

Cryptographic Reduction of Quantumand Classical ProtocolsApril 28 to May 2, 2003Org.: Claude Crépeau (McGill)

Cryptographic protocols have been studied fortwo decades in the classical scenario undervarious computational assumptions. Suchprotocols as Bit Commitment, ObliviousTransfer and Multiparty Computations have

been implemented and reduced to each other.Over the last few years, similar results are nowachieved in the context of adversaries equippedwith quantum computers. This workshop willbring together specialists of both classical andquantum cryptographic protocols who willpresent the state of the art in this fascinating areaof research.Invited speakers: D. Beaver, *C. Cachin, R. Cramer, C.Crépeau, I. Damgaard, P. Dumais, D. Gottesman, J. van deGraaf, *R. Impagliazzo, J. Kilian, D. Mayers, *M. Naor, *S.Rudich, L. Salvail, A. Smith, A. Tapp, S. Wolf, M. Yung.*to be confirmed.

Recent Advances in Machine LearningJune 2-13, 2003Org.: Yoshua Bengio (Montréal), Balázs Kégl (Montréal),Doina Precup (McGill)

Probabilities are at the core of recent advances inthe theory and practice of machine learningalgorithms. The workshop will focus on threebroad areas where these advances are crucial:statistical learning theory, learning algorithms,and reinforcement learning. The workshop willtherefore bring together experts from each ofthese three important domains. Among thesub-topics that will be covered, we note:variational methods, graphical models, the curseof dimensionality, empirical methods to takeadvantage of theories of generalization error,and some of the applications of these newmethods.Invited speakers: P. Bartlett, A. Barto, P. Frasconi, G. Hinton,M. Jordan, V. Koltchinskii, Y. Le Cun, M. Littman, G. Lugosi,S. Roweis, B. Scholkopf, D. Schuurmans, S. Singh, R. Sutton.

Coming Activities


Theme Year 2003-2004:Geometric and Spectral Analysis

Organizing CommitteeE. Bierstone (Toronto), W. Craig (McMaster),F. Finster (MPI), P. Gauthier (Montréal),D. Jakobson (McGill), V. Jaksic (McGill),N. Kamran (McGill), R. Melrose (MIT),P. Milman (Toronto), D.H. Phong (Columbia),and J. Toth (McGill).Analysis has traditionally stood at the centre ofgravity of much of the research activity inmathematics. In particular, the fields ofgeometric and spectral analysis have played afundamental role in shaping the major themes ofcurrent research in differential geometry andmathematical physics, and they stand indeed atthe core of several of the deepest and mostspectacular advances in these fields. There isnow, for example a much deeper understandingof the eigenvalues and eigenfunctions ofmanifolds than there was even five years ago.The thematic year in geometric and spectralanalysis will focus on a number of themes inwhich this interaction has been particularlyfruitful. The year is organized around twointerconnected themes: the first, whose differentsubthemes cover the whole year, is principallycentered on various questions in spectralanalysis; it comprises what is in essence twoshort programs, one on contact geometry andthe other on analysis on singular space, and amore extended period on spectral analysis inmathematical physics and number theory. Thetwo short programs have a particularly strongemphasis on developing new connections toother areas of mathematics. The second themerelates to the analysis of the Einstein equations, asubject on which there has been spectacularprogress in recent years. It is concentrated in thefall of 2003.These themes have been chosen so as to have abalance between the geometric and spectralcomponents of the scientific program, and alsowith the objective of highlighting some of themost interesting current applications of analyticideas to physics.There will be a strong emphasis on trainingthrough the short courses, which will precedethe proposed workshops, as well as through thecoordination of the graduate course offerings inanalysis and geometry in the Montréaluniversities. In particular, a minimum of eightshort courses is being planned in connectionwith the various workshops. Some of these short

courses are listed in the detailed program givenbelow.

Aisenstadt Chair Lecture SeriesThere will be two chairholders for the year:P.!Sarnak (Courant) and S. T. Yau (Harvard).

SPECTRAL ANALYSISContact geometry and analysisJuly 2003Org.: R. Melrose (MIT), D. Auroux (MIT & ÉcolePolytechnique, France)In the vigorous development of contactgeometry, which has taken place over the pastten years or so, the notion of a tight (orconversely an overtwisted) contact structure hasproved to be central, with many deep andimportant applications to three-dimensionaltopology. On the analytic side, the notion of thequantization of a contact manifold, that is theexistence of a generalized Szegö projection, hascome to play a central role in developmentsrelated to the algebra of pseudodifferentialoperators of Heisenberg type and relatedhomological questions. Both endeavours arerelated to embedding, or fillability, questionswhich remain substantially open, especially inthe three dimensional case. It is hoped that bybringing this group together they will be able tounderstand these relationships and theirrepercussions. The format is one of informallecture series over two weeks, on subjects suchas: Contact Floer homology and symplectic fieldtheory, Approximate holomorphic geometry,Gauge theory and symplectic fillings,Heisenberg algebras, Toeplitz quantization, andPowers of circle bundles.

Analysis and Resolution ofSingularitiesAugust 2003Org.: E. Bierstone (Toronto), P. Milman (Toronto), D.H.Phong (Columbia)Effective methods in resolution of singularitiesare becoming central to a modern generation ofproblems from analysis and geometry – forexample, spectral theory and Hodge theorem foralgebraic varieties, stability of oscillatingintegrals, existence of Kähler-Einstein metrics,sharp forms of Moser-Trudinger inequalities.The diversity of the problems and their verydifferent origins and aims have led to a lack ofcommunication among researchers on these and

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related topics. This program, bringing togetherleading experts in resolution of singularities,complex differential geometry, and real analysisand partial differential equations, may haveground-breaking impact.

Week 1. Workshop on oscillatory integrals andcritical integrability exponentsTopics include degeneracy of holomorphicfunctions in several variables, Legendredistributions and multiplier ideal sheaves.Week 2. Short coursesThree short courses to be accessible to graduatestudents in analysis, given by the organizers orother participants.• Effective methods in resolution of

singularities – ideas involved indesingularization algorithms, concreteexamples with a view to applications inanalysis and geometry.

• Stability questions in real and complexanalysis; for example, stable forms of themethod of stationary phase, stability ofcritical integrability exponents, ascendingchain conditions, stability problems fordegenerate Fourier integral operators.

• Real and complex blow up, resolution ofmetrics, configuration spaces and Liealgebras of vector fields – leading to adescription of harmonic forms and L 2

cohomology of various singular spaces.

Week 3. Workshop on resolution ofsingularities, metrics and the LaplacianThe Hodge theorem, describing the harmonicforms on a smooth algebraic variety and relatingthem to its cohomology, has had wide impact ondifferential and algebraic geometry, anddifferential analysis. In the more general case ofa singular projective variety, a description of theharmonic forms remains largely open, althoughthere are substantial conjectures. An approachthrough resolution of singularities depends onunderstanding the structure of the Fubini-Studymetric lifted to a resolution. The workshop willbring together researchers in geometric,algebraic and analytic areas related to thesequestions.

Sub-theme: Spectral Analysis inMathematical Physics and Number TheoryAll year

Integrable and Near-IntegrableHamiltonian Partial Differential EquationsMay 2004Org.: W. Craig (McMaster), P. Deift (Pennsylvania), H.Flaschka (Arizona), S. Kuskin (Heriot-Watt), P. Olver(Minnesota), P. Winternitz (CRM).This workshop will provide a cross-section ofthe most significant current activity in the fieldof Hamiltonian PDEs, including integrability,asymptotics in the small dispersion limit, KAMtheory, and Arnol'd stability. This workshop isorganized in conjunction with the special year inanalysis at the Fields Institute.

Spectral Theory of SchrödingerOperatorsJuly 2004Org.: V. Jaksic (McGill), Y. Last (Hebrew)The spectral theory of Schrödinger operators hasbeen the stage of spectacular developments overthe last ten years. The emphasis has shifted tothe problems involving semiclassical limits andlimits of large numbers of particles (e.g., atomicHamiltonians) and to the problems involvingquasi-periodic and random structures. The goalof the workshop is to bring together the worldleading experts, young researchers and thegraduate students in this fast developing field.The state of the art research and results will bedescribed in an accessible way, and the newdirections of research will be pointed out.

Dynamics in Statistical MechanicsJuly 2004Org.: V. Jaksic (McGill), C.-A. Pillet (Toulon)The past ten years have witnessed some majornew developments in the field of non-equilibrium statistical mechanics, owing to aninflux of fresh ideas from probability theory andC*-algebras. This progress is complemented bythe study of concrete, physically relevant modelsof infinite particle systems, for which the zerothand the second law have been now rigorouslyestablished. The goal of the workshop is to bringtogether the world’s leading experts in the field.

Semi-Classical Theory ofEigenfunctions and Partial DifferentialEquationsJune 2004, (to be held at the Fields Institute)Org.: D. Jakobson (McGill), J. Toth (McGill)Many questions in quantum chaos are motivatedby the correspondence principle in quantum

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mechanics. These include asymptotic bounds forthe eigenfunctions, integrated and pointwiseWeyl error terms, and scarring. Anotherfundamental question concerns the local andglobal statistical properties of the eigenfunctions,their nodal sets and critical points. Thesequestions will from the main theme of theworkshop.

Spectral Theory and AutomorphicFormsOrg.: Y. Petridis (CUNY), J. Toth (McGill)Analytic questions about families of L-functionsinclude the distribution of zeros and thegeneralized Riemann hypothesis, valuedistribution, special values as well asconnections with arithmetical questions such asthe distribution of primes, size of class groups,analytic ranks and elliptic curves. This workshopwill bring together some of the most activeresearchers in this rich and important area ofmathematics, which lies at the boundary ofanalysis and number theory.

ANALYSIS OF THE EINSTEINEQUATIONSSeptember-October 2003

Workshop on the Cauchy Problem forthe Einstein EquationsSeptember 2003Org.: F. Finster (MPI), N. Kamran (McGill)

A number of major advances have been achievedover the past few years in the analysis of theCauchy problem in general relativity. Theseinclude the proof of the non-linear stability ofMinkowski space, the proof of the RiemannianPenrose conjecture and the rigorous descriptionof the asymptotic behavior at infinity of theadmissible Cauchy data. This workshop willbring together some of the key players who havebeen involved in these developments, and willprovide an opportunity for exploring some ofthe remaining open problems.

Workshop on the Interaction of Gravitywith External FieldsOctober 2003Org.: F. Finster (MPI), N. Kamran (McGill)The interaction of gravity with external fields isgoverned by highly coupled systems of partialdifferential equations on manifolds. The analysisof these systems has lead to surprising results onthe role of external fields in the dynamics ofgravitational collapse and singularity formation.These results include, in the sphericallysymmetric case, the existence of stable particle-like solutions of the Einstein-Yang Millsequations, and the non-existence of black holesolutions when the gravitational field is coupledto a Dirac spinor field. One of the objectives ofthe workshop will be to review thesedevelopments, and to discuss some of thedirections for future research.Short courses: H. Friedrich (MPI), F. Finster (MPI), J. Smoller(Michigan)

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Theme Year 2004-2005:Mathematics of Complex Multiple-Scale Systems

Organizing CommitteeA. Bourlioux (Montréal), M. Delfour (Montréal),Weinan E (Princeton), M. Gander (McGill),T. Hou (Caltech), A.J. Majda (Courant),T. Souganidis (Texas), R. Sircar (Princeton),C. Schuette (Berlin), and A. Stuart (Warwick).

The 2004-2005 thematic year will be dedicated tothe applied mathematical tools (modeling,analysis, computational) needed to studycomplex systems in various domains of scienceand engineering. Complexity is used genericallyin a broad sense to encompass a wide range ofscales to be accounted for, a large number ofdegrees of freedom, couplings between severalmechanisms in the model, general nonlinearities,and much more. The domains for applicationsinclude climate modeling, turbulence, frontspropagation, molecular dynamics, materials,finances, bio-mechanical systems in medicine,quantum control. Despite the diversity in theapplications, some of the challenges andstrategies to face them have much in common:how can one include any form of knowledgeregarding the dynamic of the solution so as toproduce an useful model which captures wellthe global behavior of the system? Oneparticularly promising approach is based onstochastic models: this will be the topic for thesummer school and will also be a recurringtheme throughout the various workshops. Thosewill be an opportunity for interaction betweenapplied mathematicians specializing inmodeling and numerical simulation andresearchers in the various fields of applicationsin science and engineering.

Summer School in Stochastic Methods inApplied MathematicsJuly 2004Org.: A. Bourlioux (Montréal), E. Vanden Eijnden(Courant)

This two-week intensive preliminary workshopwill introduce graduate students and postdocs tothe basic stochastic tools to be used anddeveloped in the subsequent specializedworkshops. General topics are: stochastic partialdifferential equations, stochastic differentialequations/stochastic processes, numericalmethods for SDE/SPDE.

Aisenstadt Chair Lecture SeriesThere will be two or three Aisenstadt Chairholders who will talk on topics relevant to theapplications covered during the year, such as themathematics of climate modeling, multi-scalesimulations, and non-linear analysis applied tovarious domains.

Stochastic Partial Differential Equationsand Models of TurbulenceFall 2004Org.!: Weinan E (Princeton)

The workshop will focus on tractable modelswhich share some of the features believed tooccur in 3D turbulence, typically models whichinclude advection of a passive scalar, andrandomly driven Burgers. The workshop willcontinue this work and explore more realisticproblems, such as 2D turbulence and waveturbulence with the hope of firming up themathematical formulation of the problem andthe expected result, and identifying criticalobstacles where numerical computations andsimplified models might help.

WorkshopsRepresenting Unresolved Degrees ofFreedom in the Atmosphere and OceanFall 2004Org.: A.J. Majda (Courant)

A central problem in attempts to understand andpredict the evolution of atmospheric or oceanicflows is how best to represent the unresolvedscales: this is the parameterization problem indynamic meteorology or physical oceanographyor the closure problem in turbulence. The mostpertinent areas of analysis and appliedmathematics are homogenization theory,probability and non-linear stochastic PDEs.

Extracting Low-Dimensional EffectiveDynamics of BiomoleculesFall 2004Org.: C. Schuette (FU Berlin), J. Maddocks (EPF Lausanne),A. Stuart (Warwick)

Complexity in biomolecular dynamics rises fromfast rotating or oscillating modes super-imposedto the slow global motion of the molecule.Simply eliminating those fast modes would lead

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to a very bad approximation on the time scale ofinterest. This workshop will discuss progress inanalysis and algorithmic realization of differentstochastic approaches to this problem.

