Table of contents

Table of contents...... 1 A Word from the Director...... 3 Presenting the CRM...... 5 Personnel...... 6 Scientific Personnel...... 7 Members...... 7 Postdoctoral Fellows...... 8 Visitors ...... 10 Management...... 12 Bureau...... 12 Advisory Committee...... 12 Computer Facilities...... 13 Scientific Activities...... 14 Theme Year 2000-2001: Mathematical Methods in Biology and Medicine...... 14 Aisenstadt Chair...... 24 General Programme 2000-2001 ...... 27 CRM Prizes ...... 32 Members’ Seminars & Special Events...... 36 CRM-ISM Colloquium ...... 40 World Mathematical Year ...... 41 Coming Events ...... 43 Theme Year 2001-2002: Groups and Geometry...... 43 General Programme 2001-2002 ...... 47 Theme Year 2002-2003: Mathematical Methods of Computer Science...... 50 General Programme 2002-2003 ...... 54 Theme Year 2003-2004: Geometric and Spectral Analysis...... 56 Collaborations ...... 59 Industrial Mathematics...... 64 Awards, Distinctions, and Landmarks...... 68 Research Programmes...... 69 Publications...... 85 Recent Titles...... 85 Previous Titles...... 86 Research Reports ...... 89 Financial Report ...... 92 Financial Statements 2000-2001...... 95

CRM Annual Report 2000 - 2001 1 2 Annual Report 2000 - 2001 CRM A Word from the Director

Each year at the CRM courses in between. The event attracted over one brings its own hundred and twenty participants for the whole memorable event, period, with over seventy students. The rest of which remains in the the year is underway, with a particularly mind long after the vigorous period extending from next April to bustle of the year is June of next year. It starts with two-week session over. Last year’s was on invariant theory being organised by our the marriage of two colleagues at Queen’s and continues in Montreal participants at a CRM with an intense period on the Langlands Summer School. program, the Canadian Number theory conference, and two workshops on the This year, the image that remains is that of the interaction of algebraic geometry and Lie theory. CRM staff preparing for RECOMB. This It will also overlap with the start of the following international meeting in genomics was hosted at year, on the Mathematics of Computer Science, the CRM in 2001, and the attendance of over 600 so the place should be rather busy. was double that of the previous year. The logistics were quite daunting, and had several The year was fairly eventful on the industrial rooms full to the ceiling with books, folders, front. The area of imaging is one which has seen programs and all the miscellaneous conference considerable growth, with the CRM’s group paraphernalia. Needless to say, the event was a being involved with two large scale imaging great success, and went off without a hitch. (The initiatives, one at the Université de Montréal and needless is obvious to all those who have worked the other at McGill, as well as developing its with Louis Pelletier and Josée Laferrière, our links with the research group at the Pitié- scientific activities staff). Salpétrière. One recent development is the opening of a spin-off company by one of the The whole year was evidence of the explosive group’s students. Also, the MITACS research growth in the whole area of Mathematical network held its annual meeting in Montreal, Biology, the theme of the year. There were 1500 which was well attended, and followed by a one participants to the various activities, including week Spring School in Optimisation, ably put more than 700 graduate students and together by Patrice Marcotte and organised postdoctoral fellows. The program included a through the CRM, with over a hundred in Summer School on Nonlinear Dynamics in attendance. Biology and Medicine, two large International Annual Meetings (CPM 2000 and RECOMB), The Network for Computing and Mathematical eleven 1-week workshops, and six courses and Modelling, which is run at the CRM, has seen seminars. The holders of the Aisenstadt Chairs several interesting new developments, including represented well the two main thrusts of the a new large laboratory run with Environment year, modelling of physiological processes, and Canada, the Laboratoire Universitaire sur le inference techniques in genomics: Arthur Temps Extrême (LUTE), the development of a Winfree spoke on Vortices in Motionless Media, joint initiative with Minnesota’s IMA, and the and Michael S. Waterman lectured on incorporation of the University of Montreal’s Mathematics for Reading and Understanding Genetic new representative of the National Research Sequences. My thanks are due to the organisers of Council’s Industrial Research Assistance the year, Leon Glass, Brian Golding, Leah Program (IRAP) within the CRM. The LUTE is a Keshet, Keith Worsley and most particularly particularly exciting new development, with an Jacques Bélair and David Sankoff. investment of $300K per year, the placing of five Meteorological Service of Canada research staff The current year’s thematic activities on Groups in a university environment, and the allocation and Geometry have already started, with one of important amounts of computer time at very successful event in June on Groups and Canada’s largest computing facility at Dorval. Low-Dimensional Topology, run with great The laboratory’s official opening will be on the ability by Steve Boyer and Dani Wise. There 6th of December. were two workshops, with a week of short

CRM Annual Report 2000 - 2001 3 A w o r d f r o m t h e D i r e c t o r

The year 2000 was UNESCO’s World The whole process of renewal of our local Mathematical Year, and the CRM did its share in mathematics community proceeds apace, with the organising of activities to underline the the appearance on the scene of dynamic and occasion. Our leader in this respect was vigorous new colleagues, who were welcomed Stephane Durand, who assembled a thirty-six- with open arms and are already well involved in page insert for Québec Science on mathematics, our activities. Mathematical institutes have aimed at a general scientific audience. He also become a instrument of preference for the designed a beautiful series of posters that won development of a mathematical community, and the European Mathematical Union’s contest. it is a role that the CRM has played with These then appeared in seven different enthusiasm for many years, and, it is hoped, for countries. They are still in considerable demand. many years to come. We have reproduced them below, which give the report a much-needed touch of colour. Jacques Hurtubise

4 Annual Report 2000 - 2001 CRM Presenting the CRM

The Centre de recherches mathématiques (CRM) Technology and Complex Systems.) Another was created in 1969 by the Université de example is the National Programme Montréal through a special grant from the NRC. Committee, which provides funding for off- It became an NSERC national research centre in site research activities. 1984. It is currently funded by NSERC (Natural This national mandate is complemented by, and Sciences and Engineering Research Council), by indeed supported by, a long-standing vocation the Government of Québec through the FCAR of promoting research in the Montréal area. For (Fonds pour la formation et l'aide à la instance, recherche), by the Université de Montréal, and • the CRM supports, through partnership by private donations. The mission of the CRM is agreements, a group of local researchers to do research in mathematics and closely chosen mainly from departments of related disciplines and to provide leadership in mathematics and statistics, but also the development of the mathematical sciences in computer science, physics, economics, Canada. engineering, etc.; The CRM carries on its mission and national • it organizes series of regular seminars and mandate in several ways: lecture courses on different areas of • it organizes a series of scientific events each mathematical sciences; year, around a given theme (distinguished • it sponsors joint activities with the ISM lecture series, workshops, conferences, (Institut des sciences mathématiques) summer schools, visitor programmes, etc.); including the weekly CRM/ISM colloquium, • its general programme provides funding for graduate courses offered by distinguished conferences and special events at CRM and visitors and a programme of postdoctoral across the country; fellowships; • each year it invites, through the Aisenstadt • it works actively at developing contacts with Chair, one or two distinguished industry. Its joint activities with liaison and mathematicians, to give advanced courses as research centres (CERCA, CIRANO and part of its thematic programme; CRIM) and research centres doing applied • it awards four prizes yearly: the CRM-Fields research (CRT, GERAD and INRS Télécom) Prize recognizing major contributions to led to the creation of the Network for mathematics, the Aisenstadt Prize given for Computing and Mathematical Modelling

outstanding work done by a young (ncm2). This network is funded by NSERC Canadian mathematician, the CAP-CRM and about 20 partners such as financial Prize for exceptional achievement in institutions, high-tech companies and theoretical and mathematical physics, and government agencies. the CRM-SSC Prize for exceptional The CRM fulfils its national mission by contributions to statistics in early career; involving the largest possible number of • it publishes some 150 technical reports and Canadian mathematicians in its scientific about half a dozen books per year. Some of programmes, both as participants and as its collections are published jointly with the organizers. It also supports many events taking AMS and with Springer Verlag; place outside Montréal and the Province of • it has an extensive postdoctoral fellowship Québec. It is recognized worldwide as one of the programme, with 34 postdoctoral fellows in major institutes in the mathematical sciences. place last year, funded either solely by the CRM or in partnership with other The director of the CRM is supported by two organisations. managerial structures: the Bureau and the • it informs the community of its activities Advisory Committee. The Advisory Committee through its web site at is a group of internationally renowned mathematicians from Canada and the rest of the www.CRM.UMontreal.CA world, who approve scientific programmes and • it participates, with the other two Canadian thematic years, choose recipients of the CRM- centres, in groundbreaking national Fields and Aisenstadt prizes, and suggest new initiatives. One example is the MITACS scientific ventures to explore. project (Mathematics of Information

CRM Annual Report 2000 - 2001 5 Personnel

The Director’s Office

Jacques Hurtubise Director Jean LeTourneux Deputy Director, Publications Christian Léger Deputy Director, Scientific Program Yoshua Bengio Deputy Director, Industrial Program Diane Poulin Secretary

Administration

Béatrice Kowaliczko Head of Administration Vincent Masciotra Financial and Administrative Officer Michèle Gilbert Administrative Assistant Muriel Pasqualetti Administrative Assistant Josée Simard Secretary

Scientific Activities

Louis Pelletier Coordinator Josée Laferrière Assistant Coordinator

Publications

André Montpetit TeX Expert (1/2 time) Louise Letendre Technician Diane Brulé-De-Filippis Secretary

Computer Services

Daniel Ouimet UNIX Systems Manager André Montpetit Office systems manager (1/2 time)

Communications

Suzette Paradis Communications officer (1/2 time)

MITACS/MaTISC

Nicole Huron Administrative Assistant

6 Annual Report 2000 - 2001 CRM Scientific Personnel

Since its foundation in 1969, the CRM has been involved in a wide variety of research in mathematics as reflected by the spectrum of the research interests of its members, including the CRM’s permanent research staff, members attached to the CRM through exchange agreements with neighboring universities and industries, and long-term visitors. The presence at CRM of such an active group of researchers has brought many benefits to the centre. In particular, the CRM’s national programme is greatly facilitated by having on hand a large reserve of willing organizers, who have even contributed financially to the organization of activities. The largest partnership is with the Université de Montréal, which gives the equivalent of 5 full-time teaching positions in release time to the CRM. Release agreements with the other Montréal area universities provide for the equivalent of two more full time positions. Facilities are also provided to researchers attached to junior colleges. Several members are attached to the CRM through industrial agreements with Lockheed Martin. Members

Ali, Syed Twareque Dufresne, Daniel Koosis, Paul Rogers, Colins Math. & stat., U. Concordia Math. & stat., UdeM Math. & stat., U. McGill U. New South Wales, Australia Beaulieu, Liliane Durand, Stéphane Korotkin, Dmitri Collège Rosemont Collège Édouard-Montpetit Math. & stat., U. Concordia Rosenberg, Ivo Math. & stat., UdeM Bélair, Jacques El-Mabrouk, Nadia Lalonde, François Math. & stat., UdeM DIRO, UdeM Math., UQAM Rousseau, Christiane Math. & stat., UdeM Benali, Habib Fournier, Richard Langlands, Robert INSERM, France Collège Dawson Institute for Advanced Rousseau, Pascale Study, Princeton Math., UQAM Bengio, Yoshua Frigon, Marlène DIRO, UdeM Math. & stat., UdeM Léger, Christian Roy, Roch Math. & stat., UdeM Math. & stat., UdeM Bergeron, Nantel Gagnon, Langis Math. & stat., U. York Lockheed Martin Canada Lesage, Frédéric Sankoff, David Lockheed Martin Canada Math. & stat., UdeM Bilodeau, Martin Gander, Martin & CRM Math.& stat., UdeM Math. & stat., U. McGill Schlomiuk, Dana Lessard, Sabin Math. & stat., UdeM Boyarsky, Abraham Gauthier, Paul Math. & stat., UdeM Math.& stat., U. Concordia Math. & stat., UdeM Shahbazian, Elisa LeTourneux, Jean Lockheed Martin Canada Boyer, Steven Gora, Pawel Physique, UdeM Math., UQAM Math. & stat., U. Concordia Stern, Ronald Lina, Jean-Marc Math. & stat., U. Concordia Broer, Abraham Goulard, Bernard CRM, UdeM Math. & stat., UdeM Physique, UdeM Toth, John McKay, John Math. & stat., U. McGill Brunet, Robert Grundland, Michel Math. & stat., U. Concordia Math. & stat., UdeM Math., UQTR Valin, Pierre Meunier, Jean Lockheed Martin Canada Clarke, Francis Harnad, John DIRO, UdeM Univ. de Lyon Math. & stat., U. Concordia Vinet, Luc Nekka, Fahima Math. & Phys., U. McGill Crépeau, Claude Hurtubise, Jacques Faculté de Pharmacie, UdeM École d’informatique, Math. & stat., U. McGill Winternitz, Pavel U. McGill Patera, Jiri Math. & stat., UdeM Jakobson, D. Math. & stat., UdeM Darmon, Henri Math. & stat., U. McGill Worsley, Keith Math. & stat., U. McGill Perron, François Math. & stat., U. McGill Kamran, Niky Math. & stat., UdeM Delfour, Michel Math. & stat., U. McGill. Zolésio, Jean-Paul Math. & stat., UdeM Pichet, Claude CNRS, France Math., UQAM

CRM Annual Report 2000 - 2001 7 S c i e n t i f i c P e r s o n n e l

Postdoctoral Fellows

Each year the CRM plays host to a number of postdoctoral fellows. The sources for their funding include the NSERC postdoctoral programme, the NATO international programme administered by NSERC, the CRM (alone or with the ISM or the Fields Institute), and individual research grants from CRM’s members. The list below includes only post-doctoral fellows in residence at CRM or funded or co-funded by CRM, with their funding source given in brackets. For 2000-2001, the following fellows were in residence:

Aguiar, Marcello Bertola, Marco Deteix, Jean Loutsenko, Igor Cornell Univ. S.I.S.S.A. Univ. de Montréal Univ. de Montréal

(CRM-ISM) (CRM-ISM) (ncm2) (ncm2) Amblard, Cécile Brightwell, Mark Fowler, Thomas Polterovich, Iosif Institut National Univ. of Glasgow Georgia Institute of Moscow State Univ. Polytechnique de (CRM-ISM) Technology (CRM-ISM) Grenoble Buono, Luciano (CRM-ISM) Sikora, S. Adam m (CRM-nc 2) Univ. of Warwick Hagedorn, Thomas Univ. de Maryland Allen, Steve (NSERC) Harvard Univ. (CRM-ISM) Univ. de Sherbrooke Corteel, Sylvie (Sloan Foundation) Tokeida, Tadashi m (nc 2-Lockheed Martin) Univ. Paris-Sud Klucznik, Michael Princeton Univ. (CRM-ISM) Brandeis Univ. (CRM) (CRM)

For 2001-2002, the list comprises:

Allen, Steve Langerman, Stefan Mei, Ming Sikora, S. Adam Univ. de Sherbrooke Rutgers Univ. Kanazawa Univ. Univ. de Maryland

(ncm2-Lockheed Martin) (CRM-McGill) (CRM-McGill) (CRM-ISM) Bertola, Marco Loutsenko, Igor Pal, Ambrus Tempesta, Piergiulio S.I.S.S.A. Univ. de Montréal Colombia Univ. Univ. degli studi di

(CRM-ISM) (ncm2) (CRM-ISM) Lecce Brightwell, Mark Maillot, Sylvain Penskoi, Alexei (CRM-ISM) Univ. of Glasgow Univ. Paul Sabatier Univ. de Montréal Urquiza, José (CRM-ISM) (CRM) (CRM) Univ. Pierre et Marie Buono, Luciano Matessi, Diego Prasad, Amritanshu Curie m Univ. of Warwick Univ. of Warwick Univ. of Chicago (nc 2) (NSERC) (CRM-ISM) (CRM-McGill-CICMA) Vénéreau, Stéphane Casesnoves, Raquel Masakova, Suzana Rasmussen, Jorgen Institut Fourier Univ. de Montréal Czech Technical Univ. Univ. of Lethbridge (CRM-McGill-ISM) (CRM) (NATO) (CRM-ISM) Vitse, Pascale Chapoton, Frédéric Saikia, Anupam Univ. de Bordeaux I Paris VI Trinity College, Univ. of (CRM-ISM) (LaCIM-CRM) Cambridge Wang, Sung Ho Dai, Jack Jie (CRM-ISM) Duke Univ. Iowa State Univ. (CRM-ISM) (CRM-ISM)

8 Annual Report 2000 - 2001 CRM S c i e n t i f i c P e r s o n n e l

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

Bao, Weisheng Hadjar, Ahmed Nagih, Anass Sun, Hui Montréal Heart Institute Polytechnique HEC Montréal Heart Institute Chavez, Francisco Kagabo, Issa Rousseau, Guillaume Tateno, Katsumi Univ. of Toronto Polytechnique Univ. of Toronto Univ. McGill Deerakhchan, Katayoun Langdell, Stephen Schaefer, Carsten Villeneuve, Daniel Montréal Heart Institute Univ. de Montréal Univ. McGill Polytechnique Farhat, Abdeljelil Mladenovic, Nenad Shinagawa, Kaori Ziarati, Koorush CIRANO HEC Montréal Heart Institute HEC Hong, Gu Nagai, Yoshihiko Stojkovic, Goran Univ. of Waterloo Univ. McGill Polytechnique

MITACS Postdoctoral fellows 2001-2002:

Bao, Weisheng Hadjar, Ahmed Nagih, Anass Takafumi, Kanamori Montréal Heart Institute Polytechnique HEC Univ. de Montréal Bub, Gil Hong, Gu Shinagawa, Kaori Tateno, Katsumi McGill Univ. Waterloo Univ. Montréal Heart Institute McGill Univ. Caporossi, Gilles Ichiro, Takeuchi Slimane, Leila Villeneuve, Daniel Univ. de Montréal Univ. de Montréal Univ. Laval Polytechnique Chavez, Francisco Kagabo, Issa Stojkovic, Goran Wang, Xiangdong Univ. of Toronto Polytechnique Polytechnique Univ. de Montréal Deerakhchan, Katayoun Nagai, Yoshihilo Stojkovic, Mirela Ziarati, Koorush Montréal Heart Institute McGill Univ. Polytechnique HEC Zou, Renqiang Montréal Heart Institute

CRM Annual Report 2000 - 2001 9 S c i e n t i f i c P e r s o n n e l

Visitors Each year the CRM receives a large number of visitors. The majority are here to participate in scientific activities: in the year 2000-2001, 1797 such participants registered for workshops run solely by the CRM. In addition, the CRM helped fund about 21 other scientific events. The following list does not include those short-term visitors, only those who visited for longer periods, ranging from over a week to several months.

Abreu, Miguel Calin, Iurie Frougny, Christiane Ludwig, Andreas The Fields Institute Academy of Sciences of LIAFA (Paris) Univ. of California, Moldova Santa Barbara Arnéodo, Alain Garnero, Line C.N.R.S. Campbell, Sue Ann CHU Pitié-Salpêtrière Mardesic, Pavao Univ. of Waterloo Univ. de Bourgogne Artes, Joan C. Golding, Brian G. Univ. autonoma de Cao, Xifang McMaster Univ. McLarity, Colin Barcelona Yangzhou Univ. Case Western Reserve Univ. Grau, Maria Teresa Asanuma, Terao Chadam, John Univ. de Lleida Miasnikov, Alexei Toyama Univ. Univ. of Pittsburg City College of CUNY Grotschel, Martin Aschenbrenner, Matthias Chavarriga, Javier Univ. Berlin Michaux, Christian Univ. of Illinois Univ. de Lleida Univ. de Mons-Hainaut Guruswamy, Sathya Atoyan, Armen M. Chekanov, Yuri Institute for Theoretical Miller, Christopher Moscow Eng. Physics ETH Zurich Physics (Amsterdam) Ohio State Univ. Institute Chen, Huaihui Hadj-Amar, Hassiba Monastyrsky, Michael Auroux, Denis Nanjing Normal Univ. Institut aéronautique de ITEP École Polytechnique Saint-Cyr (Palaiseau) Cojocaru, Alina Carmen Moosa, Rahim Queen's Univ. Herz, Andreas Univ. of Illinois at Urbana- Bandrauk, André Humboldt-Univ. Berlin Champaign Univ. de Sherbrooke Cozma, Dumitru V. Tiraspol State Univ. Ilyashenko, Yulij Mourtada, Albelraouf Ben-El-Mechaiekh, H. Steklov Institute Univ. de Bourgogne Brock Univ. Cummins, Chris Univ. Concordia Jackiw, Roman W. Murty, Ram Benali, Habib MIT Queen's Univ. CHU, Pitié-Salpitrière D'Acunto, Didier Univ. de Savoie Jun, Li Novikov, Dmitry Berest, Yuri Univ. de Montréal Univ. of Toronto Cornell Univ. Dancer, Andrew Oxford Univ. Kaloshin, Vadim Ono, Kaoru Bertolini, Massimo Princeton Univ. Hokkaida Univ. Univ. di Pavia Dechevsky, Lubomir Sofia Technical Univ. Kihel, Karim Ouansafi, Abdellatif Biran, Paul Univ. Mohammed V Tel Aviv Univ. Douady, Adrien Laforge, Christophe Univ. de Paris Laboratoire de physique Patera, Jan Bolibroukh, Andrej du solide (Bruxelles) Czech Technical Univ. Univ. de Strasbourg Dubeau, François Univ. de Sherbrooke Lamb, Jeroen Pelantova, Edita Branner, Bodil Imperial College Faculty of Nuclear Sc. and Technical Univ. (Denmark) Dumortier, Freddy Physics Eng. (Czec Limburgs Univ. Le Bris, Claude Republic) Bryant, David Centrum, Belgique Ecole Nationale des ponts McGill Univ. et chaussées Pereira, Jorge Eynard, Bertrand Instituto de Matematica Buium, Alexandru CEA Saclay Llibre, Jaume Pura e Aplicada, Rio (Brazil) Univ. of New Mexico Univ. Autonoma de Françoise, Jean-Pierre Barcelona Pidstrigach, Victor Bullough, Robin Univ. Paris VI Georg-August-Univ. Univ. of Manchester Longtin, André Goettingen Frappat, Luc Univ. d'Ottawa Burnod, Yves CNRS, LAPP Pierre, Roger CHU Pitié-Salpêtrière Univ. Laval

10 Annual Report 2000 - 2001 CRM P e r s o n n e l s c i e n t i f i q u e

Polis, Michael P. Speissegger, Patrick Tremblay, André-Marie Winfree, Arthur T. Oakland Univ. Univ. of Wisconsin Univ. de Sherbrooke Univ. of Arizona Polterovich, Leonid Spiridonov, Vyacheslav Tsvelik, Alexei Yakovenko, Sergey Tel Aviv Univ. Laboratory of Theoretical Univ. of Oxford The Weizmann Institute of Physics (Dubna) Science Pong, Wai Yan Unser, Michael Univ. of Illinois at Stievenart, Nathalie Swiss Federal Institute of Young, Carmen Urbana Champaign Univ. Concordia Technology Lausanne Fields Institute Raffinot, Mathieu Suba, Alexandru Van den Dries, Lou Zell, Thierry Univ. de Versailles State Univ. of Moldova Univ. of Illinois Purdue Univ. Rolin, Jean-Philippe Svobodova, Milena Vulpe, Nicolae Zeron, Eduardo Santillan Univ. de Bourgogne Faculty of Nuclear Science Academy of sciences of Univ. Konstanz and Physics Engineering Moldova Semerdjiev, Emil A. Zhedanov, Alexei Bulgarian Academy of Thiriet, Marc Waterman, Michael Donetsk Univ. Science INRIA Univ. of Southern California Zhu, Huaiping Sikorav, Jean-Claude Tompaidis, Stathis Wiegmann, Paul Univ. of Waterloo École Normale Supérieure Univ. of Texas at Austin Univ. of Chicago de Lyon

CRM Annual Report 2000 - 2001 11 Management Bureau Advisory Committee The Bureau consists of members from the The Advisory Committee is constituted of Université de Montréal (8 to 11 members) and distinguished researchers from Canada and from the outside (2 to 5 members). The rector of abroad. Its members are either mathematicians the Université and the dean of the Faculté des or scientists with close ties to the mathematical arts et des sciences are represented on the sciences. The Advisory Committee is informed Bureau. Its role is to adopt the policies of the periodically of the activities of the Centre, Centre, to recommend the nomination and the through the director, and transmits any advice promotion of researchers and the appointment that it deems relevant to the Bureau. The of regular members, to advise the director on directors and the deputy directors are members the preparation of the budget and the of the committee; the outside members Université on the choice of the director. comprise:

Bengio, Yoshua Hussin, Véronique Borwein, Jonathan Miller, Willard Dep. Dir. CRM, Univ. de Montréal President, CMS IMA Univ. de Montréal Simon Fraser Univ. Kowaliczko, Béatrice Murty, Ram Bergeron, François Secretary Glynn, Peter Queen’s Univ. UQAM Stanford Univ. Léger, Christian Odlyzko, Andrew Brassard, Gilles Dep. Dir. CRM, Hambleton, Ian AT&T Labs Univ. de Montréal Univ. de Montréal McMaster Univ. Pianzola, Arturo Caillé, Alain Lessard, Sabin Hitchin, Nigel Univ. of Alberta Vice-rector, Research Univ. de Montréal Oxford Univ. Univ. de Montréal Putnam, Ian LeTourneux, Jean Lawless, Jerry Univ. of Victoria Cléroux, Robert Univ. de Montréal Univ. of Waterloo Univ. de Montréal Treves, Francois Rémillard, Bruno Melrose, Richard Rutgers Univ. Hubert, Joseph UQRT MIT Assoc. Dean, Research, FAS Rousseau, Christiane Univ. de Montréal Univ. de Montréal Hurtubise, Jacques Director CRM, Univ. McGill

12 Annual Report 2000 - 2001 CRM M a n a g e m e n t

Computer Facilities

The CRM offers to its members and visitors a network directly, or, from outside the CRM Unix environment based on a Sun Enterprise-450 offices, through phone links to our PPP server equipped with four 400-MHz Ultra-Sparc and its 4 modems. processors and 2 Gb of memory as a main The support staff works on Sun stations, X- server, and a secondary server Sun Sparc-1000 terminals or on Macintoshes tied to the Sun with eight 40-MHz processors and 384 Mb of server for all services, such as mail and backups. memory for lightweight tasks. In 2000, the file A 3-years plan for replacement of all support server has grown by 18 Gigabytes (for the staff computers started in 1999 will be completed research group Physnum). This computing in 2002. In Spring 2001, a project to implement power is distributed through the offices and the phase 1 of a new database was initiated. This common rooms via 35 Sun workstations (from database will help support staff to better manage Sparc-4 to Ultra-10) and several X-terminals. the contacts, activities, registrations to activities, The software libraries include compilers (FORTE and offices of CRM. Phase 1 should be environment for C, C++ and Fortran, GNU completed by end of summer 2001, and a phase compilers, Java, etc.), symbolic manipulation 2 is already planned for 2002. programs (Mathematica, Maple, Macaulay), For printing, the CRM has two HP-8000DN several text editors, web browsers, mail tools, workgroup printer (1200-dpi double-sided), a and most utilities common to the mathematical jet-ink network printer Epson-900N for color world (fftw-Discrete Fourier Transform, dstool- printing, and some small printers for support tool for dynamical systems, etc.). Upgrades to staff. TeX and its dialects are uploaded whenever they are released. Unix softwares to interwork with The CRM has its servers installed in a room PC and Mac world are also installed, such as specifically designed for computers, with SAMBA (PC file and printer server), StarOffice independent controlled environment and UPS (Office suite), and AUFS (file server for (Uninterruptible Power Supply). Macintosh). In 2001, the Web server (Apache The main server (Enterprise-450), 22 Sun under Unix) was updated with secured tool SSL workstations Ultra-5 and Ultra-10 and the and a recognized 128-bit Thawte certificate that complete Local Area Network installed in 1999 enables secured registration for participants to were all paid by a grant from the Canadian CRM activities. Also a new look to the contents Foundation for Innovation together with the of our web pages is actually in progress since the Government of the Province of Quebec and a summer of 2001. donation (20% of total value) from Sun Security awareness has triggered new measures Microsystems (for computers) and Anixter (for and updates (for instance, the installation of the network). surveillance softwares), with more to come in the future. In particular, all the CRM’s computers acquired within the last 2 years have been connected to a new alarm system. Since 1999, the CRM operates its own private local area network (LAN): five BayNetworks Baystack-450 switches, providing 120 ports on twisted-pair at 10/100 Mb/s and 4 optic fiber links supporting Gigabit Ethernet. This private local network is linked to the network of the Université de Montréal that maintains the connections with RISQ (Réseau interordinateurs scientifique québécois) and CA*net (the Canadian internet transit service). Members and guests are now able to connect their personal laptops (or computers) on the CRM private

CRM Annual Report 2000 - 2001 13 Scientific Activities

The core of each year’s scientific programme at the CRM is its thematic programme. The topic is chosen by the Advisory Committee for its scientific importance, its timeliness, and its impact on the Canadian scientific community. Preceding years’ topics include: Probability and Stochastic Control (1992-93); Dynamical Systems (1993-94); Geometry and Topology (1994-95); Applied and Numerical Analysis (1995-96); Combinatorics and Group Theory (1996-97), Statistics (1997-98), Number Theory and Arithmetic Geometry (1998-99), Mathematical Physics (1999-00). 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 post-doctoral fellowships. Typically, there is some coordination with Montréal universities to offer appropriate graduate courses in order to help graduate students participate in the activities. The reports are presented in the language in which they were submitted.

Theme Year 2000-2001: Mathematical Methods in Biology and Medicine Overview expérimentaux, tant de la littérature clinique que de simulations numériques. Elle a attiré 55 The year 2000-2001 at the CRM was devoted to participants dont 37 étudiants aux études the rapidly developing field of mathematical supérieures et boursiers postdoctoraux. methods in biology and medicine. The Deux traits distinctifs de cette École sont dignes application of mathematics contributes to the de mention. D'abord, la très étroite coordination understanding of natural processes both through entre les différents enseignants, tous choisis mathematical models and their analysis, and pour leurs connaissances acquises d'expérience through the development and application of dans l'application pratique de la dynamique non mathematical methods of inference. The year linéaire aux systèmes biologiques. Souvent, dans emphasized both aspects, with workshops de telles Écoles, les conférenciers connaissent covering various applications of non-linear seulement un des deux aspects du domaine. dynamics in biology and medicine, as well as Ensuite, un laboratoire informatique quotidien genomics, and medical imaging. planifié pour illustrer les concepts des leçons par l'entremise d'expériences numériques utilisant The year has been a great success with more un logiciel écrit par les conférenciers. Des than 1503 participants to the various activities of étudiants des deuxième et troisième cycle du the thematic year, including more than 700 CNLD, de même que les conférenciers ont fait graduate students and postdoctoral fellows. office d'assistants de laboratoire afin de servir de compléments aux instructions du manuel de 10th CRM Summer School: Nonlinear laboratoire. Dynamics in Biology and Medicine Une évaluation systématique a été recueillie May 22 - June 2, 2000 auprès des étudiants, et a démontré un taux Org. : Jacques Bélair (Montréal) uniforme de très grande satisfaction, invitant à Instructors : E. Doedel (Concordia), R. Edwards (Victoria), L. reprendre la formule dans le futur. Glass (McGill), M. Guevara (McGill), A. Longtin (Ottawa), M. C. Mackey (McGill), J. Milton (Chicago), M. Titcombe (UQAM), A. Vinet (Montréal), J. Bélair (Montréal). International Annual Meetings Reprenant la formule à succès de l'École du Combinatorial Pattern Matching (CPM même titre (tenue en 1996, puis répétée en 1997) 2000) au Centre de dynamique non linéaire en June 21 – 23, 2000 physiologie et en médecine de McGill (CNLD), Org. : Raffaele Giancarlo (Univ. of Palermo), David cette École offrait une solide introduction aux Sankoff (Montréal) outils de modélisation de régulation biologique Invited speakers : A. Broder (Altavista), F. Major (Montréal), F. Pereira (AT&T Labs), I. Witten (Waikato, New Zealand). approchée par la théorie des systèmes dynamiques. Un accent particulier a été mis sur Combinatorial Pattern Matching (CPM) les applications médicales, par une intégration addresses issues of searching and matching étroite de la théorie et des résultats strings and more complicated patterns such as