Front Propagation, HomogenizationTheory and Fully Nonlinear StochasticPartial Differential EquationsFall 2004Org.: T. Souganidis (Texas)

Models in phase transitions and combustion giverise to interfaces moving with prescribed normalvelocities. The theory of viscosity solutionsprovides a very good framework for therigorous analysis of such models, in particularfor the stochastic cases due to random media,turbulent advection, etc. This workshop willfocus on the rigorous analysis of such systems aswell as its applications to designingmathematical models and numerical algorithmsfor problems in reaction-diffusion, turbulentcombustion, particle systems, phase transitions,Hamiltonian dynamics, etc.

Stochastic Modeling in FinancialMathematicsSpring 2005Org.: R. Sircar (Princeton), J.P. Fouque (North CarolinaState)

The theme of this week is emerging directions infinancial mathematics, with emphasis onstochastic modeling of market uncertainties,asymptotic and numerical approximations topricing and stochastic control problems, anddata estimation issues. The goal is to bringtogether researchers in a variety of disciplines(mathematics, engineering, operations researchand economics, for example) to emphasisedifferent techniques and approaches.

Mini-invasive Procedures in Medicine andSurgerySpring 2005Org.: M. Delfour (Montréal), A. Fortin (Laval), A. Garon(École Polytechnique, Montréal), C. Peskin (Courant), A.Quarteroni (École Polytechnique, Lausanne), M. Thiriet(INRIA)

This extended concentration period will beconcerned with complex medical biomechanicalsystems, bringing together several facets of mini-

invasive procedures in medicine and surgeryand identifying issues, problems, trends, andmathematical and computing challenges.It will be structured around the followingthemes: medical imaging processing andgeometrical modeling, fluid-structure interactionin health problems, static/dynamical design andcontrol of (implantable) medical devices, finiteelement based computer aided manufacturing.

Integrative Multiscale Modeling andSimulation in Material Science, Fluids andEnvironmental ScienceSpring 2005Org.: T. Hou (Caltech)Introductory short coursePotential lecturers: R. Phillips and M. Ortiz (Caltech)This concluding workshop will focus oninterdisciplinary interaction with the goal todevelop some new tools that combinemathematical analysis, multiscale modeling andcomputational analysis in an integrative wayacross many scientific disciplines such asbiology, chemistry, environmental science, fluiddynamics, geophysics, information science, andmaterials science. There have been manyexciting recent, but problem-specific andfragmented, advances in multiscale analysis,modeling, and simulation. Hosting thisworkshop will provide a unique opportunity tomake significant advances and bridge the gap inresearch, training, and knowledge transferbetween mathematics and the applicationdisciplines.

Quantum Control: Mathematical andNumerical Challenges IISummer 2004Org.: M. Delfour (Montréal), A. Bandrauk (Sherbrooke),C.!Le Bris (Cermics, ENPC, Paris)

This workshop will build on the one-weekworkshop organized in October 2002 (see below)on the same topic and expand its scope to athree-week program.Even though it has a somewhat distinct flavourfrom the ones listed above, its definiteinterdisciplinary applied nature fits very well inthe overall philosophy of the thematic year.

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Interdisciplinary and Industrial ProgramJoint IMA-NCM2 Workshop onComputational Methods forLarge-Scale Integer ProgramsOctober 14-19, 2002, Minneapolis, MinnesotaOrg.: W. Cook (Rice University), M. Gendreau (CRT,Montréal), George Nemhauser, M. W. P. Savelsbergh(Georgia Institute of Technology)

In the past decade there have been significanttheoretical and computational advances in thefield of integer programming. As a result therehas been a greatly increased use of integerprogramming software in industry. However,the need to solve even larger and more complexproblems continues to grow. In this workshop,we will bring together experts in various areas ofinteger programming and its applications.Theoretical and methodological topics includedin the workshop are approximation algorithmsfor large-scale linear programs, stochastic integerprogramming, branch-and-cut and branch-and-price, algebraic and combinatorial methods,decomposition, constraint programming andparallel implementation. Application areasinclude supply-chain design and management,t e l e c o m m u n i c a t i o n s , m a n u f a c t u r i n g ,transportation, scheduling, and finance. Theworkshop will be of interest to mathematiciansand operations researchers working in discreteand combinatorial optimization, computationalscientists working in parallel computing, search,and constraint programming. Goals of theworkshop include building a research agendafor the next decade, defining new areas ofapplication, and stimulating cooperation amongthe different disciplines that contribute to thefield.

Joint IMA-NCM 2 Workshop onDistribution Systems: Location andVehicle RoutingDecember 2-6, 2002, MontréalOrg.: Michel Gendreau (CRT, Montréal) & Gilbert Laporte(CRT, HEC)The questions surrounding distribution systemsare of prime economic importance. The scale ofthese systems is increasing at a fast rate becauseof the growth of international commerce andtravel. The advent of e-commerce will onlyincrease their scale, as well as change theirnature; goods purchased over the Internet mustbe delivered; also, they often get returned.Related to these questions is the rich field ofnetwork design problems, which arise in

particular in transportation logistics and intelecommunications planning.The theory of location is evolving, withquestions such as competitive location or thelocation of non-punctual or structured objectsbeing studied; in routing, the advent of bettercommunication devices and increasedcomputational power make real-time dynamicrouting a possibility. These changes imply thatnew problems with different mathematicalproperties must be tackled and new algorithmicstrategies devised.This workshop will include a series of tensurveys, covering both the more traditional andthe newer subject areas, with additionalcontributions by conference participants. Areascovered include routing; location; economicaspects, pricing, e-commerce; fleet management;telecommunications; network design.Invited speakers: G. Laporte, A. Corberan, J.J. Salazar, D.Vigo, M. Salomon, S. Nickel, T. Lowe, P. Hansen, O. Berman,G. Wesolowsky, J. Thisse, P. Marcotte, B. Gavish, M.Gendreau, M. Savelsbergh, J.Y. Potvin, A. Balakrishnan, M.O. Ball, B. Jaumard, M. Labbé, C. Colbourn, T. Crainic, T.Magnanti

Quantum Control: Mathematical andNumerical ChallengesOctober 7-11, 2002Org.: A. Bandrauk (Sherbrooke), M. Delfour (Montréal),C.!Le Bris (ENPC, Paris)Sponsors: NSERC, CRM, Ministère de la recherche, France

This workshop will concentrate on advancednumerical methods and new mathematical andcontrol and optimization approaches and toolsfor the quantum control of matter at themolecular level using current advanced lasertechnology.An entire new branch of science now known asCoherent Control of Molecular Processes followingthe pioneering work of theoretical chemists suchas Paul Brumer (Toronto), Moshe Shapiro(Weizmann Institute), Stuart A. Rice (Chicago),and other international and Canadiandistinguished scientists is steadily making animpact on the experimental and technologicalworld.This new field of research is dedicated to “usingcurrent state of the art laser technology tocontrol and manipulate the quantum behaviourand motion of matter at the molecular level”.The basis of this new science is the encoding andcontrol of quantum information at the molecularlevel in order to control the time evolution of

Coming Activities


molecular processes, such as guiding the finaloutput of a reaction to a desired target. Most ofthe research in this area has been numerical andtheoretical, involving multidimensional time-dependent Schrödinger equations, TDSEs.Coupling these molecular processes to the laserfield equations, Maxwell’s equations, results incoupled parabolic (TDESs) and hyperbolic(Maxwell) partial differential equations. Thereare outstanding problems, both numerical andmathematical, which this workshop will addressby bringing together mathematicians, theoreticalchemists and physicists working in the area ofcontrol and optimization of systems subject toquantum laws.The workshop will involve 20-30 internationalexperts in laser molecule interactions,optimization, theory and control of moleculardynamics. It will emphasize participation ofgraduate students in applied mathematics,theoretical chemistry and physics.

Molecular and Electron ControlInvited speakers: O. Atabek (Orsay), A. D. Bandrauk(Sherbrooke), T. Brabec (Ottawa), P. Brumer (Toronto), R. deVivie-Riedle (MPI, Garching, Germany), R. Kosloff (HebrewUniversity), R. Kosut (Sc Solutions Inc.), H. Lefebvre-Brion(Paris-Sud), Y. Ohtsuki (Tohoku, Japan), H. Rabitz(Princeton).

Quantum Control: MathematicalProblems & TheoryInvited speakers: G. Chen (Texas A&M), M. Delfour(Montréal), S. K. Mitter (MIT), V. Ramakrishna (Texas,Dallas), J.-P. Zolésio (École des Mines), E. Zuazua(Complutense, Madrid).

Quantum ComputingInvited speakers: M.Y. Ivanov (NRC-Ottawa), S. Lacelle(Sherbrooke), R. Laflamme (Waterloo), D. Lidar (Toronto).

Numerical MethodsInvited speakers: T. Carrington (Montréal), M. Fortin (Laval),W. Hager (Gainesville), C. Le Bris (CERMICS, ENPC, Paris),Y. Maday (UPMC, Paris), A. Peirce (UBC), M. Schoenauer(INRIA, France), G. Turinici (INRIA-Rocquencourt), R. Wyatt(Texas).

Summer School in ComputationalBiologyJuly 2003Org: N. El-Mabrouk (Montréal) and D. Sankoff (Ottawa)

The school will deal with recent progress incomputational biology: cellular networks,structural molecular biology, and comparativegenomics.

Stochastic NetworksSummer 2004Org.: D. Dawson (Carleton), P. Glynn (Stanford), D.Macdonald (Carleton)

Stochastic modelling of communications andprocessing networks is playing a significant rolein enhancing our understanding of now toengineer and manage complex systems rangingfrom the Internet to high volume waferfabrication facilities. These new technologies areleading to an array of new mathematicalproblems and model formulations that havebrought new intellectual stimulation to the area,and have created new opportunities forapplications impact.

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General ProgramTopology of Moduli SpacesJuly 2003Org.: E. Markman (U. Mass.) & H. Nakajima (Kyoto)

There have been many deep results in recentyears concerning the topology of moduli space,whether of curves, vector bundles, instantons orHilbert schemes. One recurrent theme has beenthe discovery of deep algebraic structures whichgovern the topology: an early prototype is theoperad structure developed for loop spaces andapplied with success to moduli problems. Aparticular emphasis will be put on theexploration of these underlying structures. Manydeep links have been discovered, and they haveattracted much interest.

Group Theory and Numerical AnalysisMay 2003Org.: P. Winternitz (Montréal), D. Levi (Rome), A. Iserles(Cambridge), R. Quispel (La Trobe)

Topics to be covered include Lie group methodsin numerics, symmetries of numericaldifferential equations (discretization preservingsymmetries), symmetries of discrete systems,symbolic algebra calculations, discretedifferential forms, the Hopf algebra structure,infinite-dimensional algebras of vector fields andgroups of integrators, dynamical systems.

Short Program on RiemannianGeometrySummer 2004Org: V. Apostolov (UQAM), A. Dancer (Oxford), N. Hitchin(Oxford), M. Wang (McMaster)

Metrics whose curvature satisfies constraints, aswell as the relations between curvature andtopology have been of interest ever since thebeginning of differential geometry. Morerecently, such metrics have come to the fore inphysical problems related to string theory.Week 1: Special metrics. The workshop willfocus on three types: 1. Einstein metrics. Studiedsince the 1920s in the context of relativity; arecent source of interest has been the concept ofholography in physics. 2. Self-dual geometry.Due to the applicability of holomorphicmethods, an important source of examples.3. Special holonomy. Not only the Calabi-Yaumetrics, but also the G2 and Spin(7) examples areof physical interest.Week 2: Short courses. The aim is to presentmaterial, which graduates students, and others

need in order to tackle some of the mainstreamproblems in the area. Topics to be coveredinclude special holonomy, homogeneous andcohomogenity one methods, comparisontechniques.

Week 3: Curvature and topology. Therelationship between positive or negative aspectsof curvature and the global structure ofmanifolds is a well-established one, and interactswith the special properties of metrics (e.g., in theEinstein case, the boundedness of the Riccicurvature from below).

Short Program on Integrable SystemsSummer 2005Org.: J. Harnad (Concordia), A. Its (IUPUI), P. vanMoerbeke (Louvain), C. Tracy (UC Davis)

The topic of integrable systems has manyramif ica t ions throughout geometry ,mathematical physics, dynamical systems andnonlinear PDE. This program will survey someof the most important recent developments inthree related sub-areas: 1. the geometry ofintegrable systems, 2. isomonodromicdeformations, 3. random matrices and relatedproblems. These subjects have seen some of themost interesting developments in recent years,with ties to theoretical physics (duality in stringtheory), number theory, geometry (for example,in mirror symmetry), as well as Lie theory. Theorganizing committee consists of internationalleaders in the area.Each week there will be a series of lectures of anexpository nature given in the mornings, andseminar type talks in the afternoons.Week 1: The geometry of integrable systems.Topics covered include isospectral flows, loopalgebras, moduli spaces, Hitchin systems,classical and quantum R matrices, Darboux-Bäcklund transformations, separation ofvariables, applications of integrable systems togravitation, conformal theory, Yang-Mills,Seiberg-Witten theory, hydrodynamic equations,Frobenius manifolds.Week 2: Isomonodromic deformations andapplications. Topics covered include the inversemonodromy method, Riemann-Hilbert problem,nonlinear WKB approximation, asymptotics ofsolutions, Hamiltonian structure, duality,Painlevé transcendents, Garnier systems,Schlesinger transformations, birational

Coming Activities


transformations, relations to root lattices,reductions to linear systems, classical solutions.Week 3: Random matrices and related problems.Topics covered include the spectral theory ofrandom matrices, relations to orthogonalpolynomials, asymptotics, scaling limits,Fredholm determinants, Riemann-Hilbertmethods, Toeplitz determinants, Hankeldeterminants, random sequences and growthrates, number-theoretic correlates.

Short Program on Non-commutativeCombinatoricsSummer 2005Org.: F. Bergeron (UQAM), N. Bergeron (York), andC. Reutenauer (UQAM)

The understanding of certain non-commutativestructures in algebra is intimately linked tocertain combinatorial problems. For example, thecharacters of finite Coxeter groups and Iwahori-Hecke algebras tie in to Young tableaux,partitions and compositions. In a parallel vein,

there are intimate links between descent algebrasand non-commutative symmetric functions, asdefined by Gelfand, Lascoux, et al., with basesnaturally indexed by compositions. Problemsunder study include the explicit computation ofbases in these algebras underlying thecorresponding combinatorial structures.

Week 1: Short courses. The aim is to presentbasic notions in a format accessible to graduatestudents. Subjects for lectures include: descentalgebras, quasi-symmetric functions, non-commutative symmetric functions, and quasi-determinants.

Weeks 2 and 3: Workshop. There is to be anextended two-week workshop, with plenty ofopportunity for interaction. Part of the programwill include survey lectures on subjects actuallyor potentially related to the topic of theworkshop, such as hyperplane arrangements ornon-commutative geometry.