14 Annual Report 2000 - 2001 CRM S c i e n t i f i c A c t i v i t i e s trees, regular expressions graphs, point sets, and for the Virtual Cell: Cell Mapping Projects on the arrays. The goal is to derive non-trivial Run. combinatorial properties of such structures and There were special sessions on Protein Structure to exploit these properties in order to achieve (Chair: Isidore Rigoutsos), Molecular Interactions superior performance for the corresponding (Chair: Satoru Miyano), Expression Patterns computational problems. Over recent years a (Chair: Ron Shamir), Sequencing by steady flow of high-quality research on this Hybridization (Chair: Michal Linial), Sequence subject has changed a sparse set of isolated Analysis I (Chair: Pavel Pevzner), Phylogeny and results into a fully-fledged area of algorithmics. Gene Duplications (Chair: Tandy Warnow), This area is continuing to grow even further due Sequence Analysis II (Chair: Michael Waterman), to the increasing demand for speed and Sequencing (Chair: Martin Vingron), Proteomics, efficiency that comes from important and RNA Structure (Chair: François Major). rapidly expanding applications such as the In addition the conference attracted 130 posters. World Wide Web, computational biology, and There were 13 commercial booths, as well as multimedia systems, involving requirements for software demonstrations by Entigen, InPharmix, information retrieval, data compression, and and Biobase. pattern recognition. The objective of this annual CPM gathering was to provide to its 73 Support was received from the US Department participants an international forum for research of Energy, the US National Science Foundation, in combinatorial pattern matching and related Celera Genomics, Lion Bioscience, Compaq, the applications. Ministère de l’Industrie et du Commerce (Québec), SmithKline Beecham, Aventis Pharma, 5th Annual International Conference on the Centre de recherche en calcul appliqué Computational Molecular Biology (CERCA), the International Society for (RECOMB 01) Computational Biology and the Université de April 22 – 25, 2001 Montréal. Org. : David Sankoff (Montréal) The premier annual meeting in computational Workshop on Novel Approaches in RNA molecular biology, featuring a highly Informatics (NARI) competitive selection of the best research papers May 18 – 19, 2000 Org.: François Major (Montréal) from cutting edge projects whose subjects are Invited speakers: C. Duarte (Columbia), E. Rivas computational and mathematical in nature. (Washington), B. Shapiro (NCI), M. Venkantraman (Isis RECOMB 2001 was a great success, with over Pharmaceuticals Inc.), C. Wilson (UCSC), 600 participants. It was held at the Wyndham Cet atelier visait une discussion sur Hotel, in downtown Montreal, with a banquet in l'algorithmique derrière les systèmes the piano nobile of Place des Arts. informatiques les plus nouveaux et les plus The Distinguished Biology Lecture was given by sophistiqués en science de l'ARN. Les 46 Phillip Sharp (RNA Biology and the Genome); the participants ont bénéficié des présentations par Stanislav Ulam Memorial Computational les conférenciers invités : C. Duarte From 20 Biology Address by George M. Church, (Hunger atoms to 2 : descriptors of RNA conformation; for new technologies, metrics, and spatio-temporal E.Rivas Computational paradigms for RNA models in functional genomics) and the structure analysis and prediction : a multifaceted Distinguished New Technologies Lecture by approach; M.Venkantraman RNA structure based Mark Adams (The Sequence of the Human drug design; C.Wilson Informatic approaches to Genome). Further keynote addresses were RNA secondary and tertiary structure prediction. delivered by Yvonne Martin, The Role of Les étudiants ont également eu l’opportunité de Computational Chemistry in Translating Genomic présenter leurs travaux de recherche lors d’une Information into Bioactive Small Molecules, Roger session spéciale et sous forme d’affiches. Brent, Information processing by cells and biologists, Klaus Lindpaintner, Genetics and Genomics: Impact on Drug Discovery and Development, Mark Ptashne, Imposing Specificity by Regulated Localization, Matthias Wilm, Creating the Backbone

CRM Annual Report 2000 - 2001 15 S c i e n t i f i c A c t i v i t i e s

Workshop on Bioinformatics globales (opérations de réarrangement de blocs May 17, 2000 de gènes.) Étant donné qu'une multitude de Org. : Nadia El-Mabrouk (Montréal) génomes sont maintenant complètement Tenu dans le cadre du 68 e congrès de séquencés, en particulier des génomes de bactéries, il devient possible d'inférer des l’Association canadienne-française pour relations d'évolution à partir de la totalité du l’avancement des sciences, ce colloque d’une matériel génétique des espèces. Les études durée d’un jour a abordé des aspects variés, d'évolution ne sont pas seulement intéressantes mais complémentaires, de la bioinformatique. d'un point de vue théorique. Elles servent Le but du colloque a été de faire le point sur les également à orienter la comparaison de différentes expertises présentes au Canada et séquence d'une manière à faciliter la prédiction d'aborder les nouvelles problématiques de la des structures d'ARN et de protéines, et par bioinformatique. conséquent, la fonction de ces protéines. La journée s'est déroulée sur deux sessions. Celle Les conférenciers invités, N. El-Mabrouk du matin a porté sur l’analyse structurale et (Montréal), A. Nip (Montréal) et D. Sankoff fonctionnelle du génome. Ce domaine a pour (Montréal), ont abordé des aspects différents liés objectif d'exploiter la masse d'information à la construction d'arbres de phylogénie, au génétique disponible afin de découvrir les calcul de distances d'évolution basées sur l'ordre éléments qui jouent un rôle prépondérant dans des gènes et à la construction de cartes l'expression des gènes, la fonction et la stabilité génétiques facilitant la comparaison génomique. des protéines et les interactions protéiques. Le succès de ce colloque ne fait aucun doute La première présentation a été celle de Pierre puisque plus de 30 personnes y ont assisté, ce Rouzé (Gent) qui nous a présenté, de façon très qui dépasse toutes les estimations initiales. Les pédagogique, les différentes questions qui se participants étaient des étudiants des différentes sont posées lors du séquençage et de universités francophones et anglophones de l'annotation du génome de la plante Arabidopsis Montréal, quelques étudiants de l'Université de Thaliana, et comment ces données sont utilisées Sherbrooke et également des personnes pour déduire des informations sur l'expression travaillant dans des entreprises privées liées de des gènes. Donald Forsdyke (Queen’s) a ensuite près ou de loin à la bioinformatique. Cette présenté différents aspects liés à la composition diversité d'audience a suscité des questions et en bases de l'ADN. Cette présentation a suscité des discussions très intéressantes tout au long de une discussion très intéressante. L'un des projets la journée. majeurs des chercheurs canadiens consiste à exploiter les données structurales et Workshop on Molecular, Metabolic, fonctionnelles du génome dans le but de and Gene Control Networks comprendre, modéliser et prédire les September 9 – 13, 2000 conséquences des pathways métaboliques. Org. : Michael C. Mackey (McGill) Anthony Kusalik (Saskatoon) et Gregory Butler The living cell is a marvellous chemical machine, (Concordia) nous ont présenté des aspects carrying out thousands of chemical and physical importants de ces études. Isabelle Barrette transformations that permit its own survival and (Montréal) et Guylaine Poisson (Montréal) ont, reproduction. Every chemical and physical quant à elles, présenté une étude concernant des process within the cell must be exquisitely motifs conservés impliqués dans les maladies du regulated at the molecular level to meet the prion. Cette présentation a suscité l'intérêt de la demands of life. A fundamental goal of modern journaliste présente. cell biology is to uncover these molecular control La deuxième session, qui a eu lieu l’après-midi, circuits and to understand how they orchestrate portait sur la Génomique comparative et la the observed physiological properties of the phylogénie. La méthode traditionnelle pour living cell. déduire des relations d'évolution entre les These problems are crying out for mathematical espèces consiste à comparer les séquences d'un analysis and simulation. The Millennium Reviews même gène dans différents génomes. Cell Cependant, des gènes différents fournissent des issue of (January 7, 2000) highlighted a informations différentes. Une méthode pressing need for theoretical and computational alternative consiste à comparer l'ordre des gènes tools to make sense of the dynamical interactions dans les génomes en considérant des mutations among proteins in these fundamental regulatory

16 Annual Report 2000 - 2001 CRM S c i e n t i f i c A c t i v i t i e s networks. For instance, Brent (Genomic Biology, the four days: Dennis Bray, Stochastic Models of pp 169-183), after reviewing modern Cell Signalling; George Church, New Technologies developments in genomics and proteomics, and Models in Time-series RNA Array Data; John points out that "For a few prokaryotes and Ross, New Approaches to Determining Mechanisms subsystems within eukaryotic cells, we are at or of Complex Reactions; Joe Mahaffy, DNA near a level of description where we can Replication and Cell Growth for E. coli; Leon Glass, enumerate key players… Better predictive Can Simple Equations be Used to Model Real Gene ability may depend on representations [of the Networks?; James Ferrell, Biochemical Hysteresis key players] that incorporate kinetic and the Irreversibility of the Differentiated State; information. The classical frameworks for this John Tyson, Control of the Eukaryotic Cell Cycle: are, of course, systems of differential equations Molecules, Mechanisms, and Mathematical Models; that describe the rates at which enumerated Paul Smolen, Modeling Circadian Oscillations with species change." Interlocking Positive and Negative Feedback Loops; This workshop focused on the molecular Kurt Kohn, Molecular Interaction Maps as regulatory systems that control cell metabolism, Information Organizers and Simulation Guides; gene expression, environmental responses, Marc Roussel, Invariant Manifold Methods for development, and reproduction. As in man Metabolic Model Reduction; Moises Santillan, made machines, these regulatory networks can Mathematical Models of the Tryptophan Operon: be described by non-linear dynamical equations, Modeling Development and Stability Analysis; for example, ordinary differential equations, Denis Thieffry, Qualitative Analysis of Gene reaction-diffusion equations, stochastic Networks; Hanspeter Herzel, Extracting differential equations, or cellular automata. The Information from cDNA Arrays; James Collins, The invited talks illustrated a range of theoretical Design and Construction of a Genetic Toggle Switch; problems presented by modern concepts of Raima Larter, Calcium Waves and Other Nonlinear cellular regulation, some strategies for Dynamic Behaviors in the Brain; Albert Goldbeter, converting molecular mechanisms into Modeling the Molecular Bases of Ultradian and dynamical systems, some useful mathematical Circadian Rhythms; Roland Somogyi, Challenges in tools for analyzing and simulating these Data Mining and Computational Modeling for the systems, and the sort of results that derive from Interpretation of Molecular Networks; Johan serious interplay between theory and Paulsson, Copy Number Control in Plasmid experiment. Replication. The workshop was attended by 41 individuals Workshop on Gene Order Dynamics, from Canada, the United States, Mexico and five Comparative Mapping and Multigene European countries. They ranged from senior Families (DCAF) university faculty (20) through postdoctoral September 22 – 25, 2000, Ste-Adèle fellows (5), graduate students (12) and medical Org. : David Sankoff (Montréal), Joseph H. Nadeau (Case students (1) to undergraduates (3). According to Western Reserve University) the attendees, the workshop was highly Invited speakers: S. Andersson (Uppsala University), Jeffrey Boore (University of Michigan), P.Bork (EMBL Germany), successful. The organizer continues to receive G.Brown (Univ.Victoria), D.Bryant (McGill), A.Caprara positive comments, as well as requests for a (Univ.Padova), O.Cohen (Univ. Joseph Fourier), J.Cotton repeat venue. Another sign of its success is that (Univ. of Glasgow), J.Demongeot (Université Joseph Fourier de Grenoble), K.M. Devos (Norwich Research Park), J.Dicks the Editorial Board of the American Institute of (Norwich Research Park), E.Eichler (Case Western Reserve Physics journal Chaos invited John Tyson and University), N.El-Mabrouk (Univ.Montréal), K.Eriksson Michael Mackey to co-edit a Focus Issue of that (Malardalen Univ.), C.Gallut (Université Pierre et Marie Curie), D.Goldberg (Cornell University), A.L. Hughes journal for the first number of volume 11 (University of South Carolina), R.K. Jansen (University of (March, 2001). Texas), J.Kleinberg (Cambridge University), G.Lancia (University of Padova), D.Liben-Nowell (Massachusetts The format of three talks in the morning and two Institute of Technology), L.A. Lyons (University of talks in the afternoon afforded participants the California Davis), B.F. McAllister (University of Texas at Arlington), A.McLysaght (University of Dublin), J.Meidanis opportunity to interact informally. There were (Universidade Estadual de Campinas), A.Nip (Université de also other occasions to meet in an informal and Montréal), I.Parkin (Agriculture and Agri-Food Canada), relaxed atmosphere, which were one of the A.H. Paterson (University of Georgia), I.Pe'er (Tel Aviv University), P.A.Pevzner (University of Southern California), prime contributors to the success of the D.Sankoff (Université de Montréal), D.J.Schoen (McGill workshop. There were 19 invited talks spanning University), R.Shamir (Tel Aviv University), J.Tiuryn

CRM Annual Report 2000 - 2001 17 S c i e n t i f i c A c t i v i t i e s

(Warsaw University), Z.Trachtulec (Academy of Sciences of employer et développer des technologies the Czech Republic), T.J. Vision (Cornell University), D. Waddington (Roslin Institute, Edinburgh), J.E. Womack hautement mathématisées. D’autre part, en (Texas A&M University). France, l’acquisition conduite par la This meeting brought together 68 scholars in the modélisation y est perçue comme une voie biological and mathematical sciences working privilégiée permettant de réunir les on genome rearrangement, mapping, and the communautés du traitement de signal et evolution of gene families in human, animal, d’image et de modélisation sur des recherches plant, other eukaryote, prokaryote, organellar, communes. and viral genomes. Workshop on Memory, Delays and Workshop on Nonlinear Dynamics and Multistability in Neural Systems Biomathematics October 11-15, 2000 Org.: André Longtin, (Ottawa ) October 3 – 6, 2000 Org. : Pierre Auger (Lyon), Jacques Bélair (Montréal), The purpose of this high-level workshop was to Jacques Demongeot (Grenoble), Christiane Rousseau (Montréal), Philippe Tracqui (Grenoble) bring together scientists working on three Invited speakers: O. Arino (Pau), P. Auger (Lyon), J. Bélair aspects of neural function: 1) memory, especially (Montréal), H. Benali (CHU Pitié Salpêtrière), A. Bourdou short-term as opposed to long term; 2) delays in (INSERM), R. Bravo de la Parra (Alacala), S.A. Campbell neural activity propagation, and 3) (Waterloo), C. Chevalet (Toulouse), F. Clarke (Lyon), J.-L. Coatrieux (Rennes I), M. Courtemanche (Montréal), J. multistability, i.e. the coexistence of two or more Demongeot (Grenoble), L. Glass (McGill), A. Goldbeter (UL attractors for the dynamics of a system of Bruxelles), B. Goulard (Montréal), J.-M. Lina (Montréal), S. neurons. All invited speakers were neural Lessard (Montréal), A. Longtin (Ottawa), N. Raissi (Morocco), D. Salahub (Institut Steacie), P. Tracqui modelers with various levels of mathematical (Grenoble), B. A. Vinet (Hôpital du Sacré-Coeur), G. expertise active in one or more of these areas. Wolkowicz (McMaster). Memory and multistability go together, since a Ce colloque s’est tenu dans le cadre et sous le system with memory must evolve to one of format des Treizièmes Entretiens Jacques- many coexisting states. However, multistability Cartier. Tous les participants ont beaucoup has also been found in a variety of recent studies apprécié le colloque et noté la très grande qualité without being associated with memory. Delays des exposés. Une particularité de ce colloque est enter the picture because they can make systems que la plupart des exposés ont été donnés en multistable, and have been implicated in recent français et beaucoup de participants ont studies of memory in real and artificial neural apprécié cette chance unique qui leur avait été networks. donnée de faire de la science en français. The achievements of the workshop was to 1) Les cinq organisateurs du colloque : Pierre raise the awareness of the commonalities of Auger (Lyon 1), Président de la Société Française those areas, 2) enable new insights into solving de biologie théorique, Jacques Demongeot the mathematically challenging problems of (Grenoble), Président de la Société européenne delays and multistability in nonlinear dynamical de biologie théorique et de biomathématique, systems, 3) ignite new collaborations between Philippe Tracqui (Grenoble), Jacques Bélair the participants, and 4) spur the interaction of (CRM et SCMAI), Christiane Rousseau (CRM et theory with neurobiological experiment. This SMC) se sont rencontrés pour explorer les latter interaction was possible because almost all possibilités de collaboration future entre les speakers worked on real neural systems. Key biomathématiciens et les sociétés scientifiques figures in nonlinear delay-differential equations les représentant. Du côté canadien le réseau also extended the workshop into the realm of canadien de centres d’excellence MITACS vise à pure mathematics. développer les retombées industrielles des The open workshop attracted 50 participants. Its mathématiques dans les systèmes complexes, et format consisted of twenty-two 40-minute le secteur biomédical y occupe une place de invited talks and sixteen 20-minute contributed choix. Ce réseau suit la création du réseau de talks, and a handful of poster presentations. calcul et de modélisation mathématique, rcm2, un Each invited (contributing) speaker was consortium québécois de centre de recherches en encouraged to finish after 30 (15) minutes to sciences mathématiques visant à offrir une allow plenty of discussion time, an important vitrine unifiée aux industriels appelés à aspect of the workshop. There had been no