CRM Collaborative NetworkWithin its general mandate of promotingmathematical research, the CRM maintains awide network of collaborations at the local,national, and international levels.

A NATIONAL INSTITUTEThe CRM is strongly committed to its nationalmission. The CRM takes measures to ensure thatthe largest possible number of scientists acrossCanada benefits from its activities and becomeinvolved in their planning. For instance, itappoints to its Advisory Committee eminentCanadian scientists from various parts of thecountry; it is present at all important forumswhere the future directions of the Canadianmathematical sciences are discussed; it urges itsorganizers to make efforts to ensure theparticipation of the Canadian specialists in theiractivities; it organizes and supports scientificevents across the country; it collaborates withCanadian institutes, societies and associations. Aspecific budget is set aside each year for theparticipation of Canadian graduate students inits programs. The CRM is the only nationalinstitute that operates in the two officiallanguages of Canada and it is highly visible onthe international scene. In keeping with itsnational role, it coordinates its activities with theFields Institute, PIMS, the CanadianMathematical Society (CMS), the CanadianApplied and Industrial Mathematics Society(CAIMS), the Statistical Society of Canada (SSC),the Canadian Association of Physicists (CAP),and other societies as well as with otherinstitutes abroad.

THE FIELDS INSTITUTE (FI) AND THEPACIFIC INSTITUTE FOR THEMATHEMATICAL SCIENCES (PIMS)Since the early 1990’s two other researchinstitutes have joined the CRM on the Canadianscene: Toronto’s Fields Institute (FI), and thePacific Institute for Mathematical Sciences(PIMS). As well as coordinating their scientificactivities, the three institutes have workedclosely on a variety of initiatives, the mostimportant of which has been the Mathematics ofInformation Technology and Complex Systems,of which more is described elsewhere in thisreport.There are several other initiatives worthy ofmention. One of these is the National Program

Commitee, described in the next section.Another one is the CRM-FI prize awarded inrecognition of outstanding accomplishments inthe mathematical sciences in Canada. It wascreated in 1994. This year’s winner is John B.Friedlander of University of Toronto. Theadministrative responsibility in this matteralternates each year between the CRM and theFI. Scientific collaboration continues between theFI and the CRM, with a close coordination of theactivities for the theme year 2003–2004 inanalysis and partial differential equations. Onemajor common initiative this year was the set-upof a sound financial basis for the AtlanticA s s o c i a t i o n f o r M a t h e m a t i c a lSciences/Association des chercheurs en sciencesmathématiques de l’Atlantique (AARMS/ACSMA).

CANADIAN ASSOCIATIONS ANDPROFESSIONAL SOCIETIESThe CRM maintains close ties with the differentprofessional societies in the mathematicalsciences: CMS, CAIMS, SSC, and CAP. Thepresident of the CMS is an ex-officio member ofthe CRM advisory committee, and together withthe other institutes, the CRM organizes specialsessions at CMS meetings. The SSC meetingshave been funded through the national program;as well, the CRM gives out a prize each yearjointly with the SSC; similarly, together withCAP, it awards a prize each year inmathematical and theoretical physics. There is asection on this year’s prize-winners elsewhere inthis report.

INTERNATIONAL COLLABORATIONThe CRM has exchange protocols with OsakaUniversity, with Seoul's Asia-Pacific Center forTheoretical Physics, with the Institute ofMathematical Sciences at Nankai University,with the Czech Technical University of Pragueand the University of Rome.In its publications, the CRM is continuing itspartnership with the American MathematicalSociety, in particular with its two series of jointpublications, the CRM Monograph Series andthe CRM Proceedings and Lecture Notes. It alsohas two series with Springer-Verlag, in statisticsand in mathematical physics. It has publicationsexchange agreements with Fields Institute,PIMS, MSRI (Mathematical Sciences ResearchInstitute), the Institute for Mathematics and its

CRM Collaborative Network


Applications, École Normale Supérieure(France), and the Isaac Newton Institute.

OUR ACADEMIC PARTNERSAll this activity rests on a solid base ofcooperation with universities in the region, inparticular the Montréal universities, and mostparticularly the Université de Montréal, whosesupport for the CRM has been indefatigable. TheUniversité de Montréal releases each year five ofits faculty members to work at the CRM, and thesupport of these faculty members is an essentialasset for the CRM’s scientific activities. There isin addition a regular program of teaching releasewith the other Montréal universities, bringingthe equivalent of another two positions to theCRM each year. On an ad-hoc basis linked to thetheme program, the CRM has also beenarranging release of research personnel fromnearby universities such as Laval, Sherbrooke,Queen’s and Ottawa; some of thesearrangements are being put on a morepermanent footing. The partnerships of the CRMwith the other research institutes in the Montréalarea have been very profitable. More will be saidabout these in the next section.

NEURO-IMAGING INITIATIVE INQUÉBECIn recent years, CRM’s PhysNum laboratory hasdeveloped a strong collaborative network withvarious partners in neuro-imaging in the

Montréal area. This network has just beenformalized with the recent constitution of the“Regroupement Neuro-imagerie Québec” (RNQ)under the umbrella of the Institut Universitairede Gériatrie in Montréal. RNQ, with its 70researchers, has just been awarded a very largegrant ($11M) towards the purchase of equipmentin neuro-imaging. One of the strongest alliancesof CRM within that network is its associationwith the INSERM laboratory for brain-imagingat Jussieu, France (director: Habib Benali).

INSTITUT DES SCIENCESMATHÉMATIQUESOne important vehicle for collaboration with theQuébec universities is the Institut des sciencesmathématiques. This institute, whichencompasses most of Québec’s universities, isprincipally concerned with coordinatinggraduate training. The links with research areobvious, and indeed, the CRM and the ISM havea long-standing partnership, in particular inoffering postdoctoral fellowships, in organizingthe CRM-ISM colloquium, and in organizingspecial courses for the CRM’s thematicprograms.


AARMS/ACSMAOne of the great success stories this year was theconstitution of a sound financial basis of aregional association for mathematical research,the Atlantic Association for Research inMathematics/Association des chercheurs ensciences mathématiques de l'Atlantique.Founded in 1995, AARMS brings togetheruniversity researchers from the Atlantic region.This community, after several years of struggle,is experiencing a rebirth with twenty newresearchers hired in the past two years.During a visit past June, the three Canadianmathematics institutes’ directors, along withAARMS director, Professor Hermann Brunner,met with the top administrators of the threemost important Atlantic universities: Memorial,Dalhousie, and the University of NewBrunswick. A formula for co-sponsorship wasset-up with each of the six partners contributing30K$ to AARMS activities. The MITACSnetwork has also offered to the Atlanticcommunity important financial resources forindustrial mathematical research. This newversion of AARMS will be run by a board ofdirectors and an advisory committee with theparticipation of the three Canadian institutesand of the Atlantic mathematical community.

AARMS is already organizing a variety ofactivities, partially funded through the NationalProgram Committee of the institutes. Here aresome recent activities:• International Workshop on Groups, Rings, Lie

and Hopf Algebras (Memorial, May 28 to June1, 2001).

• International Workshop on Dynamical Systemsand Their Application to Biology (Cape Breton,August 2-6, 2001).

• Workshop on Modelling and ScientificComputation (University of New Brunswick,September 28-30, 2001).

• APICS Meeting 2001 (St. Francis XavierUniversity, September 19-21, 2001).

This year’s scientific program was also fundedby NPC and included a summer school onalgebra, fractal geometry, graph theory anddifferential equations, that took place July 22 toAugust 6, 2002, as well as two workshops:• Combinatorial Methods in Polynomial Identity

Theory (Memorial, August 2002).• 31st Annual Canadian Operator Theory and

Operator Algebras Conference (University ofNew Brunswick, May 20-24, 2003).


Industrial CollaborationsThe main vehicles for the CRM’s efforts in thisarea are the research networks to which itbelongs. There are two of these, one the Networkfor Computing and Mathematical Modelling(ncm2), involving eight research centres in theMontréal area in a multidisciplinary consortium,and MITACS, a national network focussing onthe mathematics of information technology andcomplex systems.

NETWORK FOR COMPUTING ANDMATHEMATICAL MODELLING (NCM2)The CRM serves as the organizational centre forthe Network for Computing and MathematicalModelling, ncm2 (in French: Réseau de calcul etde modélisation mathématique, rcm2) , acollaboration which allows the network torespond to the needs of industry in a largenumber of fields related to a common area ofcomputing and mathematical modelling, mostlyaround five major themes: (1) risk management,(2) information processing, imaging and parallelc o m p u t i n g , ( 3 ) t r a n s p o r t a n dtelecommunications, (4) health and (5) electroniccommerce.The five centres that established the networkwere the CRM, the Centre de recherche en calculappliqué (CERCA), the Centre interuniversitairede recherche en analyse des organisations(CIRANO), the Centre de recherche sur lestransports (CRT), and the Groupe d’études et derecherche en analyse des décisions (GERAD).Since then, three new members joined thenetwork: the Cooperative Centre for Research inMesometeorology (CCRM), the Centre deRecherche Informatique de Montréal (CRIM)and the Institut National de la RechercheScientifique – Télécommunications.NSERC funding for ncm2 with a yearly grant ofabout $650,000 came to an end this year. Thenew projects funded in the last phase of theNSERC grant included:• Analyse des écarts de rendements à échéance

entre les obligations corporatives etgouvernementalesG. Gauthier, GERAD

• Receptor-ligand molecular associationsFrançois Major, CERCA and YoshuaBengio, CRM

• Integration of real-time weather data andGeographic Information System (GIS) for use intransportation.Charles Lin, CERCA

• Modélisation et test d’Ipv6Rachida Dssouli, CRM

• The Real Options Approach to Risk ManagementPierre Lasserre and Andrey Pavlov,CIRANO

• Ingénierie des réseaux de distributionmultifournisseurAndré Langevin and Diane Riopel, GERAD

• Planification et confection d’horaires en milieuhospitalierBrigitte Jaumard, CRT

• Gestion des risques financiers: critèresprudentiels, décentralisation et contrôle deperformanceRené Garcia, CIRANO

• Localisation des sources d’activité en magnéto-encéphalographie par maximum d’entropie enmoyenne et modèles graphiques hiérarchiquesBernard Goulard, CRM

Overall, the projects have involved theparticipation of 70 researchers in the networkcentres, and 63 postdoctoral fellows andgraduate students. The total value of thecontributions of our partners in 2001-2002 was$602,000 in cash and $500,000 in kind. Theindustrial partners involved at some point withncm2’s research projects are: ADOPTTechnologies Inc., Air Canada, ANIQ R&D Inc.,AstraZeneca Banque nationale du Canada, BellMobilité, Biochem-Pharma, Boehringer-Ingelheim, CardiaNove, Centre universitaire desanté McGill (MUHC), CHUM Informatique(Centre hospitalier de l’Université de Montréal),CLSC Côte-des-Neiges, Royal Victoria Hospital,Santa Cabrini Hospital, Hôpital Sainte-Justine,Hydro-Québec, IFM2, Merck Frosst, Société del’assurance automobile du Québec, Sociétécanadienne des postes.In December 2001, ncm2 was the host of JoeKeller (Stanford) as part of the lecture seriesGrandes Conférences. He gave a talk on theMathematics of Visual Perception: Color vision.As part of a series of breakfast meetings, thedirectors of the network were able to meet PavelHamet (research director for the “Centre deRecherche du Centre hospitalier de l’Université

Industrial Collaborations


de Montréal”), Réal Decoste (director ofOuranos), and Marc Garneau (president of theCanadian Space Agency).A special day on health care issues titledComment les techniques d'optimisation peuventameliorer la gestion dans le domaine de la santé wasorganized by Brigitte Jaumard (GERAD) andBernard Gendron (CRT), with about fortyparticipants.Bernard Larrouturou, president-director ofINRIA (France), visited Montréal in January. Histalk focussed on INRIA’s research program incomputer science and applied mathematics, witha particular emphasis on life sciences.Two special days were organized in April byFahima Nekka and Jean-Marc Lina from CRMon the topic of Fractals, wavelets and medicalimaging with Jacques Lévy-Vehel (INRIA) as akeynote speaker for a workshop on Multifractalanalysis of signals and images, followed by aconference on Multifractal image denoising.There was also a workshop-conferenceorganized in May by Pierre Lasserre and AudreyPavlov (CIRANO, IFM2) on real options.

LABORATOIRES UNIVERSITAIRESBELLThe CRM is an active participant in the ncm2’sLaboratoires universitaires Bell, part of a jointproject between the ncm2 and Bell. Thelaboratories aim at creating innovations in thefield of multimedia research and applications(mainly interactive applications aimed at thegeneral public, electronic commerce applicationsand new generations of evolved networks) aswell as at promoting the training of a highlyqualified, international calibre workforce inthese areas.The guiding principles of the Bell UniversityLaboratories are: a deep integration with theuniversity environment; a balance betweenexploratory research, applied research andapplications development; a multidisciplinaryapproach.These objectives and guiding principles aremade possible thanks to a $12M investmentwhich is used to finance research projects, toendow chairs and to finance a researchinfrastructure. The laboratory has two locations,the main one being in downtown Montréal, nextto CIRANO. As well as offices, it contains astate-of-the-art simulation laboratory for

electronic commerce and experimentaleconomics. The other component is located atthe Université de Montréal, and is devoted tomultimedia research.

LABORATOIRE UNIVERSITAIRE SURLE TEMPS EXTRÊME (LUTE)The summer of 2001 saw the birth of a new ncm2laboratory, the Laboratoire Universitaire sur leTemps Extrême (LUTE). The laboratory involvesa contribution of $300,000 per year fromEnvironment Canada, a significant contribution($1M) in computer time, as well as the presencein the university environment of a good numberof Environment Canada’s researchers. Thelaboratory will involve not only meteorologicalresearch but also an extensive study into impactsas well as mitigating measures. LUTE’s officiallaunch took place on December 6, 2001, withabove 130 participants in attendance at McGillUniversity. Four speakers presented talks onextreme weather and its impact on society:Isztar Zawadzki, Director, Marshall RadarObservatory, McGill University and LeadScientist Canadian Weather Research ProgramNowcasting and Climatology of Extreme Weather.Gordon McBean, Chair, Policy, Institute forCatastrophic Loss Reduction Chair, CanadianFoundation for Climate and AtmosphericSciences (CFCAS)Dangerous Weather – What Canadians Need toKnow.Georges Beauchemin, Ministère de la SécuritéPublique, Gouvernement du Québec, Présidentdu conseil, Projet OURANOSAffronter le temps extrême: faits saillants de lanouvelle loi sur la sécurité civile et ses défis.Richard Anthes , President, UniversityCorporation for Atmospheric Research (UCAR),ColoradoGlobal Weather Services in 2025: An Update.