18 Annual Report 2000 - 2001 CRM S c i e n t i f i c A c t i v i t i e s previous workshop of this timely subject, one of down to single cell dynamics, before moving the reasons for its success. The other reason was back up to more macroscopic network dynamics. the excellence and accessibility of the talks, and E. Izhikevich proposed an impressive the willingness of this diverse group to exchange classification of bursting cells into 120 categories, in a friendly atmosphere. based on bifurcation theory. S.K. Han The workshop began with Dynamical Memory. demonstrated the stunning (and humbling!) G. Carpenter gave an overview of adaptive complexity of the bifurcation structure of a resonance theory for real-time neural networks, simple "bursting" circuit of two coupled emphasizing how synaptic strength can be neuronal oscillators. K. Aihara presented the redistributed to enhance stable pattern learning. computational and coding advantages of chaotic S. Becker modeled hippocampal-parietal spatio-temporal firing patterns. A. Herz interactions in spatial memory, exploring how reviewed how neural nets can store temporal they allow translation between allocentric and patterns, and proposed that temporal relations egocentric spatial representations. Next came could be stored and later used for nontrivial more general perspectives on Neural computations. A. Destexhe presented results on Computing. W. Maass put forth a "wetware" real neocortical cells that suggest how they can theory better suited to neurons that the Turing perform finer detection when their state is machine; it analyzes computations based on highly noisy. And W. Gerstner developed an transient events. Since responses to stimuli (such integral equation formulation of his "spike as visual perceptions) exhibit multistability with response method" to analyze the effect of delays analog properties, unlike pure digital and noise on signal transmission. multistability, Richard Hahnloser (MIT) M. Ding led the session on higher level proposed a neuromime circuit with digital-like Sensorimotor Dynamics with an analysis of long multistability and analog amplification. In the term correlations in timing errors that arise third session was on Delayed Dynamics, S.A. (likely) from neural processes acting on multiple Campbell and J. Belair gave an excellent joint time scales. R. Engbert presented a study of the tutorial on bifurcation theory and multistability delayed coordination of eye saccades and applied to delay equations modeling neural attention shifts during reading. Finally the circuits. J. Wu analyzed how various patterns workshop wrapped up with the "highest level" such as equilibria, phase locked orbits, and functions. C. Laing presented a model for standing waves arose in simple networks with binocular rivalry, a form of multistable delayed feedback. And U. Ernst showed how perception that occurs e.g. with the Necker cube. multistability can lead to phase clustering in And H. Wilson tied a single cell property subsets of cells in a neural network, with the (adaptation) to high-level multistable effects interesting result that the number of such such as perceptual oscillations (illusions, subsets decreases with increasing delay. binocular rivalry) and bursting during migraine In the session on Recurrent Dynamics and Phase auras. Resetting, Leon Glass presented results from studies on both cardiac and neural systems Workshop on Mapping and Control of where stimuli given at fixed delay can yield Complex Arrhythmia complex bursting rhythms. C. Canavier October 29– November 1, 2000 Co-sponsor: Guidant Inc. presented an analysis of loop circuits of Org. : Leon Glass (McGill) oscillators in which delayed feedback gives rise This workshop brought together a diverse group to multistability. J. Milton presented of undergraduate and graduate students, experimental work supported by theory on postdoctoral fellows, physicians, and industrial delayed recurrent neural loops that include a representatives to discuss the control of complex computer. This led to fascinating speculations on arrhythmias. There were attendees from Canada, the neural code based on multistability and the United States, France, Switzerland, statistical periodicity. K. Pakdaman gave a Germany, Belgium, and Mexico. The conference different twist to delayed dynamics by analyzing was partially funded by a grant from medical the transient properties of such circuits. The equipment manufacturer Guidant Inc. The sessions on Bursting Dynamics and Neural conference was also closely related to the Information Processing continued a progression MITACS project of Leon Glass and several

CRM Annual Report 2000 - 2001 19 S c i e n t i f i c A c t i v i t i e s individuals participating in that project attended journal Chaos. This conference should therefore and spoke at the meeting. have a long-term impact on the future The level of the presentations was uniformly development of this field. high, and there was a relaxed atmosphere and schedule that allowed lots of time for discussion. Workshop on Fractal and Modeling in Although this was particularly beneficial for Structural and Dynamical Analysis students, several of the senior scientists November 11 – 14, 2000 Org. : Jacques Bélair (Montréal), Fahima Nekka (Montréal) mentioned that unlike usual conferences, this Invited speakers: A. Arnéodo (C.N.R.S.), Y. Ashkenazy workshop had enough time for serious (Boston), D.R. Bickel (Texas), Q. Cheng (York), S. Dubuc discussion. In addition, the presence of several (Montréal), A. Einstein (Mt. Sinaï), A. Khalil (Laval), A.P. Kirilyuk (Institute of Metal Physics, Kiev), H. Kitaoka experimentalists and physicians provided (Osaka), L.S. Liebovitch (Florida Atlantic), S. Lovejoy connection with current medical and (McGill), S. Lubkin (North Carolina), F. Nekka (Montréal), B. experimental advances. The presentations of A. Sapoval (Polytechnique), C. Tricot (Clermont-Ferrand), M.J. Turner (De Montfort) Shrier (McGill), K. Stein (New York Presbyterian Hospital), S. Nattel (Montreal Heart Institute) in Les développements les plus récents de la particular generated lots of discussions about géométrie fractale, tant du point de vue experimental methods and potential connections mathématique que du point de vue des between experimental and clinical work and applications, ont été présentés. Les conférenciers theory. Powerful computational approaches ont systématiquement insisté sur les obstacles were emphasized in presentations by M. entre la théorie et la pratique, mais aussi Guevara (McGill), J. Leon (Calgary), Y. Rudy présenté des avenues fort prometteuses d'emploi (Case Western), A. Vinet (Montreal), F. Fenton des outils fractals dans l'analyse de nombreuses (Northeastern), N. Virag (Medtronic Europe), C. structures biologiques, incluant la génomique Zemlin (Berlin), N. Trayanova (Tulane), G. fonctionnelle. La lacunarité, en particulier, a été Rousseau (Paris 7). The connections between identifiée comme un concept digne d'un experimental observations and theory were an traitement mathématiquement plus approprié important element of many of these que celui disponible actuellement. presentations. In some cases, physicists and La conférence a attiré 35 personnes dont 11 mathematicians have been successful in étudiants aux études supérieures et 2 boursiers initiating experimental and clinical studies in postdoctoraux. Les commentaires des collaboration with clinical and experimental participants, comme des conférenciers, ont été colleagues and this was a primary focus of très positifs, quelques-uns de ces derniers presentations by A. Garfinkel (UCLA), D. manifestant par courriel leurs remerciements Christini (Cornell University Medical College), aux organisateurs. R. Ideker (Alabama), D. Gauthier (Duke), H. Hastings (Hofstra). Beautiful analytic work on Workshop on Mathematical Methods complex dynamics was presented by A. Karma in Brain Mapping (Northeastern) and V. Hakim (Paris). V. Krinsky December 10 – 11, 2000 (Nice) presented ideas about a new medical Org. : Keith Worsley (McGill) device to detect the source of serious Invited speakers: R. Adler (TECHNION), J. Ashburner (Inst. of Neurology Funct. Imaging Lab.), J. Aston (London), E. arrhythmias. Finally, though the focus of the Brown (Harvard), M. Chung (McGill), A. Dale (Harvard), K. conference was on cardiac arrhythmias, there Friston (Inst. of Neurology Funct. Imaging Lab.), G. Glover were also two presentations concerning control (Stanford), N. V. Hartvig (Aarhus), M. Hurdal (Florida Atlantic), S. Kiebel (Inst. of Neurology Funct. Imaging Lab.), of neurological arrhythmias by J. Collins N. Lange (Harvard Psychiatry & BioStats), J.-F. Mangin (Boston) and A. Beuter (UQAM). Overall, there (Service Hospitalier Frédéric Joliot, Orsay), T. Ozaki (Tokyo), was an excellent balance of topics on a common J.-B. Poline (CEA), J. Polzehl (Weierstrass Inst.), J. Riera (Cuban Neuroscience Center), S. Smith (Oxford), J. Taylor theme and a critical mass of superb scientists. (McGill), P. Valdes (Cuban Neuroscience Center) Indeed, there were 54 participants, including 18 Brain mapping is a rapidly growing research graduate students and 4 postdoctoral fellows. field that tries to understand human brain Although there will be no conference function and anatomy using 3D images from proceedings as such, several of the conference MRI, fMRI, PET, EEG and MEG and applying participants will be invited to contribute to a geometry, topology, statistics, and random Focus issue on Complex Arrhythmia in the fields. This workshop brought together 63

20 Annual Report 2000 - 2001 CRM S c i e n t i f i c A c t i v i t i e s participants including mathematicians and decade. The invited speakers were Manolo Gouy statisticians interested in brain mapping, and (Bernard-Lyon), Reconstruction of Distant medical researchers interested in mathematical Phylogenetic Relationships: Effect of more Realistic and statistical methods for the analysis of brain Models of Molecular Evolution, Ziheng Yang mapping data. Talks were organized in four (University College, London), Estimation of sessions: fMRI (Friston, Glover, Smith, Hartvig), Synonymous and Nonsynonymous Substitution fusion of fMRI and EEG (Dale, Brown, Riera, Rates and Evolution of Mammalian and Drosophila Ozaki, Valdes), structure (Mangin, Ashburner, Nuclear Genes, Spencer Muse (North Carolina Hurdal, Aston), cortical surface mapping State), Modeling Heterogeneity of Nucleotide (Poline, Kiebel, Chung, Polzehl, Taylor). Substitution Rates, Rasmus Nielsen (Cornell), Estimating Selection Coefficients from DNA Workshop on Population Genetics at Sequence Data using Codon based Likelihood Models, the Molecular Level Bruce Rannala (Alberta), High-resolution March 8 – 11, 2001 Multipoint Linkage Disequilibrium Mapping in the Org. : Brian Golding (McMaster) Context of a Human Genome Sequence, Andrey The focus of this workshop was the recent Rzhetsky (Columbia), Computational Analysis of developments that have occurred in population Regulatory Networks, John Huelsenbeck genetics as a result of the many new innovations (Rochester), Likelihood-based Inference of Large that have occurred in the biological technologies Phylogenies, Sudhir Kumar (Arizona State), devoted to analysing molecular variation. It is Estimating Neutral Substitution Rate in Mammals now possible to determine the differences that , exist between individuals, between populations Jeff Thorne (North Carolina State), Rate Evolution and between species in the finest molecular and Divergence Time Estimation, Daniel Schoen detail. We can now routinely determine the (McGill), Transposon Dynamics in Plants: DNA nucleotide sequence over a length of Inferences from Phylogenetic Analyses and Site thousands of base pairs from hundreds of Occupancy Data, and Brian Golding (McMaster), individuals within a week’s time. This has Methods to aid in the Determination of Allelic necessitated corresponding changes in the Histories. theory that is used to make biological sense of The first talk demonstrated that unless very this information. The amount of data and its realistic models of evolution are used to infer precision have provided far more biological phylogenetic histories then an incorrect information that was extracted by previous inference might be made. This is very important theories. The new theoretical developments have for the revolutionary finding noted above - the largely been attempts to extract this added level suggestions of horizontal transfer are based on of information present within the data but much unusual phylogenetic histories - and on the of it has also been in response to surprises that organisms that we think the lineage leading to the new data has presented. As an example of humans ultimately originated from. The next just one of these surprises is the suggestion that three talks each developed more accurate but bacterial genes are often not vertically also more complicated likelihood models that transmitted. Most students are taught that an incorporated the effects of individual individual inherits their genes one copy from nucleotides in a non-independent manner their mother and one copy from their father. Or (codon models incorporating selection) in the case of bacteria, the single copy from their throughout the length of genes. The next two parent. But the sequence data that has been talks incorporated larger data sets that are being collected so far, and or analysis of it suggests generated by genome projects to develop that this is often not the case and that bacteria methods to map human genes and to map can simply pick up new genes from their interaction pathways among proteins. The talks environment and then incorporate these genes by Dr. Huelsenbeck and Dr. Thorne made use of into their permanent genome. This unusual likelihood Monte Carlo Markov models to finding is forcing a re-interpretation of much of reconstruct large phylogenies and to determine the evolution of bacteria. when rates of evolution might have changed There were eleven invited speakers. These within a phylogeny. The talk by Dr. Kumar was individuals were chosen primarily as an attempt to use the massive amount of data representatives of the young and exciting new from many mammalian species to estimate theoreticians that will be shaping the structure of synonymous substitution rates. The talk by Dr. the population genetics theory over the coming Schoen analyzed patterns of transmission of transposable elements in plants and lastly, Dr.

CRM Annual Report 2000 - 2001 21 S c i e n t i f i c A c t i v i t i e s

Golding presented some theory that permits discovery (L.Parida); Adaptive test mining: inferring calculation of the probabilities of individual structure from sequences (I.H.Witten). allelic phylogenies. The workshop attracted a comparatively large Developing the Tools: A Canadian attendance. All told there were 62 registered Bioinformatics Workshop participants including 34 graduate students and June 26– July 1, 2000 Org. : Christopher Hogue (Toronto), François Major 7 postdoctoral fellows. There were participants (Montréal) from the United States, India, Germany, Brazil, and Canada. The purpose of the workshop was to give the participants practical expertise and skills to Workshop on Mathematical parse and to manipulate the output of Formalisms for RNA Structure bioinformatics software; to modify and to extend April 26 – 27, 2001 existing bioinformatics software tools; to Org. : François Major (Montréal) develop and to implement new bioinformatics Invited speakers: J. Brown (NCSU), J. Burke (Vermont), M. data abstractions; to develop new bioinformatics Carrillo (Stanford), D. Case (Scripps), Y. Ding (New York), S. applications using C++, Java; to build simple Harvey (Alabama), P. Legault (Georgia), S. Lemieux (Montréal), N. Leontis (Bowling Green), J.-P. Perreault tools using the NCBI toolkit. (Sherbrooke), P. Schuster (Vienna), P. Thibault (Montréal), A. Waugh (Stanford), E. Westhof (CNRS-Strasbourg). Techniques in Brain Mapping Cet atelier visait une discussion sur l'état de l'art December 5 - 8, 2000 Org. : Keith Worsley (McGill) de l'informatique de l'ARN. Nous avions invité à Invited speakers: R. Adler (TECHNION), N. Lange notre avis les experts mondiaux dans la matière (Harvard), P. Valdes (Cuban Neuroscience Center). et nos objectifs furent atteints. In preparation for the workshop on brain Les participants de l'industrie (US et Europe) et mapping, three series of introductory lectures des sciences de l'ARN du Québec et des were given to 69 participants: R. Adler Gaussian alentours furent pour la plupart impressionnés random fields: basics, maxima, Euler characteristics; par le calibre des participants et des P.Valdes EEG/MEG tomography: basics, statistical présentations. Somme toute, un excellent et de issues; N.Lange Brain mapping and anatomical haut calibre atelier dans le domaine de l'ARN, magnetic resonance, functional and pharmacological probablement un des meilleurs dans le domaine imaging. depuis la conscientisation de l'importance de l'informatique en sciences de l'ARN. Le Fractals and Wavelets in Medical Imaging programme fut complété par une session February 23 – 24, 2001 d'affiches. Org. : Jean-Marc Lina (Montréal), Fahima Nekka Les participants ont manifesté leur désir de voir (Montréal) Invited speakers: M. Unser (Swiss Federal Institute of cet évènement se répéter en 2002 et possiblement Technology, Lausanne) les années suivantes. L'atelier Ondelettes, fractales et imagerie médicale a été organisé selon le format d'une série de Courses and Seminars conférences données au Centre de Recherches Combinatorial Pattern Matching Mathématiques. La plupart des conférenciers, June 19 – 20, 2000 qui sont des experts reconnus au niveau Org. : David Sankoff (Montréal) international, ont été invités à exposer des mini- Invited speakers: D. Bryant (Montpellier), N. El-Mabrouk cours, suivi d'un séminaire portant sur les (Montréal), R. Giancarlo (Palermo), C. Lam (Concordia), L. Parida (IBM T.J. Watson Research Center), I. Witten aspects les plus récents de leur recherche. Cette (Waikato, New Zealand). formule a été autant appréciée par les conférenciers que les participants. Preceding CPM2000, this was a two-day tutorial on sequence analysis and other topics in Le premier conférencier, le Prof. M. Unser, est computational biology and pattern matching directeur du groupe d'imagerie biomédicale à that attracted 29 participants. The lectures titles l'École Polytechnique Fédérale de Lausanne (Suisse.) C'est un expert en imagerie et au BLAST ! How do you search sequence were traitement de l'information par les méthodes databases? (G.Butler, C.Lam, G.Grahne); hiérarchiques et par les analyses en ondelettes Phylogeny (D.Bryant); Algorithmic aspects of et splines. En février 2001, le Prof. Unser a speech recognition (R.Giancarlo); Genome donné quatre conférences: Splines: a perfect fit for rearrangement (N.El-Mabrouk); Flexible-pattern