INSTITUTE FOR MATHEMATICS ANDITS APPLICATIONSThe ncm2 has arranged for an exchange programwith the Institute for Mathematics and itsApplications in Minnesota. This institute is theUS’s major research institute in AppliedMathematics. As part of the IMA’s 2002program, the ncm2 will be hosting a workshopon distribution networks in the fall of 2002. As

Industrial Collaborations


well, the IMA will host a certain number of ncm2postdoctoral fellows during the year.MITACSThis network of centres of excellence onMathematics of Information Technology AndComplex Systems (MITACS) is one of 22 suchnetworks set up by the federal government.MITACS was put together by the three Canadianmathematical institutes (CRM, Fields, PIMS) in1998, and research began in the spring of 1999.The MITACS network covers the whole country,with the participation of 300 researchers, 400students and postdoctoral fellows, and morethan 75 companies.The 31 research projects are spread amonguniversities across Canada. Following the reviewof the report presented by MITACS to the NCEin March 2001, a new grant of $10.8M wasannounced by Brian Tobin, who was then theminister for industry, for each of the year2003-2004 and 2004-2005.The third annual meeting took place at theUniversity of British Columbia in Vancouver, inMay 2002. This was a large-scale event, withover 350 participants from Canada and the US,including many of the network’s researchers, alarge number of students (whose travel expenseswere partly covered by MITACS) and numerousindustrial partners.These meetings play a key role to establish newcollaborations and to maintain a strong cohesionbetween the researchers working on differentsub-domains in applied mathematics: bio-medical research, industrial and businessapplications, information technology,manufacturing, and financial mathematics. EachMITACS project belongs to one of those themes;in addition to the general annual meeting, eachtheme leader organizes specialized annualmeetings where technical details can bediscussed in more details.During the annual meeting, each research groupreported on their progress. There were alsomany interesting presentations by industryresearchers describing their more pressingmathematical needs and describing the links thathave already been established between MITACSresearchers and industrial partners.The poster session was the opportunity for thestudents affiliated with MITACS to present theirwork relevant to MITACS themes. Awards weregiven to the best among the 70 posters, includingthree first prizes and five second prizes. Among

the second prize winners, were C. Voisin, fromÉcole Polytechnique de Montréal, supervised byB.!Jaumard from Université de Montréal, andA.!Boukhtouta, supervised by B.!Lamond, fromUniversité Laval.Several important administrative changes tookplace this past year. Since March 2002, MITACSis a non-profit corporation. Also, on September1, 2002, John Schwenk was appointed as ChiefOperating Officer and Network BusinessManager. A position for an associate scientificdirector was also created.

MITACS Activity at CRM:Spring School on Optimization.May 14 – 18, 2001

This joint CRM-CRT-MITACS activity wasstarted in 2001 by Pierre Hansen of the École desHautes Études Commerciales and PatriceMarcotte from the Université de Montréal. Asecond edition took place in 2002 with a springschool on logistic and distributic, which tookplace May 8-10 at HEC, with Gilbert Laporte asits director. The school was an opportunity forstudents to enlarge their horizons in the area ofdeterministic optimization and mathematicalprogramming, with an emphasis on industrialapplications.Other MITACS activities involving the CRMincluded:

Séminaires CRM-MITACS sur l’apprentissagestatistiqueSeptember 2001 - February 2002, CRM4eInternational Conference on InformationFusionAugust 7-10, 2001, MontréalTheme Meeting of Information TechnologyNovember 10-12, 2001, CRMColloque CRDE-MITACS sur les Méthodes derééchantillonnage en économétrieOctober 13-14, 2001, Université de MontréalJournée Finance CIRANO-MITACS!: NewStatistical Methods for Old Financial ProblemsOctober 19, 2001, CIRANO

Emerging Market Risk ManagementNovember 9, 2001, CIRANO

Financial DerivativesDecember 7, 2001Conférence CIRANO-MITACS sur lesMéthodes de Monte Carlo et numériques enfinanceMarch 15, 2002, CIRANO


Awards, Distinctions and LandmarksResearchers play a key role in a research centre such as ours and we are particularly proud of the groupthat we have assembled. Their scientific and academic influence is outstanding. Here is a short list ofthe main prizes and awards that they have received in the last year.

Francis Clarke was elected senior member ofthe Institut Universitaire de France (September2001).

Henri Darmon of McGill University receivedthe prestigious Steacie Memorial fellowshipfrom NSERC.

Andrew J. Granville was awarded the CanadaResearch Chair in number theory.

Michel Grundland of the Université du Québecà Trois-Rivières was awarded the Alan RichardsFellowship from Durham University.

Dmitry Jakobson from McGill Universityreceived a Sloan Fellowship (May 2001).

Niky Kamran was elected member of the RoyalSociety of Canada.

François Lalonde of Université de Montréal,was awarded the Canada Research Chair indifferential geometry and topology.

John McKay from Concordia University waselected member of the Royal Society of Canadain 2000. He also received the faculty excellenceaward in 2001.

Alexei Miasnikov from McGill University wasawarded the Canada Research Chair incombinatorial algebra.

Christophe Reutenauer from UQAM has beenappointed as the Canada Research Chair incombinatorial algebra and mathematicalcomputing.

Christiane Rousseau from the Université deMontréal started her mandate as president of theCanadian Mathematical Society in June 2002, fora term of two years.

David Sankoff from the University of Ottawahas been named the Canada Research Chair inMathematical Genomics.

John Toth has been appointed as a Dawsonscholar at McGill (May 2001).

Pavel Winternitz from the Université deMontréal received the 2002 ACP-CRM prize inmathematical physics. The Czech newspaperLidove Noviny also named him as one of the tenmost cited Czech scientists since 1980(September 21, 2002).


Research LaboratoriesThe CRM now covers several research laboratories at the heart of the Québec mathematicalcommunity. These research centers act as focal points for local scientific activity and participateactively in the scientific direction of the CRM.

CICMA

This centre comprises researchers working innumber theory, group theory and algebraicgeometry. Contemporary number theory followstwo major courses. On the one hand, there is thetheory of special values of L-functions attachedto arithmetic objects, originating in the work ofGauss and Dirichlet and leading to the modernconjectures of Deligne, Beilinson and Bloch-Kato.On the other hand, the Langlands programpostulates a close link between arithmetic L-functions and automorphic representations. Anarea where these two currents intersect is thestudy of elliptic curves. The center is particularlywell represented in this regard with Darmon,

Iovita, Kisilevsky and Ramakrishna. On thegroup theory side, Kharlampovich andMiasnikov are world-renowned specialists ongroup varieties and McKay is one of theoriginators of the moonshine program.

Among the problems to be studied by the groupin the coming years include the construction ofrational points on elliptic curves both fromalgorithmic and theoretical viewpoints; Zetafunctions of varieties over finite fields on thealgorithmic approach; canonical lifting of ellipticcurves and Abelian varieties; cryptography andAbelian varieties.

Members of the Laboratory

Director:H. Darmon (McGill)Algebraic number theory,geometry, arithmetic, L-functions, diophantineequations, elliptic curves.

Director:H. Kisilevsky (Concordia)L-functions, Iwasawa theory,elliptic curves, class fieldtheory.

C. David (Concordia)Elliptic curves, Drinfeldmodules.

E. Goren (McGill)Arithmetic geometry, modulispaces of Abelian varieties,Hilbert modular forms, p-adic modular forms.

A. Granville (UdeM)Algebraic number theory,arithmetic geometry,combinatorics.

A. Iovita (Concordia)Number theory.

O. Kharlampovich (McGill)Combinatorial theory ofgroups and Lie algebras.

C. Lévesque (Laval)Algebraic number theory,units, class number,cyclotomic fields.

M. Makkai (McGill)Mathematical logic.

J. McKay (Concordia)Computational group theory,sporadic groups, computationof Galois groups.

A. Miasnikov (McGill)Group theory.

R. Ramakrishna (McGill)Galois representations,modular forms, ellipticcurves.

P. Russell (McGill)Algebraic geometry.

F. Thaine (Concordia)Cyclotomic fields, cyclotomy,rational points, rationalpoints on curves.

Research Laboratories


Highlights of the activities of the Laboratory and of its members in 2001-2002.Among the numerous activities in which members of the centre were involved, either as participants or asorganizers, is the concentration period on the Langlands program on function fields, organized by H.Darmon and J. Hurtubise in April-May 2002. As part of the program, there were a graduate course, athree-week workshop including a series of lectures by R. Langlands himself and a special day in hishonour.

This period was immediately followed by the 2002 Conference of the Canadian Number TheoryAssociation. E. Goren was one of the organizers.

Several ISM lectures were offered to Montréal graduate students in the context of this thematic year, as forexample, an introduction to automorphic forms (H. Darmon) and an introduction to algebraic geometry(E. Goren).

In the course of the year, the Québec-Vermont Number Theory Seminar(http://www.crm.umontreal.ca/fr/niveau2/index_gro.html) took place alternately in Montréal andBurlington, totalling about forty talks.



CIRGET(Le Centre inter-universitaire de géométrie différentielle et de topologie)

Geometry and topologya r e f u n d a m e n t a ld i s c i p l i n e s o fmathematics. Theirrichness and vitalitythroughout humanhistory is reflected bytheir deep link to ourexperience of theuniverse. They are at acrucial crossing point ofmodern mathematics

and in effect several domains of mathematicshave recently shown a strong trend towards ageometrization of ideas and methods: two cases

in point are mathematical physics and numbertheory. During the last fifteen years, a group ofresearchers of international calibre in geometryand number theory has been hired by Québecuniversities. The research centre based at UQAMnow comprises fourteen professors-researchersand one research associate.

The main themes to be pursued in the comingyears include Dehn surgery and geometrizationà la Thurston; quantization of Hitchin systemsand geometric Langlands program; classificationof special Kähler metrics; the study of symplecticinvariants, especially in dimension 4;Hamiltonian dynamical systems.

Members of the LaboratoryDirector!:S. Boyer (UQAM)Knot theory, geometry of 3-dimensional manifolds, Dehnsurgery, character manifolds.

S. T. Ali (Concordia)Mathematical physics,quantization, coherent states.

V. Apostolov (UQAM)Riemannian geometry,general relativity, complexand symplectic 4-dimensionalmanifolds, (almost)Hermitian, Kähler andEinstein metrics.

A. Broer (UdeM)Algebraic transformationgroups and invariant theory.

O. Collin (UQAM)Gauge theory and topology of3-dimensional manifolds.

J. Harnad (Concordia)Integrable systems,symplectic geometry, randommatrices.

J. Hurtubise (McGill)Integrable systems, gaugetheory, moduli spaces.

A. Joyal (UQAM)Homotopy, categories,algebraic topology.

N. Kamran, (McGill)Differential geometry,differential systems,geometric integrability,conservation laws, spectra ofoperators, Lie algebras.

F. Lalonde (UdeM)Symplectic geometry andtopology, Hamiltonianmechanics

I. Polterovich (UdeM)Heat equation, Riemannianmanifolds, asymptoticdevelopments, combinatorialidentities.

K. P. Russell (McGill)Affine algebraic geometry,group actions.

J. Toth (McGill)Spectral theory, semi-classicalanalysis, micro-local analysis,Hamiltonian mechanics.

D. Wise (McGill)Residually finite groups, lowdimensional topology, 3-dimensional manifolds.



Highlights of the activities of the laboratory and of its members in 2001-2002.

The CRM just ended a thematic year in Groups and Geometry, which considerably pushed forwardthe CIRGET in several important domains: during the 2001 summer, a concentration period on 3-dimensional manifolds and geometric group theory attracted more than a hundred participantsduring three weeks, of whom one half were graduate students, to the most important conference inthe subject in several years. During the fall, a conference on infinite dimensional Lie groups shed somelight on a difficult and diverse subject. The second semester was devoted to the study of the linksbetween group theory and algebraic geometry, with an extended period on Langlands theory forfunction fields, which focussed attention on a leading subject to which access is quite difficult.

Aside from these events, thirty talks (twenty of which by speakers from outside Montréal) were givenin the context of the weekly CIRGET seminar (http://www.math.uqam.ca/cirget/seminar01-02.html)organized by Olivier Collin. Also, two CIRGET workshops took place at UQAM in April 2002:Casson’s Invariant: 17 years on (April 13-14, organized by Olivier Collin) and The hyperbolic volumeconjecture (April 20-21, organized by Steven Boyer and Adam Sikora).

In conclusion, we wish to congratulate Niky Kamran for his election to the Royal Society of Canada.



LACIM(Laboratoire de combinatoire et d’informatique mathématique)

LACIM is a researchl a b o r a t o r y o f t h e

Université du Québec àMontréal, which wasofficially establishedin 1989. Its researchactivities concentrate

on enumerative algebra,algebraic combinatorics,

computer science and theirapplications to other scientific domains, suchas the analysis of algorithms, statisticalmechanics and computational biology.

Research areasDiscrete mathematics has lately become animportant field of practical research, witness thenew heading in Mathematical Reviews 05E ofalgebraic combinatorics with subheadingsindicating interactions with the newest areas ofmathematics, such as group representations,quantum groups, discrete algebraic geometry,special functions. Combinatorics benefits fromthe revival of the concrete computational aspectin mathematics after decades of abstractstructuralism. Algebra is enriched in afundamental manner by combinatorics, as thecommutative algebra book by Eisenbuddemonstrates, highlighting constructivegeometric methods. Moreover, combinatoricsapplies to computer sciences (theory ofautomata, analysis of algorithms), to statisticalphysics (computation of configuration spacesand of critical exponents, discrete models), bio-informatics (combinatorics of words applied togenomic sequences). The youth, dynamism,utility and applicability of this research domainare highlighted in the modern world, wherediscrete structures (trees, graphs, permutations)are more and more present in communications,

networks and research engines, of which the useis growing exponentially in this 21st century.

The researchersThe laboratory is comprised of twelve principalresearchers, all professors at UQAM, fourassociate members in North America andthirteen in Europe. Notably, ChristopheReutenauer (regular member) and NantelBergeron (associate member, York University)hold Canadian research chairs. A team of fourLACIM members is supported by a grant fromFCAR. André Joyal, past member of LACIM andcurrent member of CIRGET, is involved inseveral activities at LACIM, both formal andinformal. LACIM is the largest research group incombinatorics in Canada and is knownworldwide in its field. The UQAM team hascontributed to the emergence and establishmentof combinatorics as a mathematical discipline.For example, several LACIM members haveplayed and continue to play an important role inthe organization of the international colloquiumSéries formelles et combinatoire algébrique, which isbilingual and is held yearly, alternately inEurope and North America. Its success iswithout question.