22 Annual Report 2000 - 2001 CRM S c i e n t i f i c A c t i v i t i e s image processing, Pyramids and wavelets, Wavelets development that gave the diversity of life on in biomedical imaging et Towards a unification: earth. Phylogenetics is important not only for Wavelets, fractals, and radial basis functions. fundamental research; there are important Les autres évènements se rattachant à cet atelier applications in medicine, agriculture, sont des conférences et tutoriaux présentés au conservation and ecology. The last decade or so cours de l'automne 2001. En octobre, le Prof. has seen a remarkable growth in the field of Noel Cressie (Dep. of Math. and Statistics, Ohio evolutionary biology, due mainly to the State Univ.) présente les modèles graphiques hiérarchiques et leurs applications en interaction with molecular biology. Nucleotide, estimation de processus spatiaux (imagerie protein and, more recently, genomic data have cérébrale); en novembre, le Prof. Rolf Riedi proven to be invaluable sources of phylogenetic (Rice Univ., Texas) donne un exposé sur les information. processus multifractals; cet exposé est suivi par Phylogenetics is now a thoroughly inter- celui du Prof. Paul Scheunder, directeur du disciplinary field, involving researchers from Vision Lab. Department of Physics à biology, ecology, bio-chemistry, computer l'Universitée de Antwerp (Belgique), à propos science, mathematics and statistics. Inevitably, de traitement de l'information dans les images médicales. Les autres conférenciers sollicités such diversity in backgrounds has led to sont les Prof. Stella Atkins (Simon Fraser difficulties in communication between Univ.), Jacques Levy-Vehel (INRIA, Fr.) et researchers from different areas. The main goal Heinz-Otto Peitgen, directeur de CeVis & of SCOPH was to begin to break down some of MeVis à l'Université de Bremen (Germany). these barriers. We invited leading experts of phylogenetic technologies to present ninety- Showcase for Competing Technologies for minute lectures covering both background Phylogenetics (SCOPH) material and recent developments. The speakers April 19 – 21, 2001 were encouraged to stimulate discussion and Org.: David Bryant (Montréal), David Sankoff (Montréal) questions, and the attendees had the Invited speakers: Olivier Gascuel (Montpellier, France), Tandy Warnow (Austin), David Bryant, Andreas Dress opportunity to have their phylogenetic questions (Bielefeld, Germany), Kevin Nixon (Cornell), David Sankoff, answered by some of the top experts in the field. David Swofford, John Hulsenbeck (Rochester), Mike Steel The approach proved popular: so popular in fact (Canterbury, NZ), Tom Hagedorn, and Joe Felsenstein (U. Washington) that we were forced to limit the number of registrants to the conference. Phylogenetics is the study of evolutionary history: the patterns of speciation and

CRM Annual Report 2000 - 2001 23 S c i e n t i f i c A c t i v i t i e s

Aisenstadt Chair

The Aisenstadt Chair was endowed by Montréal philanthropist Dr. André Aisenstadt. Under its auspices, one or two distinguished mathematicians are invited each year for a period of at least one week, ideally one or two months. During their stay the lecturers present a series of courses on a specialized subject. They are also invited to prepare a monograph. At the request of Dr. Aisenstadt, the first of their lectures should be accessible to a wide audience. Previous holders of the Aisenstadt Chair are: Marc Kac, Eduardo Zarantonello, Robert Hermann, Marcos Moshinsky, Sybren de Groot, Donald Knuth, 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, Dan Voiculescu, James Arthur, Eugene B. Dynkin, David P. Ruelle, Robert Bryant, Blaine Lawson, Yves Meyer, Ioannis Karatzas, László Babai, Efim I. Zelmanov, Peter Hall, David Cox, Frans Oort, Joel S. Feldman, Roman Jackiw, and Duong H. Phong. The CRM was honoured to have as Aisenstadt chairholder, during the 2000-2001 theme year in Mathematical Methods in Biology and Medicine, Professors Michael S. Waterman of the University of Southern California and Arthur T. Winfree of the University of Arizona.

Professor Michael S. Waterman of its steering and programme committees. He University of Southern California has also served on many Editorial Boards, Michael S. Waterman including as co-founder and Editor-in-chief of is Professor of the Journal of Computational Biology and Associate Mathematics, of Editor of the Bulletin of Mathematical Biology, and Biological Sciences, of the Annals of Combinatorics. He has published Computer Science, and more than 150 journal articles, one book, and University Professor at edited or co-edited eight volumes. the University of Southern California. His research concentrates on using He obtained a B.S. and computational approaches to study molecular an M.S. in Mathematics sequence data. Currently the sequence databases from Oregon State University before earning an double in size every two years, and new M.A. and a Ph.D. in Statistics from Michigan developments in sequencing technology could State University. He started his academic career accelerate this rate of growth. The importance of at the Idaho State University before spending computational methods to molecular biology is more than five years at the Los Alamos National certainly growing proportionally. Part of his Laboratory, including two years as Project work has been to develop relevant and rigorous Leader. He took his current position in 1982. algorithms to compare and analyze nucleic acid and protein sequences. He was the first to Many awards have been bestowed on Professor introduce multiple gap weights to alignment Waterman, including being named Fellow of the algorithms and is co-developer of the Smith- American Association for the Advancement of Waterman algorithm. He is now studying the Science, of the Institute of Mathematical effects of different weighting schemes such as Statistics, of the John Simon Guggenheim Foundation, and of the American Academy of the Dayhoff matrix on the resulting optimal Arts and Sciences. He is also one of only eight alignments. Also he has been studying the USC professors to hold the rank of University expected progress of physical mapping Professor and the first person to be appointed experiments which depends on the cloning Celera Genomics Fellow. vector, the fingerprinting scheme, etc.

He has served the community in various Professor Waterman made two visits to the different ways, including as a member on CRM. During his first visit, he gave three talks. Scientific Advisory Boards, session chair at an Reading DNA Molecules, covered computational Oberwolfach meeting, member of the aspects of DNA sequencing which is at the Programme Committee of the 9th Genome intersection of molecular biology, biotechnology, Informatics Workshop in Japan, and co-founder and computing. In Estimating Optical Maps, he of the conference RECOMB, as well as member considered a fundamentally new experimental

24 Annual Report 2000-2001 CRM S c i e n t i f i c A c t i v i t i e s approach to constructing restriction maps called D. and Catherine T. MacArthur Prize in Optimal Mapping, developed by Schwartz et al. theoretical biology. His contributions to (1993), which can rapidly produce ordered cardiology were later recognized by the restriction maps of single DNA molecules by Einthoven Award given by the Netherlands fluorescence microscopy. He discussed the use Royal Academy of Sciences, the InterUniversity of a hierarchical Bayes model based on a mixture Cardiology Institute, and the Einthoven model with normal and random noise, a highly Foundation. Recently, he was awarded the computer-intensive method for which an Norbert Wiener Prize of 2000-2004 of the efficient algorithm is required. The Probability of American Mathematical Society and the Society Matching Random Maps considers the challenging for Industrial and Applied Mathematics for problem of estimating the probability of innovations related to biological rhythms. observing a random match as good as obtained from the comparison of ordered restriction maps He has served on various editorial boards produced by gel electrophoresis or by optical including Ecology & Ecological Monographs, mapping. In his second visit, Professor Journal of Theoretical Biology, Physica D, Waterman made two presentations. Sequence International Journal of Chaos and Bifurcations, Comparison and Database Searches touched upon and Chaos. He has written three well-known the dynamic programming approaches to books, including The Timing of Biological sequence analysis for the comparison of a DNA Clocks which was also published in French, or protein sequence with a database of known German, Russian, Dutch, and Japanese. He also sequences. He also developed the statistical wrote more than 160 papers. aspects of estimating statistical significance by Poisson approximation. Finally, in Oceans and Professor Winfree’s research has had a profound Islands: Physical Mapping of DNA, he looked at a impact on the important field of biological simple statistical model that yields formulas to rhythms, otherwise known as coupled non- predict progress of physical mapping projects linear oscillators. An experimental that are made by overlapping random clones. mathematician, he has set the agenda in that The case of clones with characterized ends was field. He was the first to determine the also covered. conditions under which a large population of coupled non-linear oscillators would Professor Arthur T. Winfree synchronize. Many original ideas that have since University of Arizona borne mathematical fruit were put forth by Arthur T. Winfree is Winfree in the course of this research. One was Regents Professor and the reduced description of a population of Professor of Ecology weakly coupled non-linear oscillators in terms of and Evolutionary the phase of each oscillator. In studying the Biology at the entrainment of biological clocks by pulses of University of Arizona. light, he realized that topological transitions He obtained a might occur as the amplitude of the stimulus Bachelor’s degree in changes. This led to a topological classification Engineering Physics that is used today to report the results of from Cornell virtually every phase-resetting experiment on a University and a Ph.D. in Biology from biological system. It also led him to the Princeton University. He began his academic realization that there must be special stimuli that career as Assistant Professor of Theoretical would make a non-linear oscillator phaseless, Biology at the University of Chicago before i.e., stop the oscillation. His notion of a phase moving to Purdue University. He is at the singularity has proved to be the key to the University of Arizona since 1986. understanding of spiral waves in two- dimensional and of scroll waves in three- Throughout his career, he has received a number dimensional excitable media, such as cardiac of honours and awards. In 1981, he received the tissue. The impact of these ideas on cardiac Japanese Society Promotion of Science Research electrophysiology has been enormous; indeed, Fellowship. He then received the John Simon they completely define the field. Guggenheim Memorial Fellowship and the John

CRM Annual Report 2000 - 2001 25 S c i e n t i f i c A c t i v i t i e s

During his one-month stay, Dr. Winfree gave many curious properties in three dimensions five talks. The first one, Vortices in Motionless which are better understood by computation. Media, looked at how certain chemical gels and The properties of rings in excitable media were living heart muscle share an ability to excite in a further explored in Linked and Knotted Vortex way that propagates by chemical reaction or Rings in Excitable Media and in Some Challenging bioelectric currents. Both media support two Puzzles Suggested by Vortices in Excitable Media. modes of propagation: one in a rectilinear Finally, Phase Patterns in Biological and velocity, like sound or light, and one with an Chemical Oscillators took a look at circadian angular, rotational velocity, like a tornado, the body clocks whose synchronization by the latter causing sudden cardiac death. Much has light/dark cycle determines a global pattern, been learned about it from the chemical analogy with singularities at the poles. Chemical and the mathematical principles common to oscillators also exhibit phase patterns in three- both. In Unsolved Problems of the Heart, he dimensional space. These seemed hard to considers the two kinds of action potential of the observe, but there is a computationally intensive electric behaviour of the heart muscle: the optical trick that makes it easy. Filaments of linearly propagating pulse of the textbooks, and phase singularity are seen. alternative vortex-like solutions. The latter have

26 Annual Report 2000 - 2001 CRM S c i e n t i f i c A c t i v i t i e s

General Programme 2000-2001 The CRM’s general programme funds a wide variety of scientific events, both on-site and around the world. Whether it be for specialized workshops for a small number of researchers, large meetings for hundreds of participants or activities for high school or undergraduate students, the general programme promotes research in mathematical sciences at all levels. The programme is quite flexible, to allow for opportunities as they arise.

Canadian Journal of Statistics Read Les séries asymptotiques jouent un rôle Paper Session important en équations différentielles et en June 4, 2000, Ottawa, Ontario dynamique nonlinéaire. Elles contiennent des Org. : Christian Genest (Laval) informations précieuses sur les solutions des During the Annual Meeting of the Statistical équations et sur la dynamique. Society of Canada, a major scientific contribution Basée sur les travaux de Ellis Kolchin et Joseph was read and discussed publicly. The paper is Fels Ritt, l’algèbre différentielle moderne est The Estimating Function Bootstrap of John D. présentement un domaine très actif de Kalbfleisch (Waterloo) and Heifang Hu recherche. À l’intérieur de cette discipline, qui a (Singapore). The paper was discussed by Jim eu comme point de départ l’étude des Zidek (British Columbia), Tom Diccicio (Cornell) transcendantes définies par les équations and Rob Tibshirani (Stanford), Christian Léger différentielles, on distingue deux directions: la (Montréal), and Angelo Canty (Concordia). This théorie de Galois différentielle dont la théorie event, inspired by a similar activity of the Royal moderne part d’un travail de Kolchin (1948) et la Statistical Society of the United Kingdom, was a géométrie algébrique différentielle ayant comme first for the Canadian Journal of Statistics. More point de départ un travail de Ritt (1938.) than 100 participants attended the event. Les problèmes de finitude en dynamique Québec Math Camp 2000 nonlinéaire qui depuis longtemps ont défié les mathématiciens, impliquent l’usage des séries June 2000, Université du Québec à Trois-Rivières, Trois- Rivières asymptotiques et entraînent des relations avec Org. : Harry White (Université du Québec à Trois-Rivières) l’algèbre différentielle. Le camp mathématique est une activité Le thème de l’Atelier fut celui d’explorer et parrainée par l'Association mathématique du approfondir les interconnexions entre ces trois Québec (AMQ) dans le but de mettre en contact directions de recherche ainsi que leurs des étudiants doués pour les mathématiques applications aux problèmes de finitude en avec des mathématiciens professionnels. Les systèmes dynamiques nonlinéaires. campeurs sont sélectionnés parmi ceux qui ont le Un autre but de l’Atelier a été celui de mieux réussi au concours de l'AMQ (niveau familiariser les chercheurs de ces disciplines collégial.) avec les travaux des spécialistes en théorie des modèles qui ont introduit des nouvelles Short programme: Asymptotic series, approches portant sur le thème de l’Atelier differential algebra and finiteness (exemples sont: la notion de o-minimalité ainsi problems in non-linear dynamical que les travaux de van den Dries sur la classe systems universelle des transséries d’Ecalle) et donner la June 18 - July 7, 2000 Org. : Dana Schlomiuk (Montréal), Luc Bélair (UQAM) possibilité à des spécialistes en théorie des Invited participants F. Dumortier (Limburgs Universitairt modèles de discuter avec les autres participants. Centrum, Diepenbeck, Belgium), J-P. Françoise (Université Le programme a été conçu de sorte à permettre de Paris VI), Yu. Il’yashenko (Moscow Independent University and Cornell University), J. Llibre (Universitat de nombreuses discussions. De nouveaux Autònoma de Barcelona), C. Miller (Ohio State University), travaux de collaboration ont été initiés durant les R. Moosa (Univ. of Ill. Urbana), A. Mourtada (Univ. de trois semaines de l’Atelier et ces collaborations Bourgogne), P.-P. Rolin (Université de Bourgogne), Ch. Rousseau (Univ. de Montréal), P. Speissegger (Univ. of se sont poursuivies après. L’étendue du thème Wisconsin), H. Zhu (Univ. of Waterloo), A.Buium (Steklov ainsi que la participation des spécialistes à Institute of Mathematical Sciences and Univ.Louis Pasteur Strasbourg), A.Buium (Univ. of New Mexico), Vadim orientations différentes mais ayant des Kaloshin (Courant Institute), S. Yakovenko (Weitzmann problèmes reliés a engendré une atmosphère qui Institute of Science). fut très stimulante.

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En début d’atelier, cinq mini-cours furent Fête en l'honneur de Walter Hengartner présentés au bénéfice des étudiants gradués et «Hengartnerfest» des chercheurs nouveaux dans le domaine: July 7 – 8, 2000 Org. : Richard Fournier (CRM), Paul Gauthier (Montréal), Andrey Bolibrukh (5 heures) Asymptotic series Thomas Ransford (Laval) and Differential Equations; Alexandru Buium (5 heures) Differential algebraic geometry and Cette conférence visait à honorer la carrière du Diophantine Geometry; Vadim Kaloshin (5 heures) professeur Walter Hengartner à l'occasion de sa Finiteness Theorems in Dynamical Systems; L. Van retraite de l'Université Laval. Les conférences den Dries (4 heures) Logarithmic-exponential series portaient sur divers sujets de la théorie des and o-minimality; Sergei Yakovenko (5 heures) fonctions reliés à ses travaux, notamment sur Quantitative Theory of Ordinary Differential l'analyse complexe. La fête a eu lieu durant le Equations and tangential Hilbert 16th problem. Séminaire de Mathématiques Supérieures dont le sujet était Approximation, analyse complexe et Séminaire de mathématiques supéri- théorie du potentiel. Les conférenciers invités ont eures: Approximation, Complex été Daoud Bshouty (Technion-Israel), Ted Analysis, and Potential Theory Suffridge (Kentucky), Peter Duren (Michigan), July 3 - 14 , 2000, Université de Montréal, Montréal Walter Hayman (Imperial College), Line Org. : A. Daigneault (Montréal), N. Arakelian (Armenian Baribeau (Laval), Tom Bagby (Indiana) et Paul National Academy of Sciences), P. Gauthier (Montréal), D. Gauthier (Montréal). Armitage (Queen's University of Belfast), D. Drasin (Purdue), A. Gonchar (Steklov), S. Lessard (Montréal), G. Sabidussi (Montréal) Histoires de structures et de catégories August 10, CRM The 2000 SMS focussed on the interplay between Org. : Michael Barr (McGill) & Liliane Beaulieu (CRM) complex analysis and potential theory. Complex Le développement des mathématiques du analysis relies heavily on potential theory, since vingtième siècle a été marqué par les concepts the absolute value (as well as the logarithm) of a unificateurs de structures et catégories. Toutefois holomorphic function is a subharmonic function. la valeur des théories que ces termes ont In the other direction, much research in potential désignées, quant à elle, fait encore l'objet de theory has been inspired by the attempt to seek controverses rétrospectives dans la communauté analogues to complex phenomena. This is des mathématiciens. Cet atelier, qui réunit especially true in approximation theory, a mathématiciens, historiens et philosophes des central theme of this SMS. mathématiques, s’est donné pour objectif de The main lectures were given by A. Ancona faire le point sur les histoires des structures et de (Paris-Sud), Topics on Martin Boundaries, Positive la théorie des catégories. Par son contenu, cet Harmonic Functions and Green's Functions; N. atelier se situe dans le prolongement des ateliers Arakelian (Armenian National Academy of d'apprentissage et du séminaire qu'ont organisés Sciences), Approximation and Value Distribution; Luc Bélair (UQAM) et Jean-Pierre Marquis D. Armitage (Queen's University of Belfast), (Montréal) en 1998, 1999 et 2000. Uniform and Tangential Harmonic Approximation; À ce jour, les historiens qui se sont penchés sur T. Bagby (Indiana), Sobolev Spaces and I’histoire des structures ont surtout parlé de Approximation Problems for Differential Operators; I’histoire de différentes structures M. Bonk (Michigan), Negative Curvature in Real mathématiques. Peu de travaux se sont and Complex Analysis; H. Chen (Nanjing Normal intéressés au développement du concept général University, China) The Bloch Constant for One and de structure, comme notion mathématique ou Several Variables, Holomorphic and Harmonic métamathématique. L’histoire de la théorie des Mappings; D. Drasin (Purdue), Approximation catégories, pour sa part, est encore à faire, mais Theorem, Normal Families, and Meromorphic puisque plusieurs protagonistes du Functions; S. Gardiner (University College, développement de cette théorie peuvent livrer Dublin), Harmonic Approximation and its leurs témoignages, il convient de leur donner Applications; P. Gauthier (Montréal), d’abord la parole. En outre, nous sommes Approximation on Riemann Surfaces and Complex intéressés à I’essor des catégories en Amérique Manifolds; T. Ransford (Laval), Jensen Measures; du Nord, en général, et dans les universités and A. Stray (Bergen), Simultaneous. montréalaises, en particulier. Approximation in Various Function Spaces

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Les principaux exposés de ce cette année furent: XIIth Meeting on the Representation Michael Barr (McGill) Category theory and Theory of Algebras homological algebra, Jean-Pierre Marquis September 29 – 30, 2000, Bishop’s University, Lennoxville Org. : Ibrahim Assem (Sherbrooke), Andrew Dean (Montréal) Classes, universaux et types: structures (Bishop’s), François Huard (Bishop’s), Pierre-Yves Leduc catégoriques et structures conceptuelles, Colin (Sherbrooke), Shiping Liu (Sherbrooke) Categories along the th McLarty (Case Western) This is the 12 of a series of annual meetings Seaway. held each autumn, alternately at the Université Un deuxième volet est prévu pour I’année 2000- de Sherbrooke and at Bishop's University. These 2001. Voir la rubrique Activités futures de ce meetings are devoted to the Representation rapport. Theory of Associative Algebras, an area of mathematics which is presently very well Colloque LACIM 2000 developed, and connected to many other areas September 7 – 10, 2000, UQAM, Montréal (such as, for instance, commutative algebra, Org.: Pierre Leroux (UQAM), Robert Bédard (UQAM), Srecko Brlek (UQAM) , Manon Blais (UQAM). algebraic geometry, algebraic topology, Co-sponsors: Université du Québec à Montréal (UQAM), le singularity theory and Lie theory). Ministère de la Recherche, de la Science et de la This year's programme included invited talks of Technologie (Québec). 45-50 minutes given by Luchevar Avramov Invited speakers: Jean Berstel (Marne-la-Vallée), Richard (Purdue), Vlastimil Dlab (Carleton), Alex Ehrenborg (KTH), Nadia El-Mabrouk (Montréal), Dominique Foata (Strasbourg and UQAM), Adriano Garsia (UCSD), Martsinkovsky (Northeastern), Cristian Novoa Pierre Lalonde, Christophe Reutenauer (Strasbourg,UQAM), (Catholic University of Goias, Brazil), Claus Richard Stanley (Massacchusetts Institute of Technology), Xavier Viennot (LaBRI, Bordeaux I), Doron Zeilberger Michael Ringel (Bielefeld), Shaobin Tan (Fields), (Temple). Dan Zacharia (Syracuse), and Rita Zuazua L'année 2000, année mondiale des (National Autonomous University of Mexico). mathématiques sous l'égide de l'UNESCO, marquait, parmi tant d'autres anniversaires, les Conférence «Adrien Douady» October 20 – 21, 2000 dix ans du Laboratoire de combinatoire et Org. : Dana Schlomiuk (Montréal), Norbert Schlomiuk d'informatique mathématique de l'UQAM. Les (Montréal). Bodil Branner (Technical University of disciplines couvertes par le LaCIM ont connu Denmark), Wellington de Melo (IMPA), Raphaël Douady (CNRS, ENS de Cachan), John Hubbard (Cornell Univ.), des développements remarquables au cours des Mikhail Lyubich (SUNY - Stony Brook), John Milnor dix dernières années, que ce soit sur le plan (SUNY - Stony Brook), Raghavan Narasimhan (Univ. of théorique, en combinatoire énumérative ou Chicago), Curtis McMullen (Harvard), Mitsuhiro Shishikura (University of Hiroshima). algébrique, ou au niveau des applications, en analyse classique, en calcul formel, en géométrie This conference was held to celebrate the 65th algorithmique, en chimie combinatoire, en birthday of Adrien Douady and to highlight his physique statistique, et, plus récemment, en bio- numerous important contributions to informatique. mathematics, most notably to dynamical systems and to analytic geometry. The two-day event Le but du colloque était de faire le point sur had a large turnout, who came to hear some very quelques-uns de ces développements en eminent speakers discuss their work and its réunissant des experts internationaux de ces relation to Adrien Douady’s. Talks included domaines. Nous souhaitions également donner B.Branner, Quasi-conformality and surgery in la chance aux chercheurs jeunes ou plus holomorphic dynamics, R.Douady, EDP, controle expérimentés de faire connaître leurs résultats stochastique et evaluation des options, J.Hubbard, récents. Le programme comprenait dix Exploring the parameter space for Henon mappings, conférences plénières ainsi que des M.Lyubich, Quadratic-like maps, complex communications sélectionnées par le comité renormalization, and their implications, scientifique. Afin de favoriser une plus grande C.McMullen, Dynamics on K3 surfaces, W. de interaction, ces communications ont été Melo, Regular or stochastic dynamics in real analytic regroupées à l'intérieur d'une séance d'affichage. families of unimodal maps, J.Milnor, Dynamics and Un numéro spécial de la revue Discrete the brain, R.Narasimhan, Gromov’s elliptic Oka Mathematics sera consacré aux actes du Colloque principle, M. Shishikura, Thurston’s algorithm for sous la direction de Gilbert Labelle et Pierre exponential maps. Leroux.

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A Series of Conferences by Professor The joint FI-CRM program was the main Alexei Miasnikov international event on these subjects to take March 2 – 30, 2001 place in 2000-2001. It was preceded by the Org. : O. Kharlampovich (McGill) program on Infinite Dimensional Lie Theory and This was a series of ten lectures on equations Its Applications. As a bridge between the two over free groups and free semigroups. In programs, Eckhard Meinrenken gave a graduate theoretical computer science, this topic is known course on Symplectic Geometry during the first as the unification problem. Professor Miasnikov semester. discussed recent developments in this area The first activity of Symplectic Topology, related to algebraic geometry over groups, Geometry and Gauge Theory Program was the Tarski's problems, and complexity of the workshop on Quasiclassical and Quantum unification problem. Structures held from January 9 to 14, 2001, organised by Etingof and Khesin. The main Symplectic and Contact Topology, topics included classical and quantum integrable Quantum Cohomology, Symplectic systems, Macdonald theory, Poisson-Lie groups, Field Theory and Higher-Dimensional quantum groups, and quantization of infinite Gauge Theory dimensional Lie algebras. It attracted some of the March 23 - April 7, 2001, Fields Institute, Toronto, Ontario, & CRM best mathematicians and mathematical Org. : S. Donaldson (London), B. Dubrovin (Trieste), Y. physicists: Kac, Jimbo, A. Kirillov, Miwa, Eliashberg (Stanford), A. Givental (Berkeley), B. Khesin Reshetikhin, and many others. The interplay (Toronto), F. Lalonde (Montréal) between algebra and geometry, between The Symplectic Topology, Geometry and Gauge mathematics and physics gave rise to very January 2001 to June 2001 was the very first stimulating discussions. thematic program organised jointly by the Fields During the two months from mid-January to Institute and the CRM. mid-March, three graduate courses were given At the moment of writing these lines, the by Jeffrey, Khesin, and Meinrenken, and a week semester still had a month and a half to go – the of lectures by Eliashberg. With about eight last workshop on Hamiltonian Group Actions postdoctoral fellows and many long-term and Quantization had not yet taken place. But it visitors, these activities were an essential part of is certainly not premature to say that this the program. The courses covered the following semester has been a success from many points of topics: Symplectic Geometry and Hamiltonian view. Group Actions by Jeffrey; Infinite Dimensional First of all, the subject itself is amongst the Lie Groups and Gauge Theory by Khesin; deepest and most exciting areas of research in Moduli Spaces of Flat Connections by pure mathematics and in theoretical physics. Meinrenken; and finally an introduction to Symplectic geometry is a classical subject, whose Symplectic Field Theory by Eliashberg. This roots go back to the development of analytical minicourse by Eliashberg was splendid: it ran mechanics by the French school in the eighteenth from Monday to Friday, 2 hours a day, and century. But gauge theory and symplectic covered the essential features of Symplectic Field topology are much more recent: the former was theory. This theory was introduced very recently introduced in physics in the middle of the by Eliashberg, Givental and Hofer, and aims to century, while symplectic topology really began give an extension of the usual notion of Gromov- in the seventies when the first case of the famous Witten invariants when one replaces a closed Arnold conjectures was solved. The symplectic manifold by a symplectic manifold mathematical development of the former whose boundary realises a cobordism between received a definitive impulse when Donaldson contact manifolds. The theory intertwines applied gauge theoretic methods to the study of contact homologies (Eliashberg), homological four-dimensional topology. The introduction of algebras (Givental) and symplectic homologies the pseudoholomorphic method by Gromov in (Floer-Hofer). It has some very interesting 1985 had a similar effect on symplectic topology. applications to invariants and obstructions in Taubes’ recent work on the Seiberg-Witten symplectic topology and contact geometry. invariants has established a strong link between The long-awaited two-week workshop on the two fields. Symplectic and Contact Topology, Quantum

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Cohomology, Symplectic Field Theory and The last workshop on Hamiltonian Group Higher-Dimensional Gauge Theory was held Actions and Quantization will be held from June from March 23 to April 7. The first week took 4 - 13, 2001. It is organised by Audin, Hurtubise, place at the Fields Institute and the second week Jeffrey, and Meinrenken. The main topics at the CRM. It was organised by Donaldson, include geometric quantization and the Eliashberg, Givental, Khesin, and Lalonde. The Guillemin-Sternberg conjecture, generalized organisers reserved two full VIA rail cars with moment map theories, symplectic cobordisms, meals to take the participants from Toronto to relation with geometric invariant theory, Montreal during the weekend between the two cohomology rings of symplectic quotients, and weeks. This workshop was definitely one of the flat connections on Riemann surfaces. The list of highlights of the year in symplectic geometry speakers can be found on the Fields website. and topology. It gave rise to lots of interactions, (http://www.fields.utoronto.ca/programs/scienti discussions, and joint works that were taking fic/00-01/symplectic/hamiltonian/) place everywhere, even in the train. Its main The participants were especially pleased by the goal was to discuss the recent developments in quality of the work done by the staff and the the construction and computations of invariants kindness of the welcome that they received both of symplectic and contact manifolds and their in Toronto and in Montreal. I would like to take automorphism groups, using methods of the this opportunity to thank Alison Conway and theory of J-holomorphic curves, as well as those Elena Kaufman at the Fields Institute, and Louis from gauge theory and dynamical Hamiltonian Pelletier and Josée Laferrière at the CRM. systems. The theory of these invariants is tightly related to enumerative algebraic geometry, Knots in Montreal quantum cohomology and mirror symmetry. April 7-8, 2001 Recent results, of both mathematicians and Org.: S. Boyer (UQAM) & A.S. Sikora (UQAM) physicists, manifest the existence of surprising This short conference brought together correspondences between various gauge theories mathematicians interested in knot theory and 3- on real and complex manifolds. The level of dimensional topology from Canada and the maturity and clarity that the whole field has now northern and eastern parts of the United States. attained, the fecundity of its applications and the It took place at the Université du Québec à depth of its conceptual framework are the Montréal. striking features of this year’s event. The Speakers included D. Rolfsen, Orderable 3- workshop was such a success that we had to manifold groups, W. Menasco, Y. Rong, F. Luo, limit the number of applicants – the rooms were Grothendieck's reconstruction principle for SL(2) full both in Toronto and in Montreal – so that characters. L. H. Kauffman, Virtual Knot Theory sometimes the workshop looked more like a and Detecting Knots with the Jones Polynomial T. conference. Some of the main speakers included Mattman, Seifert surgeries which do not arise from Auroux, Chekanov, Eliashberg, Fuchs, Fukaya, primitive/Seifert constructions T. Kerler, Integral Getzler, Kotschick, McDuff, Parker, Polterovich, TQFT's, cut-numbers, and the mapping class groups Salamon, Sikorav and many others. The J. Conant, Grope cobordism of classical knots J. H. organisers have decided to publish the Przytycki, Lagrangian tangles in Fox coloring spaces proceedings of that workshop in the Fields and theirt-deformations Institute Communications Series.