Research activities at LACIMA.!Joyal enriched the counting theory of Polyaby including the theories of grouprepresentations and symmetric functions. Underthe name of theory of species, this theorymarked the emergence of the UQAMcombinatorics group about twenty years ago.From that time research has diversified greatly atLACIM: a) classical enumerative combinatoricsand its applications (counting of discreteconfigurations and planar maps); b) algebraiccombinatorics; c) theoretical computer science; d)bio-informatics.




Director!:C. Reutenauer (UQAM)Algebraic combinatorics, non-commutative algebra,automata, codes, freealgebras.

R. Bédard (UQAM),Representations of finitegroups, Lie theory.

A. Bergeron (UQAM)Bio-informatics.

F. Bergeron (UQAM)Combinatorics, algebras,representations of finitegroups.

S. Brlek (UQAM)Combinatorics of words,algorithmics.

C. Chauve (UQAM)Enumerative combinatorics,trees, bio-informatics.

G. Labelle (UQAM)Enumerative combinatorics,analysis.

J. Labelle (UQAM)Combinatorics, topology.

L. Laforest (UQAM)Data structures,combinatorics, asymptoticalanalysis, quaternary trees.

P. Leroux (UQAM)Combinatorics.

V. Makarenkov (UQAM)Computational biology,mathematical classification.

O. Marcotte (UQAM)Operational research,combinatorial optimization,graph theory.

T. Walsh UQAM)Algorithmics, enumerativecombinatorics, graphs.

Highlights of the activities of laboratory and of its members in 2001-2002.

Since January 2001, C. Reutenauer has held a senior Canada Research Chair.The 57e Colloque des Sciences mathématiques du Québec was organized in April 2002 by R. Bédard, P.Bouchard and L. Bélair (the latter two being collaborating members at LACIM).

R. Bédard also co-organized the CRM winter school on Coxeter groups in January 2002.

A special AMS session on combinatorial Hopf algebras was organized in May 2002, by F. Bergeron, C.Reutenauer and M. Aguiar (the latter being a collaborating member at LACIM).

A session parallel to the 2002 SMC summer meeting was organized by C. Chauve, P. Leroux and SylvieCorteel (the latter being a collaborating member at LACIM). C. Reutenauer was one of the plenaryspeakers at this meeting.

F. Bergeron was an invited speaker at the SIAM colloquium in San Diego in August 2002.



Mathematical Analysis LaboratoryAt the same time classical and central to modernmathematics, analysis involves studyingcontinuous systems from dynamical systems tosolutions of partial differential equations andspectra of operators. The Québec group ofanalysts has lately recruited an impressivenumber of researchers. The creation of alaboratory allowing them to pursue theirdevelopment will be welcome. The groupmembers belong to six Québec universities witha particular concentration at Laval and McGill.Many of the main currents of modern analysisare studied by the group. Among the researchsubjects of the group, one finds conjectures on

random waves and quantum chaos, Hamiltonianformalism in statistical mechanics far fromequilibrium, asymptotic properties of wavefunctions, Hilbert 16th problem and Hardyconjecture.Besides two active seminars, the program of thelaboratory includes a plan of intense activities, athematic year in analysis, focussing on spectralanalysis and geometric analysis, including ashort program on contact geometry and contactanalysis, a short program on the analysis ofsingular spaces, two workshops in analysis ofgeneral relativity and five workshops ondifferent aspects of spectral analysis.


Director!:D. Jakobson (McGill)Harmonic analysis, spectralgeometry.

L. Baribeau (Laval)Complex and functionalanalysis, Banach algebras,holomorphic iterations,discrete groups.

F. Clarke (Univ. Lyon I)Nonlinear and dynamicanalysis, control theory,calculus of variations.

G. Dafni (Concordia)Harmonic analysis, partialderivative equations, complexvariables.

D. Dawson (McGill)Probability, stochasticprocesses.

S. Drury (McGill)Harmonic analysis, matrixtheory.

R. Duncan (UdeM)Ergodic theory, probability.

R. Fournier (Dawson)Complex analysis, univalentfunctions, conformaltransformations.

M. Frigon (UdeM)Nonlinear analysis,differential equations, fixedpoint theory, critical point,theory.

P. Gauthier (UdeM)Complex analysis,holomorphy, harmonicity,analytic approximation.

P. Gora (Concordia)Ergodic theory, dynamicsystems, fractal geometry.

F. Gourdeau (Laval)Banach algebras,cohomology, amenability,functional analysis.

K.N. GowriSankaran(McGill)Potential theory.

V. Jaksic (McGill)Mathematical physics.

T. Kaczynski (Sherbrooke)Topological methods, Conleyindex, applications todynamical systems.

I. Klemes (McGill)Harmonic analysis,trigonometric series.

P. Koosis (McGill)Harmonic analysis.

J. Mashreghi (Laval)Complex analysis, harmonicanalysis, Hardy spaces.

I. Polterovich (UdeM)Partial derivative equations,spectral theory, differentialgeometry.

T. Ransford (Laval)Complex analysis, functionalanalysis, spectral theory,potential theory, Jensenmeasures.

D. Rochon (UQTR)Numbers, analysis, dynamiccomplexes.



C. Rousseau (UdeM)Dynamical systems,bifurcations, qualitativetheory, polynomial systems,analytic invariants, integrablesystems.

D. Schlomiuk (UdeM)Global analysis, dynamicalsystems, singularities,bifurcations, algebraic curves,primary integral.

R. Stern (Concordia)


The members of the laboratory worked as participants and organizers at numerous conferences. Forexample:• NATO Advances Study Institute, CRM, July 2002: Normal forms, bifurcations and finiteness problems for

differential equations, organized by C. Rousseau.• Session in Analysis, CMS meeting, Laval, June 2002, organized by T. Ransford.• AMS meeting, UdeM, May 2002:ß Session in Potential Theory, organized by P. Gauthier, K.N. GowriSankaran et al.ß Session in Functions Spaces in Harmonic Analysis and Partial Derivative Equations, organized by

G.!Dafni, J. Xiao.ß Session in Spectral Geometry, organized by D. Jakobson, Y. Petridis.

• Workshop on Spectral Statistics and High Energy Eigenstates at CRM, Aug. 25-Sept. 2 2001, organized byJ. Toth, D. Jakobson, Y. Petridis.

• 55th Quebec Mathematics Colloquium at Bishop’s University, April 28, 2001• Special day on Dynamic Systems, organized yearly by C. Rousseau and D. Schlomiuk.As a complement of these activities, regular seminars are co-organized at McGill by G. Dafni, D. Jakobson,V. Jaksic, at Université de Montréal by P. Gauthier and at Laval by T. Ransford. Moreover, D. Schlomiukis co-organizer of the CRM-ISM Colloquium.Concerning prizes, we note the Sloan Fellowship held by D. Jakobson and the Dawson Fellowship held byJ. Toth both obtained in May 2001.



Applied Mathematics LaboratoryThe new Montréal laboratory in appliedmathematics and scientific computation reflectsan expanding domain as many of its membershave been recruited lately. It is characterized bythe intensity of its multidisciplinarycollaborations, since all its researchers areworking on the development of mathematicalmodels and numerical methods for multipleapplications to science and engineering.

Another notable characteristic of this group isthe intensive use of cutting edge computerscience means for advanced numericalcomputations. The augmentation of the numberof researchers in this domain in Montréal reflectsindeed the spectacular expansion of thecomputation power in Montréal.


Director:A. Bourlioux (UdeM)Modeling, numericalsimulation in turbulentcombustion.

Director!:M. Gander (McGill)Domain decomposition, pre-conditioning.

P. Arminjon (UdeM)Numerical methods in fluidmechanics.

A. Bandrauk (Sherbrooke)Quantum chemistry.

P. Bartello (McGill)Turbulence, CFD.

M. Delfour (UdeM)Control, optimization, design,shells, calculus, bio-mechanics.

A. Humphreys (McGill)Numerical analysis,differential equations.

S. Maslowe (McGill)Asymptotic methods, fluidmechanics.

N. Nigam (McGill)Applied analysis, numericalmethods inelectromagnetism.

G. Schmidt (McGill)Control of partial differentialequations.

J.P. Zolésio (INRIA)Control, optimization.


The members of the laboratory maintained an extensive complete calendar of seminars in Montréal:applied mathematics seminar at Université de Montréal, organized by M. Delfour; computational scienceand engineering seminar at McGill University (see http://www.math.mcgill.ca/~chang/CSE), organizedby Martin Gander, twelve speakers; applied mathematics seminar at McGill (seehttp://www.math.mcgill//nigam/AMCSEseminar.htm), organized by Nilima Nigam, 18 speakers.

A. Bourlioux and M. Gander were scientific directors of the Séminaire de Mathématiques Supérieures in July2001, on the theme Modern methods in scientific computation and applications.

Martin Gander and Nilima Nigam were members of the McGill team that won the first prize at thecompetition in numerical analysis organized by N. Trefethen, Decimal Decathlon, and publicized by SIAM.

Michel Delfour and André Bandrauk in collaboration with C. LeBris from CERMICS, Paris, co-organized agroup of activities in quantum control, which was the theme of a workshop in fall 2002. Furthermore, M.Delfour also collaborates with André Garon and his group of engineers at École Polytechnique of Montréaland with Marc Thiriet and his team at INRIA on a major initiative in mathematical modeling andnumerical simulation in medicine.

André Bandrauk was given a Canada Research Chair in computational and photonic chemistry.



Mathematical Physics LaboratoryMathematical physics represents one of thetraditional strengths of the CRM ever since thearrival of J. Patera and P. Winternitz at theCentre at the beginning of the 1970’s. The grouphas considerably grown in the last years throughthe hiring of new researchers with a total oftwenty academic researchers affiliated to sevenQuébec universities.Mathematical and theoretical physics hasbroadened its spectrum of activities in the lasttwenty years and has become an importantsource of conjectures in pure mathematics.

The group carries out research in severalscientific domains among the most active ones inmathematical physics, for example: nonlinearcoherent fluids systems, plasmas and optics,integrable systems and classical and quantumsupranaturalisms, analysis of partial differentialequations via symmetry, spectral theory ofSchrödinger operators and random matrices,quasi-crystals, percolation, theory of conformalfields, statistical quantum mechanics andsymmetry of finite different equations.


Director :J. Harnad (Concordia)Geometric methods,integrable systems,isospectral flows, loopalgebras.

S. T. Ali (Concordia)Coherent states, wavelets.

M. Bertola (Concordia)Axiomatic quantum fieldtheory, invariant theory ofdiscrete groups.

C. Cummins (Concordia)Group theory, modularfunctions, Moonshine.

S. Durand (É.-Montpetit)

M. Grundland (UQTR)Symmetry of differentialequations in physics.

R. Hall (Concordia)Quantum mechanics,geometry, spectral inversion,many-body problem.

J. Hurtubise (UdeM)Integrable systems, gaugetheory, moduli spaces.

V. Hussin (UdeM)Quantum mechanics,differential equations,groups, Lie algebras, groupdeformations,supersymmetries.

D. Jakobson (McGill)Quantum chaos, spectralgeometry, harmonic analysis.

V. Jaksic (McGill)Quantum mechanics,statistics, randomSchrödinger operators.

N. Kamran (McGill)Differential geometry, partialdifferential equations.

D. Korotkin (Concordia)Integrable systems, classicaland quantum gravity.

F. Lalonde (UdeM)Symplectic topology andgeometry, global analysis onmanifolds, infinitedimensional transformationgroups.

R. Langlands (Princeton)Automorphic forms, criticalphenomena, Ising models,percolation, phase transition,finite models in statisticalphysics.

J. LeTourneux (UdeM)Symmetry properties ofsystems, special functions.

P. Mathieu (Laval)Conformal field theory,classical and quantumintegrable systems, affine Liealgebras.

J. Patera (UdeM)Applications of group theory,quasi-crystals, Lie algebras.

Y. Saint-Aubin (UdeM)Conformal field theory,statistical mechanics, 2-dimensional phase transitionmodel.

J. Toth (McGill)Spectral theory, semi-classicalanalysis, micro-local analysis,Hamiltonian mechanics.

L. Vinet (McGill)Symmetric properties ofsystems, special functions.

P. Winternitz (UdeM)Methods of group theory inphysics, nonlinearphenomena, symmetries ofdifference equations,superintegrability.

C. Van Vliet (Miami)




S.T. Ali was part of the organizing committee of the 21st workshop on Geometrical Methods in Physics, inBialowieza, Poland, July 2002. John Harnad was a plenary speaker there for a series of three talks on thetheme of random matrices, isomonodromic deformations, duality, and so on. S.T Ali was also co-organizer of the 4th workshop on Wavelets, Quantization and Differential Equations, which found place in LaHavana, Cuba, in February 2002.

C. Cummins organized the Moonshine session of the SMC winter meeting 2001.

John Harnad co-organized several CRM workshops, beginning in May 2000 with a workshop onisomonodromic deformations and their applications to physics, the proceedings of which will bepublished by the CRM. Then in September 2002, he was member of the organizing committee (togetherwith P. Winternitz, C.!S. Lam and J. Patera, the former being in charge of it) of the workshop onsymmetries in physics to the memory of R.!T. Sharp. Later in the month, another workshop onsuperintegrability in classical and quantum systems was organized in collaboration with P. Winternitz, P.Tempesta, W. Miller, G. Pogosyan and M. Rodriguez.

Niky Kamran gave a plenary talk at the 2001 AMS meeting. Together with B. Khesin, he organized aworkshop at the CRM on the geometry of Lie groups in infinite dimension in October 2001.

P. Mathieu was invited to participate to an IPAM (UCLA) workshop on conformal fields, where hepresented four talks and lectures.

Pavel Winternitz received the 2001-2002 ACP-CRM prize in mathematical and theoretical physics. He wasalso acknowledged by the Czech journal Lidove Noviny of September 21, 2002, as belonging to the veryprestigious club of the ten most quoted Czech scientists since 1980. He was invited many times to giveplenary talks, as for example at the SYMPHYS conference in Yerevan, Armenia, July 2001; to the NEEDSconference, Cadiz, June 2002, and to the European Conference of the Newton Institute, Cambridge,August 2001 (two talks in the subject What is Integrability?).

John Harnad and Niky Kamran are very involved in NSERC committees. Harnad is a member of thephysics committee and responsible for the membership committee. Kamran heads the B committee in pureand applied mathematics.



PhysNum

During the last year, the PhysNum groupdeveloped its research activities in brain imagingby pursuing the study of the inverse problem inMEG (magneto-encephalography) andbeginning the study of problems of the sametype in optical imaging. This work involves themain researchers of the group (B. Goulard, J.M.