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CRM Prizes CRM-Fields Prize Professor Tutte’s research is in graph theory and In 1994 the Centre de recherches related areas of discrete mathematics, and he has mathématiques (CRM) and the Fields Institute done so for the last 60 years or so. This was the announced the creation of a new prize to be period of coming of age of graph theory; it awarded for exceptional contributions to the changed from being a collection of rather easy mathematical sciences. The recipient of the theorems and some good open problems, to prize is chosen by the Comité consultatif of the being a well-developed branch of mathematics, CRM and the Scientific Advisory Committee of stocked with rich and deep results. There were the Fields Institute according to the criterion of only a few prime movers who brought this excellence in research. The prize consists of about; the ones that come to mind are Erdös, Wagner and Halin, and Tutte. Professor Tutte both a $5 000 award and a medal, and the winner is required to give a lecture at the CRM took the opportunity to do initial, and the Fields Institute. The past recipients are: groundbreaking work in several new areas that H.S.M. Coxeter (1995), G.A. Elliot (1996), J. were later to grow to major fields of discrete Arthur (1997), R.V. Moody (1998), Stephen A. mathematics. Cook (1999), and Israel Michael Sigal (2000). The CRM-Fields Institute 2001 Prize is Few theorems in mathematics are honoured by awarded to Dr. William T. Tutte. the general public by naming them after the mathematician who proved them. Professor William T. Tutte is Tutte’s wide influence in the field of Distinguished combinatorics can be illustrated by pointing out Professor Emeritus of a number of results commonly named after him. Combinatorics and For somebody working in matching theory, Optimization at the Tutte’s Theorem means his characterization of University of regular graph having a perfect matching — for a Waterloo. Professor matroid theorist, his characterization of regular Tutte received his matroids — for somebody studying Hamilton education at cycles, it means his result that every 4-connected Cambridge planar graph has a Hamilton cycle. In algebraic University, graduating with his Ph.D. in 1948. combinatorics, there is the Tutte polynomial of a He then joined the faculty of the University of graph and of a matroid. The important Toronto and moved to the University of complexity classification by Welsh and his group Waterloo in 1962. of many graphical enumeration problems uses the Tutte plane. He is a Fellow of the Royal Societies of London and Canada, of the American Association for the In summary, William Tutte grabbed all the best Advancement of Science and of the New York theorems while they were still up for grabs. But Academy of Sciences. He also received a Killam more than that; his work (both written and Prize, the Tory Medal of the Royal Society of lecture) was really beautiful — it was always a Canada, and was Jeffery-Williams Lecturer of fantastic experience to watch him take on some the Canadian Mathematical Society. He was the problem, apply some strange algebraic Editor-in-Chief of the Journal of Combinatorial machinery to it, and make showers of Theory during 17 years and is the Honorary consequences fall out, in the most elegant way. Director of the Centre for Applied Cryptographic Research. He is the author of more than 160 articles and 5 books.

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André-Aisenstadt Prize symplectic manifolds formed by dividing out Created in 1991, the André-Aisenstadt symmetries of a symplectic manifold with a Mathematics Prize is intended to recognize and group action. His first major result in that area reward talented young Canadian came in 1994 when he proved a longstanding mathematicians. The Prize, which is given for conjecture of Guillemin and Sternberg research achievement in pure and applied concerning the quantization of symplectic mathematics, consists of a $3000 award. The quotients, better known as quantization commutes recipient is chosen by the CRM Advisory with reduction. In collaboration with Sjamaar, Committee. At the time of nomination, Meinrenken has now extended his previous candidates must be Canadian citizens or results to singular symplectic quotients. permanent residents of Canada, and no more than seven years from their Ph.D. The previous A second important topic in Meinrenken's work winners of the André-Aisenstadt Prize were: was the development of techniques to study Niky Kamran (1991), Ian Putnam (1992), moduli spaces of flat connections on Riemann Michael Ward and Nigel Higson (1994), Adrian surfaces. His first approach (with Woodward) S. Lewis (1995), Henri Darmon and Lisa Jeffrey involved studying Hamiltonian actions of loop (1996), Boris Khesin (1997), John Toth (1998), groups leading to a proof of the Verlinde and Changgeng Gui (1999). CRM was formula. Another powerful approach (with delighted to award the 2000 André-Aisenstadt Alekseev and Malkin) involves studying Prize to Dr. Eckhard Meinrenken of the manifolds with group actions and a University of Toronto. generalization of the moment map that takes values not in the dual of the Lie algebra, but in Eckhard Meinrenken the corresponding Lie group. Finally, with completed a Ph. D. in Alekseev and Woodward, Professor Meinrenken Physics at Freiburg has obtained generalizations of many of the University in 1994. He standard results associated to manifolds was a Postdoctoral equipped with Hamiltonian group actions, such Research Fellow at the as the convexity theorem, the localization Massachusetts formula for equivariant cohomology, and the Institute of Duistermaat-Heckman theorem. Technology from 1995 to 1997 before Professor Meinrenken received his Prize on becoming Assistant Professor of Mathematics at February 9, 2001 at CRM. He spoke on Matrices, the University of Toronto in 1998. He was Moment Maps, and Moduli Spaces where he promoted to Associate Professor in 2000. explained the main properties of non-linear moment maps, a mathematical generalization of Professor Meinrenken works in symplectic angular momentum in classical mechanics. He geometry, a very active and rapidly expanding also discussed their applications to eigenvalue mathematical discipline whose roots lie in problems for matrices and to moduli spaces of classical mechanics. He works on group actions flat connections over a surface. arising as Hamiltonian flows on symplectic manifolds, and on symplectic quotients,

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CRM-CAP Prize Mandelbrot's fractal geometry and applied to the Awarded for the first time in 1995, the CRM- percolation phenomenon in disordered media. CAP Prize is given for outstanding His more recent work on the effect of electron- contributions to theoretical and mathematical electron interactions in solids has contributed to physics. It consists of a $2000 award and a our understanding of high-temperature medal. Previous winners were Werner Israel superconductivity. In particular, he has (1995), William G. Unruh (1996), Ian Affleck developed efficient theoretical methods for the (1997), J. Richard Bond (1998), David J. Rowe study of physical systems in which conduction (1999), and Gordon W. Semenoff (2000). The electrons are strongly correlated, that is, in 2001 CRM-CAP prize has been awarded to Dr. which they interact too strongly to be treated as André-Marie Tremblay. free particles, but not strongly enough to be completely localized. André-Marie Tremblay is Professor CRM-SSC Prize at Université de Sherbrooke. He holds In 1999, the Centre de recherches a B.Sc. from mathématiques (CRM) and the Statistical Université de Society of Canada created the CRM-SSC Prize Montréal and a Ph.D. in statistics in recognition of outstanding from the contributions to the Statistical Sciences during Massachusetts the recipient’s first 15 years after earning a Institute of doctorate. The CRM-SSC Prize in Statistics Technology. After a two-year postdoctoral consists of a $3000 award and a medal. The fellowship at Cornell University, he joined the recipient is chosen by a joint CRM/SSC Physics Department at Université de advisory committee, consisting of three Sherbrooke. members named by the SSC and two, including a president, by the CRM. Previous Professor Tremblay was awarded the Herzberg winners were Christian Genest (1999) and Medal of the Canadian Association of Physicists Robert Tibshirani (2000). This year, the Centre (CAP) in 1986, the Steacie Fellowship from de recherches mathématiques and the NSERC in 1987, and a Killam Fellowship from Statistical Society of Canada have awarded the 1992-1994. He is a member of the Canadian CRM-SSC 2001 Prize in Statistics to Dr. Colleen Institute for Advanced Research and holds a Cutler of the University of Waterloo. Canada Research Chair on the Condensed Colleen Cutler grew Matter Physics at Université de Sherbrooke. He up in Manitoba where is the author of over one hundred publications in she received her early well-known scientific journals. schooling. She received a Bachelor of The CRM-CAP Prize in Theoretical and Science degree from Mathematical Physics was awarded to Professor the University of Tremblay for his outstanding contributions to Manitoba, and theoretical condensed matter physics, including Masters and PhD progress on the challenging problem of degrees from Carleton understanding the behavior of strongly University, the latter in 1985 under the correlated electron systems. André-Marie supervision of Donald Dawson. She was on Tremblay is well known for his original faculty in the Department of Statistics at the contributions to the theory of solids over the last University of Manitoba from 1983-1986. Since twenty years. He has developed several 1986 she has been a faculty member in the theoretical methods aimed at predicting the Department of Statistics and Actuarial Science at behaviour of electrons in, among other things, the University of Waterloo, where she holds the metals, disordered materials, and rank of Professor. superconductors. He is one of the inventors of the multifractal concept, inspired by

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Professor Cutler's work has been recognized in knowledge to researchers outside the various ways. Among the major invited mathematics and statistics communities. Her presentations that she has delivered, note the fundamental results on fractal dimensions and IMS Special Invited Paper at the 7th Vilnius their estimation are major contributions at the Conference on Probability Theory and interface between dynamical systems and Mathematical Statistics/22nd European Meeting statistics, and are well known by physicists and of Statisticians and SPA 98, the 25th International other scientists. She was a pioneer in the Conference on Stochastic Processes and their rigorous mathematical study of the relations of Applications sponsored by the Bernoulli Society. these quantities and their statistical estimation where much of the published research was Dr. Cutler's work has had a very substantial empirical or intuitive. She has also made impact in probability and statistics, but also in important contributions to the problem of other areas of science. It is particularly distinguishing between stochastic and noteworthy that she has published in some of deterministic chaotic time series. Finally, her the very best journals of statistics and work on the scaling behaviour of probability probability, but also of mathematics and physics, measures is widely used and cited by including review papers that have reached a mathematicians. broad readership and helped a lot to spread out

CRM Annual Report 2000 - 2001 35 S c i e n t i f i c A c t i v i t i e s

Members’ Seminars & Special Events

The members of the CRM are encouraged to organize seminars and other scientific activities during their stay at the CRM. These activities take the form of courses, workshops and research seminars

December 6, 2000 Post-doctoral Fellows Seminar Emmanuel Montoki, Univ. de Montréal Org.: Pietro-Luciano Buono (CRM) Méthodes topologiques appliquées aux équations March 7, 2001 différentielles du second ordre Pietro-Luciano Buono, CRM December 13, 2000 Equivariant Bifurcation Theory Emmanuel Montoki, Univ. de Montréal March 28, 2001 Méthodes topologiques appliquées aux équations Marco Bertola, CRM différentielles du second ordre II (Nonperturbative) Quantum Field Theory in January 15, 2001 presence of Gravitation A. Granas, Univ. de Montréal April 11, 2001 Théorie des ANR's et analyse non linéaire Steve Allen, CRM January 23, 2001 Contours actifs géométriques en imagerie: théorie et A. Granas, Univ. de Montréal applications Théorie des ANR's et analyse non linéaire II Seminar in Non-linear Analysis January 31, 2001 Org.: Marlène Frigon, (Univ de Montréal) Emmanuel Montoki, Univ. de Montréal October 4, 2000 Equations différentielles du second ordre avec Nicolas Beauchemin, Univ. de Montréal opérateur monotone Introduction à la théorie des points critiques February 7, 2001 multivoques Emmanuel Montoki, Univ. de Montréal October 18, 2000 Equations différentielles du second ordre avec Nicolas Beauchemin, Univ. de Montréal opérateur monotone II Introduction à la théorie des points critiques February 21, 2001 multivoques II Alexandre Girouard, Univ. de Montréal October 25, 2000 Introduction à l'homologie relative Tomasz Kaczynski, Univ. de Sherbrooke February 28, 2001 L'indice de Conley d'une application continue: de la Salem Rabhi, Univ. de Montréal théorie au calcul Solutions des équations elliptiques et indice de Morse November 1, 2000 March 7, 2001 Paul Deguise, Univ. de Moncton Paul Deguise, Univ. de Moncton Introduction aux applications KKM Quelques résultats en théorie de coincidence November 8, 2000 March 14, 2001 Iddris Addou Salem Rabhi, Univ. de Montréal Nombre de solutions de problèmes aux limites Solutions des équations elliptiques et indice de Morse elliptiques quasi-linéaire par la méthode de March 21, 2001 quadratures A. Granas, Univ. de Montréal November 22, 2000 Prolongement d'applications compactes et le principe Nicolas Beauchemin, Univ. de Montréal de Leray-Schauder dans les ANRs. Méthodes variationnelles appliquées aux inclusions aux dérivées partielles March 28, 2001 November 29, 2000 A. Granas, Univ. de Montréal Nicolas Beauchemin, Univ. de Montréal Prolongement d'applications compactes et le principe Méthodes variationnelles appliquées aux inclusions de Leray-Schauder dans les ANRs. II aux dérivées partielles II

36 Annual Report 2000 - 2001 CRM S c i e n t i f i c A c t i v i t i e s

April 11, 2001 C-* algebras of pseudodifferential operators Noha El Khattabi, Univ. Mohamed V, Rabat inpolyhedrons Sur et sous-solutions dans la théorie des équations November 30, 2000 différentielles Henning Samtleben April 25, 2001 Gauged supergravity in three dimensions Alexandre Girouard, Univ. de Montréal December 7, 2000 Théorie de Morse en analyse non linéaire Dmitri Scherbin, CRM May 2, 2001 Fermionic represenation for basic hypergeometric A. Granas, Univ. de Montréal functions related to Schur polynomials Théorèmes de point fixe dans les ANRs The Langlands Geometric Programme May 16, 2001 Org.: Jacques Hurtubise (McGill) Alexandre Girouard, Univ. de Montréal Inégalités d Morse January 13, 2000 Eyal Z. Goren, McGill Univ. May 30, 2001 Vector Bundles Alexandre Girouard, Univ. de Montréal Applications de la théorie de Morse aux équations January 27, 2000 différentielles Eyal Z. Goren, McGill Univ. Vector Bundles, II Analysis Seminar CRM-ISM February 10, 2000 Org.: Paul Gauthier (CRM & Univ. de Montréal) Jacques Hurtubise, CRM & McGill Univ. June 2, 2000 Hitchin's integrable systems on the moduli of stable Javad Mashreghi, McGill Univ. pairs Paley-Wiener Functions on the Real Line March 9, 2000 June 9, 2000 Jacques Hurtubise, CRM & McGill Univ. Alexandre Girouard Quantification des systèmes de Hitchin Volume de la n-boule et mesure de Hausdorff March 28, 2000 June 16, 2000 Henri Darmon, McGill Univ. Richard Fournier, CRM Correspondance Fonctions-faisceaux Sur le lemme de Jack Seminar in Mathematical Physics June 23, 2000 Org.: John Harnad & Marco Bertola (CRM & Univ. Jean-Philippe Samson de Montréal) Sommation complexe de séries réelles September 19, 2000 July 21, 2000 Hartmut Fuehr, Technische Univ. Dominic Rochon, Univ. de Montréal Continuous Wavelet Transforms and Plancherel Dynamique bicomplexe » Theory of Locally Compact Groups July 28, 2000 September 26, 2000 Marta Kosek Univ. Jagiellónski Ametepe Lionel Hohoueto, Concordia Univ. Extremal function of Julia Type sets in Cm Coherent States lattices of Semi-direct Product August 25, 2000 Groups Sébastien Manka, DMS October 3, 2000 Familles normales et théorème de Picard Marco Bertola, CRM & Concordia Univ. September 1, 2000 Mass Spectra Generation by dimensional reduction Eduardo Zeron, CRM November 14, 2000 Topology of rationally convex sets Xifang Cao, CRM & Univ. Yangzhou Study Workshop: Physique Bäcklund transformations on Weingarten surfaces mathématique (Systèmes intégrables) November 28, 2000 Org.: John Harnad & Marco Bertola (CRM & Univ. Anatole Odzijewicz, Univ. of Bialystok, Poland de Montréal) Multiboson computations using Hahn polynomials September 28, 2000 Alexey Kokotov

CRM Annual Report 2000 - 2001 37 S c i e n t i f i c A c t i v i t i e s

January 9, 2001 Isomonodromic deformations and Hurwitz spaces: Jorgen Rasmussen, Univ. of Lethbridge tau-function and determinant of Laplacian operator II su(N) tensor product multiplicities and virtual April 24, 2001 Berenstein-Zelevinsky triangles Anna Krasowska, Concordia Univ. January 23, 2001 Wigner functions for semidirect product groups Rn Luc Frappat, CNRS, LAPP \rtimes H Elliptic algebras, q-deformed W-algebras and May 1, 2001 Yangian limits Marco Bertola, CRM & Concordia Univ. January 30, 2001 Duality in Random Matrices and Biorthogonal Bertrand Eynard, SPHT Saclay (France) Polynomials Random matrices and (skew)-orthogonal polynomials CRM Statistics Seminar February 6, 2001 Org.: Christian Léger, Martin Bilodeau (CRM & J. Harnad, CRM & Concordia Univ. Univ. de Montréal) Multi-Hamiltonian structures, R-matrices and spectralseparation of variables I September 6, 2000 Djamal Louani, Univ. de Paris VI February 13, 2001 Some applications of Large Deviations Results in Bertrand Eynard, SPHT Saclay (France) Nonparametric function estimation Random Matrix 0(n) Model September 14, 2000 February 20, 2001 Martin Bilodeau, Univ. de Montréal Jacques Hurtubise, CRM & McGill Univ. Inférence robuste en analyse multivariée Multi-Hamiltonian structures, R-matrices and spectral separation of variables, II September 28, 2000 David B. Wolfson, McGill Univ. February 27, 2001 Problems and solutions associated with length-biased Oksana Yermolayeva, CRM & Concordia Univ. sampling A review of the f-g method in orthogonal polynomials October 5, 2000 March 13, 2001 Bruno Rémillard, Univ. du Québec à Trois- A. Zhedanov, CRM & Univ. Donetsk Rivières Integrable chains, algorithms and orthogonality I Un test non paramétrique d'indépendance sérielle March 20, 2001 pour des séries chronologiques A. Zhedanov, CRM & Univ. Donetsk November 2, 2000 Integrable chains, algorithms and orthogonality II Xiang Sun, Ontario Cancer Institute March 22, 2001 The lasso's implementation for neural networks C. Klein, Eberhard-Karls-Universität, Tübingen November 23, 2000 Relativistic dust disks and hyperelliptic Riemann Josée Dupuis, Genome Therapeutics Corporation surfaces Linkage Analysis of the Pseudoautosomal Regions March 27, 2001 November 23, 2000 Paul Bracken, CRM Eric Kolaczyk, Boston Univ. Symmetries, Integrability and MultiSoliton Solutions A Multiresolution Analysis for Likelihoods of the Generalized Weierstrass System December 7, 2000 April 3, 2001 Geneviève Gauthier, HEC Chongying Dong, Univ. of California, Santa Estimation par la méthode du maximum de Cruz vraisemblance des paramètres du modèle de risque de Monster, Moonshine and Vertex (Operator) Algebras crédit de Merton April 10, 2001 February 8, 2001 Dmitri Korotkin, CRM & Concordia Univ. Nicolas Molinari, IURC , Univ. Montpellier 1 Isomonodromic deformations and Hurwitz spaces: Optimisation des noeuds en régression spline: tau-function and determinant of Laplacian operator I applications aux Biostatistiques April 17, 2001 February 15, 2001 Dmitri Korotkin, CRM & Concordia Univ. Jonathan Taylor, McGill Univ.