Lina and F. Lesage) as well as graduate students(E. Lapalme, F. Levac, MD).Another direction of research concerns theanalysis of wavelets applied to the study of one-dimensional signals (turbulence, EEG) andmammography imaging. In this direction, onestudies random process attached to nodes of atree or a graph whose depth is differentresolution, from the coarser to the finer scale.This work is lead by the researchers of PhysNum(J.M. Lina, B. Goulard) together with PhDstudents (P. St-Jean, D. Clonda) and the Master’sstudents (G. Sitzia). Notable is the presence of ajunior analyst (Y. Basile-Belavance) who is incharge of the developpement, for the group, ofsome of the computation libraries used in thisresearch.


B. Goulard (UdeM)Brain imaging.

H. Benali (INSERM, France)Brain imaging.

F. Lesage (CRM)Conformal theory, integrablesystems, inverse problems.

J.M. Lina (CRM)Imaging, statistical inference,wavelets.

F. Nekka (UdeM)Fractal analysis.

K. Worsley (McGill)Geometry of random imagesin medicine and astrophysics.

Highlights of the activities of the laboratory and of its members in 2001-2002.The ability of visualizing in vivo cerebral regions used in cognitive tasks by the human brain has modifieddeeply most of the domains in neurosciences. Until recently, the study of human cognition was mostlyfounded on the analysis of cerebral lesions. With the help of new techniques in functional imaging (IRM,MEG, NIRS, etc.), this discipline made remarkable progress in the comprehension of the spatial-temporalmechanisms managing the operation of the brain. It remains that the problems of detecting cerebralactivity and connectivity, between the cerebral regions spatial as well as temporal, remain importantsubjects of research, the main concern of neuroscientists being to solve these problems beyond any doubtas to the hypotheses guaranteeing the uniqueness of the solution. The mathematical and statisticalapproaches studied by the PhysNum group, in collaboration with the INSERM U494 unit tend to define amethodology based only on reliable hypotheses and knowledge at the anatomical and physiologicallevels. Two domains are principally concerned by this study: Magneto-Encephalography and opticalimaging.

Cerebral imaging (MEG)In the context of Magneto-Encephalography applied to the study of cerebral functional connectivity, thissubject acknowledged important developments can be summarized in the following way:

• Probabilistic model based on graphic models applied to hidden Markov variables and resolution ofthe inverse problem by maximal entropy,

• MiniMax approach on entropy and reduction of the space of features (space of data) MEG.



• PCA approach on the direct problem and reduction of the space of sources (space of dipolesdistributed on the cortical surface) of activation. This study was conducted mostly by the membersof the U494 unit headed by H. Benali at the INSERM.

This collaboration between CRM-INSERM (U494) was formalised by the nomination of H. Benali and J.M.Lina to the status of member researchers at both institutions. Notable is the emergence of anotherinternational collaboration with the Center of Excellence in Taiwan, which invited one of the groupmembers (J.M. Lina) to give a series of seminars at the Central National University of Taipei.

Cerebral imaging (NIRS)Optical imaging offers possibilities of analysis of how the brain operates on objects usually difficult toobserve with conventional tools (IRM, MEG, EGG). At the moment, there exists no strong method fordetecting the active cortical zones from the infra-red (IR) optical signal interacting with the brain. Such amethod, as it is the case with MEG, must take into account certain knowledge about the solution. Onespeaks of the regularization of the inverse problem through a priori knowledge. The approach developedin MEG (see preceding section) is certainly transposable into the context of optical imaging. The stakebeing probably more interesting for neuroscientists because of the flexibility of the technique used(compared to IRM or MEG imaging), PhysNum has defined of a research axis devoted to the resolution ofthe inverse problem for this kind of imaging. Up to now, the researchers involved in this direction ofresearch have concentrated their efforts in understanding the problem in terms of the physics ofinteractions between laser beam and biological material and the transport equations that describe theprogression of the laser beam trough the gray and white matter, starting from the source (placed on thesurface of the scalp) to the detectors (situated on the surface of the scalp).

Graphical models and waveletsThe PhysNum group made its name in the context of multiresolution analysis in studying and applyingthe Daubechies complex wavelets. During the last year, the work of one of its students (D. Clonda) haveunderlined the role of the phase of the coefficients in complex wavelets in the multiresolution treatment ofimages. Two typical applications were considered: estimation (denoising) and classification (texturessegmentation). In both cases, the study proved that a modeling of the signal taking into account the phaseof the coefficients in wavelets gives better results.

Models in cascadeSome members of the PhysNum group (J.M. Lina, B. Goulard, P. St-Jean, D. Clonda, G. Sitzia) areinvolved in work related to analysis through continuous wavelets and particularly to analytical tools inimaging for breast cancer.

Most of this research is conducted in collaboration with academics (J. Doyon, F. Lepore, UdeM), foreignresearch organizations (H. Benali, INSERM; L. Garnero, CNRS, France) and a hospital (L. Lalonde,CHUM).

Scale invariance and fractal analysisF. Nekka and her students have pursued their work of classification of complex structures, in particularthose representing a spatial scale invariance through derived tools of fractal analysis. This team perfecteda method based on the spectrum of Hausdorff measures (when the Lebesgue measure degenerates) inorder to distinguish the sets that are not via fractal dimension. This method was validated on sets calledthin fractals. One obtains in this way one index allowing not only to distinguish sets of the samedimension, but also to classify them with respect to their homogeneity degree. The use of this method wasextended to sets known as fat fractals. These sets have a practical interest, since they are considered assynthetic models of porous material. The whole method was written into a Matlab software. This softwareallows also the analysis of real images for classification.



Statistics LaboratoryStatistics is undergoing a revolution in itstechniques and its approaches. This revolutionhas been driven by the need to analyze verylarge complex data sets and by the advent ofpowerful computers. For example, statisticalmethodology is central to the analysis of genomedata generated by micro-array images. Data-mining is one of the tools used. The laboratoryaims at structuring the Québec community inorder to engage with this revolution at a time ofan important renewal of academic personnel.

This structure will also allow the Québeccommunity to benefit from a new pan-Canadianprogram in analysis of complex data organizedby the three Canadian mathematics institutes.The laboratory is composed of the leaders of theQuébec school of statistics who work on subjectssuch as statistical learning and neuronalnetworks, analysis of functional data, statisticalanalysis of images, dependence structures,Bayesian analysis, analysis of chronologicalseries, of financial data and resampling methods.


Director :Christian Léger (UdeM)Resampling methods,adaptive estimation, modelselection, robustness, datamining applications.

Jean-François Angers(UdeM)Decision theory, Bayesianstatistics, robustness withrespect to prior information,function estimation.

Yoshua Bengio (UdeM,DIRO)Algorithms for statisticallearning, neural networks,Kernel methods, probabilisticmodels, data mining,applications to finance,applications to statisticalmodeling of language.

Martin Bilodeau (UdeM)Multivariate analysis,decision theory, asymptoticmethods.

Yogendra Chaubey(Concordia)Sampling, linear models,resampling, survival analysis.

René Ferland (UQAM)Probability, stochasticprocesses, applications tofinancial mathematics.

Christian Genest (Laval)Multivariate analysis,measure of dependence,nonparametric statistics,decision theory, applicationsto actuarial sciences, financeand psychology.

Nadia Ghazzali (Laval)Multivariate analysis, neuralnetworks and geneticalgorithms, applications toastrophysics and biostatistics.

Brenda MacGibbon (UQAM)Mathematical statistics,decision theory, bio-statistics.

François Perron (UdeM)Decision theory, multivariateanalysis, Bayesian statistics.

Jim Ramsay (McGill)Functional data analysis,smoothing andnonparametric regression,curves scaling.

Bruno Rémillard (HEC)Probability, empiricalprocesses, time series,non-linear filtering,applications to finance.

Louis-Paul Rivest (Laval)Linear models, robustness,directional data, sampling,diverse applications.

Roch Roy (UdeM)Time series analysis,forecasting methods,applications to econometricsand epidemiology.

David Wolfson (McGill)Change points problems,survival analysis, Bayesiananalysis, optimal design,applications to medicine.

Keith Worsley (McGill)Geometry and analysis ofrandom images in medicineand astrophysics.




The researchers of the laboratory were very busy this year and several distinguished themselves. YoshuaBengio has held the Canada Research Chair on algorithms of statistical learning since 2001. Moreover,Keith Worsley is the first Killam Fellow in statistics. The academic and scientific leadership of the groupwas acknowledged in several ways this year. For instance, in 2002, Jim Ramsay was president-elect andLouis-Paul Rivest was past-president of the Statistics Society of Canada. Christian Genest and BrunoRémillard were members of the statistics and probability committee in the context of the reallocationsexercise at NSERC. Yoshua Bengio is a member of the selection committee of the discovery grantscommittee of NSERC in computer science. Even our students distinguished themselves: Alexis Gerbeau,Masters student of Roch Roy, was recipient of the gold medal of the Governor General.

The laboratory took part in the organization of the conference Statistics 2001 Canada at ConcordiaUniversity, in the presentation of the third public conference of the Canadian Journal of statistics in March2002, as well as to the conference Statistique mathématique 2002 the honour of the 75th anniversary ofConstance van Eeden. Yoshua Bengio was a member of the organizing committee of the conferenceLearning 2002. Roch Roy organized a session at the Joint Statistical Meetings 2001 in Atlanta and ChristianLéger was part of the program committee of the Joint Statistical Meetings 2002 in New York. Among themain conferences to which the researchers of the laboratory were invited, there are the InternationalConference and Instructional Workshop on Wavelets and their Applications in Chennai, India (Jean-FrançoisAngers) and Neural Networks for Signal (Yoshua Bengio). The researchers gave talks around the world,notably at UCLA (Christian Genest) and at the Université Montpellier II (Martin Bilodeau). Finally, fourresearch seminars series were organized by members of the laboratory, namely the CRM StatisticsSeminar, the Statistics Seminars of McGill and Laval Universities and the joint UQAM-Concordia StatisticsSeminar.


PublicationsThe CRM publishes monographs, lecture notes, proceedings, software, videos and research reports. Ithas several collections. The in-house collection Les Publications CRM offers many titles in bothEnglish and French. The CRM also has publishing agreements with the American MathematicalSociety (AMS), Springer-Verlag and International Press. Since 1992, two collections, edited by CRM,have been published and distributed by the AMS. They are the CRM Monograph Series and the CRMProceedings and Lecture Notes. Springer-Verlag publishes the CRM Series in Mathematical Physicsand the CRM Subseries of the Springer Lecture Notes in Statistics. The following list of Recent Titlescontains books that have appeared during the year 2001-2002 or that will be published soon.

Recent Titles

AMS: CRM Monograph Series• Eyal Z. Goren, Lectures on Hilbert Modular

Varieties and Modular Forms, vol. 14, 2002• Jose I. Burgos, The Regulators of Beilinson and

Borel, vol.15, 2002• Joel Feldman, Horst Knörrer & Eugene

Trubowitz, Fermionic Functional Integrals andthe Renormalization Group, vo. 16, 2002.

• Michael Barr, Acyclic Models, vol. 17, 2002.

AMS: CRM Proceedings & Lecture Notes• Israel M. Sigal & Catherine Sulem, Nonlinear

Dynamics and Renormalization Group, vol. 27,2001.

• J.C. Taylor (ed.), Topics in Probability and LieGroups: Boundary Theory, vol. 28, 2001.

• Alan Coley, Decio Levi, Robert Milson, ColinRogers & Pavel Winternitz (eds.), Bäcklundand Darboux Transformations: The Geometry ofSoliton, vol. 29, 2001.

• John McKay & Abdellah Sebbar (eds.),Proceedings on Moonshine and Related Topics,vol. 30, 2001.

• John Harnad et Alexander R. Its (eds.),Isomonodromic Deformations and Applicationsin Physics, vol. 31, 2002 .

• Vadim B. Kuznetsov (éd.), The KowalevskiProperty, vol. 32, 2002.

Springer-Verlag: CRM Series inMathematical Physics• Yvan Saint-Aubin & Luc Vinet (eds.),

Theoretical Physics at the End of the XXthCentury. 2001.

• Roman Jackiw, Lectures on Fluid Dynamics,2002.

• David Sénéchal, André-Marie Tremblay &Claude Bourbonnais, Theoretical Methods forStrongly Correlated Electrons, (to appear).

CRM Subseries of the Springer-VerlagSeries: Lecture Notes in Statistics• S. Ejaz Ahmed & Nancy Reid (eds.),

Empirical Bayes and Likelihood Inference, 2001.• Marc Moore (ed.), Spatial Statistics, 2001.

Les Publications CRM• Nadia El-Mabrouk, Thomas Lengauer &

David Sankoff (eds.), Currents inComputational Molecular Biology 2001.

• Armel Mercier, Fonctions de plusieursvariables!: Différentiation, 2002.

Publications


Previous TitlesAMS: CRM Monograph Series• Michael Baake & Robert V. Moody (eds.),

Directions in Mathematical Quasicrystals, vol.13, 2000.

• Masayoshi Miyanishi, Open AlgebraicSurfaces, vol. 12, 2001.

• Spencer J. Bloch, Higher Regulators, AlgebraicK-Theory, and Zeta Functions of Elliptic Curves,vol. 11, 2000.

• James D. Lewis, A Survey of the HodgeConjecture, 2e Édition (with an appendix byB. Brent Gordon), vol. 10, 1999.

• Yves Meyer, Wavelets, Vibrations and Scaling,vol. 9, 1997.

• Ioannis Karatzas, Lectures on Mathematics ofFinance, vol. 8, 1996.

• John Milton, Dynamics of Small NeuralPopulations, vol. 7, 1996.

• Eugene B. Dynkin, An Introduction toBranching Measure-Valued Processes, vol. 6,1994.

• Andrew M. Bruckner, Differentiation of RealFunctions, vol. 5, 1994.

• David Ruelle, Dynamical Zeta Functions forPiecewise Monotone Maps of the Interval, vol. 4,1994.

• V. Kumar Murty, Introduction to AbelianVarieties, vol. 3, 1993.

• Maximilian Ya. Antimirov, Andrei A.Kolyshkin, & Rémi Vaillancourt, AppliedIntegral Transforms, vol. 2, 1993.

• Dan V. Voiculescu, Kenneth J. Dykema, &Alexandru Nica, Free Random Variables, vol.1, 1992.

AMS: CRM Proceedings & Lecture Notes• John Harnad, Gert Sabidussi & Pavel

Winternitz (eds.), Integrable Systems: FromClassical to Quantum, vol. 26, 2000.

• Decio Levi & Orlando Ragnisco (eds.), SIDEIII - Symmetry and Integrability of DifferenceEquations, vol. 25, 2000.

• B. Brent Gordon, James D. Lewis, StefanMüller-Stach, Shuji Saito & Noriko Yui(eds.), The Arithmetic and Geometry ofAlgebraic Cycles, vol. 24, 2000.

• Pierre Hansen & Odile Marcotte (eds.),Graph Colouring and Applications, vol. 23,1999.

• Jan Felipe van Diejen & Luc Vinet (eds.),Algebraic Methods and q-Special Functions, vol.22, 1999.

• Michel Fortin (ed.), Plates and Shells, vol. 21,1999.

• Katie Coughlin (ed.), Semi-Analytic Methodsfor the Navier-Stokes Equations, vol. 20, 1999.

• Rajiv Gupta & Kenneth S. Williams (eds.),Number Theory, vol. 19, 1999.

• Serge Dubuc & Gilles Deslauriers (eds.),Spline Functions and the Theory of Wavelets,vol. 18, 1999

• Olga Karlampovich (ed.), Summer School inGroup Theory (Banff, 1996), vol. 17, 1998.

• Alain Vincent (ed.), Numerical Methods inFluid Mechanics (Montréal, 1995), vol. 16,1998.

• François Lalonde (ed.), Geometry, Topologyand Dynamics, (Montréal, 1995), vol. 15, 1998.

• John Harnad & Alex Kasman (eds.), TheBispectral Problem (Montréal, 1997), vol. 14,1998.

• Michel Delfour (ed.), Boundaries, Interfacesand Transitions (Banff, 1995), vol. 13, 1998.

• Peter G. Greiner, Victor Ivrii, Luis A. Seco &Catherine Sulem (eds.), Partial DifferentialEquations and their Applications (Toronto,1995), vol. 12, 1997.

• Luc Vinet (ed.), Advances in MathematicalSciences: CRM’s 25 Years (Montréal, 1994),vol. 11, 1997.

• Donald E. Knuth, Stable Marriage and itsRelation to Other Combinatorial Problems. AnIntroduction to the Mathematical Analysis ofAlgorithms, vol. 10, 1996.

• Decio Levi, Luc Vinet, & Pavel Winternitz(eds . ) , Symmetries and Integrability ofDifference Equations (Estérel, 1994), vol. 9,1995.

• Joel S. Feldman, Richard Froese, & Lon M.Rosen (eds.), Mathematical Quantum TheoryII: Schrödinger Operator (Vancouver, 1993),vol. 8, 1995.

• Joel S. Feldman, Richard Froese, & Lon M.Rosen (eds.), Mathematical Quantum Theory I:Many-Body Theory and Group Theory(Vancouver, 1993), vol. 7, 1994.

• Guido Mislin (ed.), The Hilton Symposium1993 : Topics in Topology and Group Theory(Montréal, 1993), vol. 6, 1994.

• Donald A. Dawson (ed.), Measure-valuedProcesses, Stochastic Partial DifferentialEquations and Interacting Systems (Montréal,1992), vol. 5, 1994.

Publications


• Hershy Kisilevsky & M. Ram Murty (eds.),Elliptic Curves and Related Topics (Sainte-Adèle, 1992), vol. 4, 1994.

• Andrei L. Smirnov & Rémi Vaillancourt(eds.), Asymptotic Methods in Mechanics, vol.3, 1993.

• Philip D. Loewen, Optimal Control viaNonsmooth Analysis, vol. 2, 1993.

• M. Ram Murty (ed.), Theta Functions. Fromthe Classical to the Modern, vol. 1, 1993.

Springer-Verlag: CRM Series inMathematical Physics• Yvan Saint-Aubin & Luc Vinet (eds.),

Algebraic Methods in Physics - A Symposiumfor the 60th Birthday of Jíri Patera and PavelWinternitz, 2000.

• Jan Felipe van Diejen & Luc Vinet (eds.),Calogero-Moser-Sutherland Models, 1999.

• Robert Conte (ed.), The Painlevé Property: OneCentury Later, 1999

• Richard MacKenzie, Manu B. Paranjape &Wojciech J. M. Zakrzewski (eds.), Soliton:Properties, Dynamics, Interactions, Appli-cations, 1999

• Luc Vinet & Gordon Semenoff (eds.),Particles and Fields (Banff, 1994), CRM Seriesin Mathematical Physics, Springer, NewYork, 1998.

Les Publications CRM• James G. Huard & Kenneth S. Williams

(eds.), The Collected Papers of SarvadamanChowla, I, II, III, 2000.

• Michael Barr & Charles Wells, CategoryTheory for Computing Science, 1999

• Maximilian Ya. Antimirov, Andrei A.Kolyshkin & Rémi Vail lancourt ,Mathematical Models for Eddy Current Testing,1998.

• Xavier Fernique, Fonctions aléatoiresgaussiennes, vecteurs aléatoires gaussiens,Montréal, 1997.

• Faqir Khanna & Luc Vinet (eds.), FieldTheory, Integrable Systems and Symmetries,Montréal, 1997.

• Paul Koosis, Leçons sur le théorème de Beurlingat Malliavin, 1996.

• David W. Rand, Concorder Version Three:Concordance Software for the Macintosh,Montréal, 1996 (software and user guide).

• Decio Levi, Curtis R. Menyuk, & PavelWinternitz, Self-Similarity in Stimulated

Raman Scattering (Montréal, 1993), Montréal,1994.

• Jacques Gauvin, Theory of NonconvexProgramming, Montréal, 1994.

• Rémi Vaillancourt, Compléments demathématiques pour ingénieurs, Montréal,1993.

• Robert P. Langlands & DinakarRamakrishnan (eds.), The Zeta Functions ofPicard Modular Surfaces (Montréal, 1988),Montréal, 1992.

• Florin N. Diacu, Singularities of the N-BodyProblem, Montréal, 1992.

• Jacques Gauvin, Théorie de la programmationmathématique non convexe, Montréal, 1992.

• Pierre Ferland, Claude Tricot, & Axel van deWalle, Analyse fractale: Application W indows™ 3.x d’initiation aux ensembles fractals,Montréal, 1992 (software and user guide).

• Stéphane Baldo, Introduction à la topologie desensembles fractals, 1991.

• Robert Bédard, Groupes linéaires algébriques,Montréal, 1991.

• Rudolf Beran & Gilles R. Ducharme,Asymptotic Theory for Bootstrap Methods inStatistics, Montréal, 1991.

• James D. Lewis, A Survey of the HodgeConjecture, Montréal, 1991.

• David W. Rand & Tatiana Patera, Concorder:Concordance Software for the Macintosh,Montréal, 1991 (software and user guide).

• David W. Rand & Tatiana Patera, L eConcordeur: un logiciel de concordances pour leMacintosh, Montréal, 1991 (software and userguide).

• Véronique Hussin (ed.), Lie Theory,Differential Equations and RepresentationTheory (Montréal, 1989), Montréal, 1990.

• John Harnad & Jerrold E. Marsden (eds.),Hamiltonian Systems, Transformation Groupsand Spectral Transform Methods (Montréal,1989), Montréal, 1990.

• M. Ram Murty (ed.) Automorphic Forms andAnalytic Number Theory (Montréal, 1989),Montréal, 1990.

• Wendy G. McKay, Jirí Patera & David W.Rand, Tables of Representations of Simple LieAlgebras. I. Ex-ceptional Simple Lie Algebras,Montréal, 1990.

• Anthony W. Knapp, Representations of RealReduc-tive Groups, Montréal, 1990.

• Wendy G. McKay, Jirí Patera & David W.Rand, SimpLie User’s Manual–MacintoshSoftware for Representations of Simple Lie

Publications


Algebras, Montréal, 1990 (software and userguide).

• Francis H. Clarke, Optimization andNonsmooth Analysis, Montréal, 1989.

• Hedy Attouch, Jean-Pierre Aubin, FrancisClarke & Ivar Ekeland (eds.), Analyse nonlinéaire (Perpignan, 1987), Montréal &Gauthiers-Villars, Paris, 1989.

• Samuel Zaidman, Une introduction à la théoriedes équations aux dérivées partielles, Montréal,1989.

• Lucien Le Cam, Notes on Asymptotic Methodsin Statistical Decision Theory, Montréal, 1974.

AMS/International Press• Duong H. Phong, Luc Vinet & Shing-Tung

Yau (eds.), Mirror Manifolds and Geometry,AMS/IP Studies in Advanced Mathematics,Amer. Math. Soc., Providence, RI, Internat.Press, Cambridge, MA, & CRM, Montréal,1998(vol.10).

Aisenstadt Chair Collection• Yuri I. Manin, Quantum Groups and

Noncommutative Geometry, Les PublicationsCRM, 1988.

• Laurent Schwartz, Semimartingales and TheirStochastic Calculus on Manifolds, Presses del’Université de Montréal, 1984.

• Yuval Ne’eman, Symétries, jauges et variétés degroupe, Presses de l’Université de Montréal,1979.

• R. Tyrrell Rockafellar, La théorie des sous-gradients et ses applications à l’optimisation,fonctions convexes et non convexes, Presses del’Université de Montréal, 1979.

• Jacques-Louis Lions, Sur quelques questionsd’analyse, de mécanique et de contrôle optimal,Presses de l’Université de Montréal, 1976.

• Donald E. Knuth, Mariage stables et leursrelations avec d’autres problèmes combinatoires,Presses de l’Université de Montréal, 1976.

• Robert Hermann, Physical Aspects of LieGroup Theory, Presses de l’Université deMontréal, 1974.

• Mark Kac, Quelques problèmes mathématiquesen physique statistique, Presses de l’Universitéde Montréal, 1974.

• Sybreen de Groot, La transformation de Weylet la fonction de Wigner: une forme alternative dela mécanique quantique, Presses del’Université de Montréal, 1974.

Miscellaneous• Pierre Ferland, Claude Tricot, & Axel van de

W a l l e , Fractal analysis user’s guide.Introduction to fractal sets using Windows ™3.x., Amer. Math. Soc., Providence, RI &Centre de recherches mathématiques,Montréal, 1994.

Publications


Research Reports[CRM-2746] S. Allen, L. Gagnon & F. Lesage,Hydrous area segmentation in radar imagery by levelset-based snakes, June 2001.[CRM-2747] S. Allen. Signal based features withapplications to ship recognition in FLIR imagery,June 2001.[CRM-2748] S. Tremblay & P. Winternitz.Invariants of the nilpotent and solvable triangular Liealgebras, June 2001.[CRM-2749] M. Bertola, B. Eynard & J. Harnad.Duality, biorthogonal polynomials and multi-matrixmodels, July 2001.[CRM-2750] S. Durand. Non-local wave functionreduction modeled by wormhole-based time travel,August 2001.[CRM-2751] P. Duchesne & R. Roy. Robust testsfor independence of two time series, August 2001.[CRM-2752] J. Karrakchou. Linear quadraticoptimal control of linear time invariant systems withdelays in state, control, and observation variables,September 2001.[CRM-2753] P. Bracken & A. M. Grundland. Oncomplete integrability of the generalized Weierstrasssystem, September 2001.[CRM-2754] A. M. Grundland & W. J.Zakrzewski. Some geometric aspects of CP2 maps,September 2001.[CRM-2755] B. Eynard. A concise expression for theODE’s of orthogonal polynomials, September 2001.[CRM-2756] É. Marchand & F. Perron. On theminimax estimator of a bounded normal mean,September 2001.[CRM-2757] J.-F. Angers & A. Biswas. A Bayesiananalysis of the four-year follow-up data of theWisconsin epidemiologic study of diabeticretinopathy, September 2001.[CRM-2758] P. Valin. Unified framework forinformation fusion, September 2001.[CRM-2759] P. Valin. Reasoning frameworks forfusion of imaging and non-imaging sensorinformation, September 2001.[CRM-2760] M. J. Gander. F r e q u e n c ydecomposition and subspace iteration for nonlinearevolution equations, September 2001.[CRM-2761] M. Haddou, J.-F. Angers & R.Cléroux. Utilisation de modèles linéaires dynamiques

pour l’optimisation de portefeuilles, une approchebayésienne, September 2001.[CRM-2762] L.-S. Guimond, Z. Masáková & E.Pelantová. Combinatorial properties of infinitewords associated with cut-and-project sequences,October 2001.[CRM-2763] L.-S. Guimond, Z. Masáková & E.Pelantová. Arithmetics on beta-expansions, October2001.[CRM-2827] S. Durand. Non-local indeterministicquantum behaviors modeled by wormhole-based timetravel, November 2001.[CRM-2828] M. Bertola, B. Eynard & J. Harnad.Duality of spectral curves arising in two-matrixmodel, November 2001.[CRM-2829] P. Winternitz. Lie point symmetriesand commuting flows for equations on lattices,November 2001.[CRM-2830] J. Patera & R. Twarock. Affineextension of noncrystallographic Coxeter groups andquasicrystals, November 2001.[CRM-2831] D. Schlomiuk & N. Vulpe. Geometryof quadratic differential systems in the neighbourhoodof the line at infinity, December 2001.[CRM-2832] P. Bracken & A. M. Grundland.Affine extension of noncrystallographic Coxetergroups and quasicrystals, January 2002.[CRM-2833] J.-F. Angers. Curves comparison usingwavelet, February 2002.[CRM-2834] A. Leblanc & J.-F. Angers. Priordensity estimation via Haar deconvolution, February2002.[CRM-2835] R. Fournier & P. Mocanu.Differential inequalities which imply starlikeness,March 2002.[CRM-2836] A. Atoyan & C. D. Dermer. High-energy neutrinos from photomeson processes inblazars, October 2001.[CRM-2837] P.-L. Buono & J. Bélair. Restrictionsand unfolding of double Hopf bifurcation infunctional differential equations, March 2002.[CRM-2838] F. H. Clarke & R. J. Stern. Stateconstrained feedback stabilization, March 2002.[CRM-2839] R. J. Stern. Brockett’s condition forstabilization in the state constrained case 2839,March 2002.

Publications


[CRM-2840] F Nekka & J. Li. Investigation ofintersection of triadic Cantor sets with theirtranslates for a classification purpose, March 2002.[CRM-2841] M. Bertola, B. Eynard & J. Harnad.Partition functions for matrix models andisomonodromic tau functions, April 2002.[CRM-2842] M. Bertola. Bilinear semi-classicalmoment functionals and their integral representation,May 2002.[CRM-2843] A. M. Grunland, P. Tempesta & P.Winternitz. Weak transversality and partiallyinvariant solutions, May 2002.[CRM-2844] J. Hurtubise & E. Markman. EllipticSklyanin integrable systems for arbitrary reductivegroups, March 2002.[CRM-2846] N. Alvarez & V. Hussin.Generalized coherent and squeezed states based onthe h(1) ⊕ su(2) algebra, December 2001.[CRM-2847] M. Daoud & V. Hussin. General setsof coherent states and the Jaynes-Cummings model,May 2002.[CRM-2872] A. Granville & K. Soundararajan.Upper bounds for |L(1,c)|, June 2001.[CRM-2873] S. Twareque Ali, H. Fuehr & A. E.Krasowska. Plancherel Inversion as UnifiedApproach to Wavelet Transforms and WignerFunctions, June 2001.[CRM-2874] N. Bergeron & M. Zabrocki. q andq,t-Analogs of Non-commutative SymmetricFunctions, June 2001.[CRM-2875] D. Korotkin. Matrix Riemann-Hilbertproblems related to branched coverings of CP1, June2001.[CRM-2876] J.-C. Aval & N. Bergeron. Vanishingideals of Lattice Diagram determinants, July 2001. [CRM-2877] R. L. Hall & Qutaibeh D. Katatbeh.Spectral bounds for the Hellmann potential, July2001.[CRM-2878] J. Hurtubise & E. Markman. Surfacesand the Sklyanin bracket, July 2001.[CRM-2879] F. Finster, N. Kamran, J. Smoller &S.-T. Yau. Decay Rates and Probability Estimates forMassive Dirac Particles in the Kerr-Newman BlackHole, July 2001.[CRM-2880] L. Bégin, C. Cummins, L. Lapointe& P. Mathieu. Fusion bases as facets of polytopes,August 2001.

[CRM-2881] P. Jacob & P. Mathieu. Parafermionicquasi-particle basis and fermionic-type characters,August 2001.[CRM-2882] E. G. Kalnins, J. M. Kress & P.Winternitz. Superintegrability in a two-dimensionalspace of non-constant curvature, August 2001.[CRM-2883] L. Martina, M. B. Sheftel & P.Winternitz. Group foliation and non-invariantsolutions of the heavenly equation, August 2001.[CRM-2884] V. Apostolov, J. Armstrong & T.Draghici. Local models and integrability of certainalmost Kahler 4-manifolds, September 2001.[CRM-2885] J.-C. Aval & N. Bergeron. Catalanpaths, Quasi-symmetric Functions and Super-Harmonic Spaces, September 2001.[CRM-2886] R. L. Hall, N. Saad & A. B. vonKeviczky. Spiked harmonic oscillators, September2001.[CRM-2887] L. Bégin, C. Cummins, L. Lapointe& P. Mathieu. Fusion bases as facets of polytopes,September 2001.[CRM-2888] F. Gungor & P. Winternitz.Generalized Kadomtsev-Petviashvili equation with aninfinite dimensional symmetry algebra, September2001.[CRM-2889] A. Granville, I. Laba & Y. Wang, Acharacterization of finite sets that tile the integers,October 2001.[CRM-2890] R. L. Hall, N. Saad & A. B. vonKeviczky. Closed-form sums for some perturbationseries involving associated Laguerre polynomials,October 2001.[CRM-2891] R. L. Hall, W. Lucha & F. F.Schoberl. Relativistic N-Boson Systems Bound byOscillator Pair Potentials, October 2001.[CRM-2892] M. A. Rodriguez & P. Winternitz.Quantum superintegrability and exact solvability inN dimensions, October 2001.[CRM-2893] J.-C. Aval & N. Bergeron. SchurPartial Derivative Operators, November 2001.[CRM-2894] M. Bertola, B. Eynard & J. Harnad.Duality of spectral curves arising in two-matrixmodels, December 2001.[CRM-2895] A. Kokotov & D. Korotkin. Someintegrable systems on Hurwitz espaces, December2001.[CRM-2896] A. E. Krasowska & S. Twareque Ali.Wigner Functions for a Class of Semidirect ProductGroups, January 2002.

Publications


[CRM-2897] R. L. Hall & Q. D. Katatbeh. Spectralbounds for the cutoff Coulomb potential, January2002.[CRM-2898] V. Apostolov, D. M. J. Calderbank &P. Gauduchon. Hamiltonian 2-forms in Kahlergeometry I, February 2002.[CRM-2899] J.-C. Aval, F. Bergeron & N.Bergeron. Ideals of Quasi-Symmetric Functions andSuper-Covariant Polynomials for Sn, February 2002. [CRM-2900] A. Kokotov & D.Korotkin. Tau-function on Hurwitz spaces in genus zero and one,February 2002.[CRM-2901] G. Labelle, C. Lamathe & P. Leroux.A classification of plane and planar 2-trees, February2002.

[CRM-2902] R. Fintushel, J. Park & R. J. Stern.Rational surfaces and symplectic 4-manifolds withone basic class, February 2002.[CRM-2903] N. Saad & R. L. Hall. Closed-formsums for some perturbation series involvinghypergeometric functions, March 2002.[CRM-2904] A. Granville & K. Soundararajan.The distribution of values of L(1, c_d), June 2002.[CRM-2905] E. Kerman & F. Lalonde. Lengthminimizing Hamiltonian paths for symplecticallyaspherical manifolds, June 2002.[CRM-2906] S. Gravel & P. Winternitz.Superintegrability with third order invariants inquantum and classical mechanics, June 2002.


Financial Report at 31 May 2002The CRM benefits from several sources offunding to sustain its various sectors of activity.This report distinguishes the amounts awardedto the CRM from those awarded to the Centre’sresearchers.

The Centre’s FundingThe various sources of funding are presented inTable 1. In 2001-2002, the CRM received the thirdinstalment of $874,650 of a four-year NSERCinstitutes grant. This grant enables the Centre tofulfil its national mandate focussed on theannual organization of scientific activities(postdoctoral fellowships, student scholarships,visiting researchers, thematic scientific programas well as a general program of scientificactivities, and research support personnel). (Formore details, see below the section titled“Financial statements”.)

The Comité d’étude et d’administration de larecherche (CÉDAR) of the Université deMontréal provided an operating grant of$820,000 in 2001-2002. This budget is principallyallocated for the remuneration of the scientificpersonnel of the Centre. The budget also coversthe release time of the faculty members whodirect the CRM and a part of the salary ofadministrative staff as well as some operatingand computer expenses.

The Fonds FCAR also supports the operations ofthe CRM. The Centre received the finalinstalment of $210,000 of a three-year operatinggrant in 2001-2002. This grant covers a part ofthe salary expenditures for the research supportpersonnel, the publications personnel, theadministrative personnel and operating costs.An annual amount of $14,000 from this grant isset aside for the research activities of two college(CEGEP) researchers on release time to the CRM.

The CRM manages the collective scientificactivities and the general administration of theNetwork for Computing and MathematicalModeling (ncm2). A budget of $83,894 wasallocated for these tasks in 2001-2002. Inaddition, the CRM received $110,000 from theNetwork to finance the research projects of threeof its members. These amounts come from theNetwork’s annual NSERC grant of $648,894. Thebalance of this amount goes to the researchprojects of the four other founding centres of

ncm2: the Centre de recherche en calcul appliqué(CERCA); the Centre interuniversitaire derecherche en analyse des organizations(CIRANO); the Centre de recherche sur lestransports (CRT); and the Groupe d’études et derecherche en analyse des décisions (GERAD).

As one of the three mathematics institutes inCanada that jointly established the Mathematicsof Information Technology and ComplexSystems Network of Centres of Excellence(MITACS), the CRM supervises the activities ofsix of the Network’s research projects. It alsopromotes networking activities. The CRMreceived $97,000 in 2001-2002 for these tasksfrom the overall NCE funding provided toMITACS. In addition, the research projects justmentioned received $623,000 in NCE funding inthe fiscal year. This last amount is not accountedin the financial statement of the Centre because itis awarded directly to the researchers.

The CRM’s André Aisenstadt endowmentcontributed revenues of $76,206 in 2001-2002.These funds serve for the Centre’s scientificactivities, particularly the annual AndréAisenstadt Prize and Aisenstadt Chairs. TheCRM also received in fiscal year 2001-2002 (withthe university’s departments of mathematics andcomputer science) revenue from the estate of thelate Serge Bissonnette ($4,527). In addition theCentre received a grant from the CanadianInstitute for Advanced Research (CIAR).

The CRM received other contributions totalling$420,181 from universities and partnerorganizations. The Institut des sciencesmathématiques (ISM) contributed funds for jointCRM-ISM postdoctoral fellowships ($64,467) andthe joint colloquium series ($7,685). Researchersfrom other Montréal and Québec universitiescontributed $290,825 for joint postdoctoralfellowships, student scholarships, researchfellows, research professionals and invitedscholars. In addition, there were sponsorshipsfor two international conferences, RECOMB2001and STOC 2002, and a contribution of $4,500 forthe 2001 annual conference of the CanadianNumber Theory Association” The three eventswere held in connection with the CRM’sthematic years.

Financial Report


The CRM generated revenues of $51,646 from itspublishing programs (sales and royalties fromthe CRM’s series with the AmericanMathematical Society and Springer-Verlag NewYork, and from the CRM’s in-house collection).Revenue from registrations to scientific activitieswas much higher than usual in 2001-2002because three international conferences wereaccounted during fiscal year. These conferenceswere RECOMB2001 (registrations totalling$265,200), STOC2002 ($129,155) and CCC2002($29,980). Other scientific events generatedregistration revenue of $31,615. Other fundscame from compensation for services renderedand operating costs ($12,724).

Table 1Main sources de funding of the CRM, 2001-2002Source $ AmountNSERC (Institutes and Initiatives Program) 874!650Université de Montréal (CÉDAR) 820!000FCAR (Research Centres Program) 210!000NSERC (Research Network Program, ncm2) 193!894National Centres of Excellence (MITACS) 97!000Contributions from universities & partners 420!181Other grants et revenue from endowments 201!535Sales, registrations & other revenues 520!320Total 3!337!581

Funding for ResearchIn addition to the CRM’s grants, its researchersobtain in funding for their research projects inthe form of grants and contracts. Total fundingfor the research projects of CRM members wasabout $2.5M in 2001-2002. The CRM directlymanaged about $672,000 in research grants.

Financial StatementThe following financial statement presents, on acash accounting basis, the revenues andexpenditures of the CRM for the fiscal year thatended on May 31, 2002. The financial statementdoes not include the research funding ofindividual researchers.

Expenditures are divided in three broadcategories: Scientific Activities, Publications, andAdministration.

The main line items under Scientific Activities are:• scientific personnel, that is, remuneration of

professors and research fellows at theUniversité de Montréal who undertakeresearch on a full-time basis at the CRM;expenses associated with the release of

professors and researchers from otherinstitutions for prolonged periods; traveland accommodation expenses of invitedresearchers (this includes the AisenstadtChairs and the visiting researchers takingpart in the scientific activities of the Centre);postdoctoral fellowships and studentscholarships;

• scientific p r o g r a m s , that is, the annualthematic program; the general scientificprogram made up of events organized bythe CRM and of contributions to off-sitescientific activities and events, mini-programs on particular topics, colloquiaorganized jointly with the ISM, and expensesassociated with the four prizes of excellencein the mathematical sciences (the AndréAisenstadt Prize, the CRM-Fields InstitutePrize, the CAP-CRM Prize in Theoretical andMathematical Physics, and the CRM-SSCPrize in Statistics); and finally, the scientificprograms of the two networks, MITACS andncm2 (workshops, seminars, lectures,conferences);

• the personne l involved directly in theorganization and management of thescientific programs; and

• the research support personnel deliveringcomputer services and electronic-publishingservices for the preparation of researchreports.

The rubric Publications includes production costsassociated with the CRM’s publishing programs(remuneration of personnel preparingpublications as well as direct costs such asprinting of in-house collection publications).

Finally, the rubric Administration covers theremuneration of the CRM’s executive, theadministrative personnel, the computer systemsanalysts (who support the Centre’s network,hardware and software used in its scientific,management, communications and administra-tive activities), and the communicationspersonnel (Web, newsletter and annual report),as well as expenses related to executive andadvisory business meetings, current operatingcosts, and computer equipment andmaintenance costs.

The 2001-2002 year-end surplus is minimal.

Financial Report


Financial Statement 2001-2002

NSERC-Centre

NSERC-ncm2

FCAR-Centre

NCE-MITACS

Univ. deMontréal

Othersources

OverallTotal

Scientific activities ! ! ! ! ! ! !Scientific Personnel ! ! ! ! ! ! !Visitors and Chairs 67 682 - 1 561 - - 21 955 91 198Partnerships - - - - 15 000 45 000 60 000Université de Montréal - - - - 690 498 50 559 741 057Postdoctoral fellows 135 825 22 013 - - 2 427 280 871 441 136Research professionals - - - - - 18 645 18 645Students 3 127 83 995 - - - 17 700 104 821Subtotal: Scientific personnel 206 633 106 008 1 561 - 707 925 434 730 1 456 857Scientific Programs ! ! ! ! ! ! !Thematic Years ! ! ! ! ! ! !Math. Methods in Biology and Medicine 42 - - - - 258 092 258 133Groups and Geometry 169 681 - - - - 61 404 231 085Math in Computer Science 13 456 - - - - 104 415 117 871

Subtotal: Thematic years 183 179 - - - - 423 910 607 089General scientific program 148 678 - - - - 40 174 188 852Network activities - 8 436 - 38 989 - 200 47 625Other 12 719 - 6 631 - 9 892 14 181 43 422Subtotal: Scientific programs 344 576 8 436 6 631 38 989 9 892 478 465 886 988Personnel - Scientific programs 155 637 - - - - - 155 637Personnel – Direct research support 81 112 - 35 527 - - - 116 639Total: Scientific Activities 787 957 114 444 43 719 38 989 717 817 913 195 2 616 121

Publications ! ! ! ! ! ! !Personnel - - 88 668 - - - 88 668Direct publication expenses - - - - - 6 143 6 143Total: Publications - - 88 668 - - 6 143 94 811

Administration ! ! ! ! ! !Personnel ! ! ! ! ! !Executive 42 450 15 000 - 181 46 536 - 104 168Administration and research 57 513 42 914 76 454 57 401 71 406 6 699 312 388Systems experts & communications - 5 969 - - 31 437 861 38 267

Subtotal: Personnel 99 964 63 883 76 454 57 583 149 379 7 560 454 822Advisory and other committees 13 919 - - - - 3 724 17 643Operating expenses 37 231 1 321 8 914 2 213 12 353 11 656 73 688Computer equipment 8 469 2 193 16 181 - 3 168 14 271 44 282Total: Administration 159 583 67 397 101 548 59 795 164 901 37 211 590 435Total Expenditures 947 540 181 841 233 936 98 784 882 717 956 548 3 301 367

Revenues ! ! ! ! ! ! !Operating grants 874 650 - 210 000 - 820 000 - 1 904 650Research networks, equipment and othergrants - 193 894 - 97 000 - 201 535 492 429Contributions from universities andpartners - - - - - 420 181 420 181Sales, registrations and other revenues - - - - - 520 320 520 320Total Revenues 874 650 193 894 210 000 97 000 820 000 1 142 037 3 337 581

Surplus (Deficit) (72 890) 12 053 (23 936) (1 784) (62 717) 185 489 36 214

A Word from the Director..........................................................

Documents

Transcript of A Word from the Director..........................................................