38 Annual Report 2000 - 2001 CRM S c i e n t i f i c A c t i v i t i e s

Processus gaussiens non-stationaires indexés par des December 11, 2000 surfaces avec applications à l'imagerie cérébrale Claude Le Bris (CERMICS, Ecole Nationale des February 22, 2001 Ponts et Chaussées) Gérard Biau, McGill Univ. Théorie du contrôle et méthodes d'optimisation en Estimation minimax d'un système dynamique sciences moléculaires chaotique mutlidimensional Org.: Jean-Marc Lina January 16, 2001 March 1, 2001 Christian Boudreau, Univ. of Waterloo Raouf Hamzaoui, University of Leipzig Analyse de Survie et Plans d'Échantillonnage non Complexity Reduction Methods for Fractal Image Informatifs Compession March 22, 2001 Dynamical Systems Days Louis-Paul Rivest, Univ. Laval Org. : Dana Schlomiuk & Christiane Rousseau Modèle de capture-recapture pour l'estimation de la (Univ. de Montréal) taille d'une population finie November 21, 2000 March 27, 2001 Nicolae Vulpe, Académie des sciences de Hung Thao Tran, Institut de Mathematiques du Moldavie Viet Nam Applications of Algébraic Invariants in the Processus de type ARIMA fractionnaire Qualitative analysis of two-dimensional Polynomial April 19, 2001 Differential Systems Robert Tibshirani, Univ. Stanford November 21, 2000 Statistical challenges in the analysis of DNA Joan Carles Artes, Univ. Autonoma de microarray data barcelona, Espagne Structurally Stable quadratic Systems Special Lectures November 21, 2000 Org. : Jacques Hurtubise (CRM) Pavao Mardesic, Univ. de Bourgogne, France June 19, 2000 Complex Isochonous Saddle Points Michel Monastyrsky, Instiute of Theoretical and November 22, 2000 Experimental Physics Dana Schlomiuk, Univ. de Montréal Topological Problems in Physics Classifying Quadratic Systems June 21, 2000 November 22, 2000 Michel Monastyrsky, Instiute of Theoretical and Christianne Rousseau, Univ. de Montréal Experimental Physics The Meaning of the Martinet-Ramis Invariants in the Statistics of Knots and some relations with random Unfolding of a Saddle-node walks on Riemann surfaces and 2-dimensional conformal models CRM-EJC Colloquium Org. : Michel Delfour, Univ. de Montréal Org. : Christiane Rousseau (Univ. de Montréal) November 3, 2000 October 5, 2000 Marc Thiriet, INRIA Rocquencourt, France Francis Clarke, Institut Desargues, Univ. Lyon I Sur les endoprothèses Modélisation bioéconomique des ressources renouvelables Org.: Michel Delfour (UdeM) and André Bandrauk (Sherbrooke)

CRM Annual Report 2000 - 2001 39 S c i e n t i f i c A c t i v i t i e s

CRM-ISM Colloquium The CRM, together with the Institut des sciences mathématiques (the Québec university graduate mathematics consortium), runs the Montréal mathematics colloquium, which, during the university year, organises survey talks by distinguished mathematicians on topics of current interest.

Autumn 2000 Winter 2001 September 8, 2000 February 2, 2001 Arthur Winfree, Univ. of Arizona Damien Roy, Univ. d'Ottawa Vortices in Motionless Media Interpolation en plusieurs variables September 15, 2000 February 9, 2001 Ram Murty, Queen's Univ. Eckhard Meinrenken, Univ. of Toronto The Rieman Hypothesis: A Statut Report Matrices, Moment Maps, and Moduli Spaces September 22, 2000 February 16, 2001 Michael Cahen, Univ. Libre de Bruxelles Andrew Granville, Univ. of Georgia A conjecture on symplectic connections The distribution of multiplicative functions and integral October 6, 2000 delay equations Clauss Michael Ringel, Univ. de Bielefeld March 2, 2001 Combinatorial representation theory - history and future William Duke, Rutgers Univ. October 20, 2000 Recent directions in analytic number theory Mikhail Lyubich, SUNY - Stony Brook March 16, 2001 Quadratic-like maps, complex renormalization, and their Serge Lang, Yale Univ. implications Heat kernels, theta functions and zeta functions October 27, 2000 March 23, 2001 Avner Ash, Boston College Michael Waterman, Univ. of Southern California The Galois group of the field of algebraic numbers Reading DNA Molecules November 3, 2000 March 30, 2001 Konstantin Mischaikow, Georgia Institute of Stephen Watson, York Univ. Technology Existential Quantifiers in the Uncountable Competition, Dispersal, and Spatiotemporal Heterogeneity November 10, 2000 April 6, 2001 Israel Michael Sigal, Univ. of Toronto Joel Smoller, Univ. of Michigan Renormalization Group Approach to Spectral Problems Shock Waves in General Relativity with Application to Theory of Radiation April 12, 2001 November 17, 2000 Leonid Polterovich, Tel Aviv Univ. Walter Neumann, Columbia Univ. Kick stability in groups and dynamical systems Hilbert's 3rd problem and invariants of 3-manifolds April 19, 2001 November 24, 2000 Rob Tibshirani, Stanford Univ. Monique Jeanblanc, Univ. Evry Statistical challenges in the analysis of DNA microarray Assurance de portefeuille data December 1, 2000 April 27, 2001 Marco Avellaneda, Courant Institute Robert Sedgewick, Princeton Univ. Financial Modelling and Probability New research on the theory and practice of sorting May 4, 2001 Dominic Welsh The Complexity of Some Classical Polynomials

40 Annual Report 2000 - 2001 CRM World Mathematical Year

Sponsored by the International Mathematical Union and UNESCO, the year 2000 was declared the World Mathematical Year. On this occasion, many special activities were held all year long throughout the country. Many of them were organized by CRM members.

Mathematical Posters Operation Subway 2000 Stéphane Durand, a CRM member, was awarded One of the activities of the World Mathematical first prize in the international poster contest Year was a series of exhibits of mathematical organized by the European Mathematical posters in the subways of the world's biggest Society. His entry consisted of a series of seven cities. In January 2000, Montréal's subway was posters on the links between mathematics and the first to display these mathematical posters. nature. These posters have been used and The campaign was organized by Christiane adapted in many countries in different ways Rousseau, a CRM member. (posters in the subway, postcards, CD-ROM, etc.): Public Lectures • Montréal (posters in the subway) Les Belles Soirées of the Université de Montréal • France (posters and postcards) consist of lectures for a wide audience on a • Denmark (postcards) variety of topics. To mark the World • Belgium and Holland (posters) Mathematical Year, three lectures on • Italy (Archimède journal) mathematics were given in October 2000. The • UK and Portugal (CD-M) lecturers were Adrien Douady of Paris-Sud XI • Germany (CD-ROM) University at Orsay (La dimension fractale) and Three of the posters were printed in Québec. Stéphane Durand of CRM (Structure universelle... Besides their use in Montréal's subway, they vraiment? Les mathématiques dans la nature: du have also been widely circulated in the schools. and léopard au tournesol... .

What do a Why do snail and the sunflower number seeds show a √ (1+ 5)/2 pattern of 34 have in clockwise curves common? and 21 counterclockwise curves?

Why do buttercups have 5 petals? Why do pineapples have 8 The number (1+√5)/2 is the golden mean which is found in diagonals in one direction and 13 in the other? Why do daisies many parts of nature. The spiral shell of the nautilus is an generally have 34, 55, or 89 petals? All these numbers are part example of a geometric construction based on this number. of the Fibonacci sequence (1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,…) Even Stradivarius used it when constructing his famous related to the golden mean, and where each number is violins. obtained by adding the two previous ones. Only recently have we understood why these numbers are important in nature.

CRM Annual Report 2000 - 2001 41 W o r l d M a t h e m a t i c a l Y e a r

Mathematical Insert Exhibition To show the general public the importance and An exhibition called 1, 2, 3 Math. was prepared the presence of mathematics in modern life, jointly by the Museum of the Séminaire de CRM has prepared a popular document on the Sherbrooke, the Association Mathématique du mathematical sciences in Québec. Entitled Québec, and Université de Montréal. It was Math2000, it was published in the magazine inaugurated in May 2000 and since then has Québec Science in May 2000. This document was travelled in Québec and the rest of Canada. This edited by Stéphane Durand in collaboration with animated and interactive travelling exhibition is Québec Science and 40,000 copies were printed. intended for the general public and school- The document has also been widely distributed children. Some CRM members participated in its in schools, colleges, and university departments development, including Stéphane Durand, Jean- of mathematics education. Marc Lina, and Christiane Rousseau. When it came to the Exhibit Centre of Université de Montréal from October 3rd through November 10th 2000, guided tours were offered to schoolchildren. They were led by students from the Department of Mathematics and Statistics.

Mega-Congress of Year 2000 Mathematics educators, from grade school to university, met during a mega-congress sponsored by the Ministry of Education of the Province of Québec. It was held last May at the Université Laval. Seven associations dedicated to the promotion of mathematics in Québec hosted this meeting.

Television Programmes Hosted by Jean-Marie De Koninck of Université Laval, the television series, C'est mathématique, of 16 half-hour programmes was produced by Productions Téléfiction and shown on Canal Z during Winter 2000. The following CRM members participated: Jacques Bélair, Stéphane Durand, Jean-Marc Lina, Christiane Rousseau, and Yvan Saint-Aubin. Following its release, the Another document, entitled Mathématiques An series was bought by many schools. A sequel is 2000, was prepared jointly by the Institut des being planned. sciences mathématiques and by the Association mathématique du Québec. Giving a brief survey of Radio shows research in mathematics, it was distributed with Interface, the magazine of the Association As part of the radio programme Les nourritures canadienne-française pour l'avancement des sciences terrestres of the French CBC Radio 2, a half-hour (ACFAS). interview with Stéphane Durand on mathematics was broadcast on October 26, 2000. A paper called Décoder la nature was also published in the magazine Quatre-temps of the Montréal Botanical Garden (vol 24, no 4, december 2000).

42 Annual Report 2000 - 2001 CRM Coming Events

Theme Year 2001-2002: Groups and Geometry

Organizing Committee groups, decomposition theorems, A. Broer (Montréal), S. Boyer (UQAM), quasiconvexity, coherence, etc. Our goal is to J. Carrell (UBC), W. Casselman (UBC), bring together students and researchers from H. Darmon (McGill), I. Hambleton (McMaster), these active research areas over a three-week J. Hurtubise (CRM), N. Kamran (McGill), period in order to underline and foster the B. Khesin (Toronto), F. Knop (Rutgers), connections between them. R. Lee (Yale), D. Wise (Brandeis and McGill). Workshop on Groups and 3-manifolds Overview June 25 – 29, 2001 The role of group actions and groups in general This workshop will focus on recent progress on is ubiquitous in geometry, and the year's various open topological and geometric programme will concentrate on some areas in classification problems as well as some of the which there has been newer research directions. There will be four 50- important recent minute talks per day, leaving plenty of time for progress. informal discussions amongst the participants. The year consists of They include: M. Boileau (Univ. Paul Sabatier), D. Calegari two segments, the (Harvard), A. Casson (Yale), D. Cooper (California at Santa Barbara), M. Culler (Illinois at Chicago), D. Gabai, (California first more Institute of Technology), C. McA. Gordon (Texas at Austin), differential- S. Kerchoff (Stanford), M. Lackenby (Oxford), D. Long geometric in flavour, (California at Santa Barbara), J. Luecke (Texas at Austin), Y. Moriah (Technion), J. Porti (Barcelona), A. Reid (Texas at and the other one Austin), H. Rubinstein (Melbourne), P. Shalen (Illinois at concentrating Chicago), Y.-Q. Wu (Iowa), X. Zhang (State Univ. of New specifically on the York at Buffalo). links between algebraic geometry, group theory, and representation theory. Mini-courses July 2 – 6, 2001 GROUPS, TOPOLOGY AND Michel Boileau (Univ. Paul Sabatier) DIFFERENTIAL GEOMETRY Geometrization of 3-dimensional orbifolds June - December 2001 Martin Bridson (Univ. of Oxford) Groups and Low-Dimensional Topology Non-positively Curved Spaces and Hyperbolic June - July 2001 Groups Org. : Steven Boyer (UQAM), Dani Wise (Brandeis & McGill) Ruth Charney (Ohio State Univ.) Throughout the 20th century there has been a The Geometry of Coxeter and Artin Groups remarkably fruitful interplay between group Benson Farb (Univ. of Chicago) theory and the geometry and topology of low- A Crash Course on the Geometry of Groups dimensional manifolds. The study of 3- Peter Shalen (Univ. of Illinois at Chicago) manifolds through their fundamental groups Representations of 3-manifold Groups and symmetries has turned out to be a particularly rich vein with applications to such Workshop on Geometric Group Theory topics as the tabulation of knots, geometrization July 9 – 13, 2001 problems, group actions, and surgery theory. Org.: Dani Wise (Brandeis & McGill) Conversely, results of 3-dimensional topology The theory of infinite groups was revolutionized have been fundamental in motivating many by an infusion of ideas from geometry and exciting developments in geometric group topology. This has led to the resolution of many theory: actions on R-trees, word-hyperbolic old problems and the formulation of new

CRM Annual Report 2000 - 2001 43 C o m i n g E v e n t s problems and methods that have broadened the Infinite-Dimensional Lie Groups scope of the field. This workshop will focus on October - November 2001 these new developments in geometric group Org. : Niky Kamran (McGill), Boris Khesin (Toronto) theory. There will be four 50-minute talks per From a differential-geometric point-of-view, day, leaving plenty of time for informal infinite-dimensional Lie groups arise as discussions amongst the participants. automorphism groups of various geometric They include: W. Ballmann (Bonn), M. Bestvina (Utah), B. structures on the manifolds, such as a volume Bowditch (Southampton), M. Bridson (Oxford), R. Charney form, a foliation, a contact structure or a (Ohio State), B. Farb (Chicago), M. Feighn (Rutgers), I. Kapovich (University of Illinois at Urbana-Champaign), M. symplectic structure. The study of these infinite- Kapovich (Utah), O. Kharlampovich (McGill), J. dimensional Lie groups becomes a fundamental McCammond (Texas A & M), A. Myasnikov (CCNY), P. Papazoglou (Paris-Sud), M. Sapir (Vanderbilt), M. Sageev problem in areas of mathematics as diverse as (Technion) , Z. Sela (Hebrew University). hydrodynamics and symplectic topology. Another wide class of infinite-dimensional Lie Topology of Manifolds and Group Actions groups is formed by loop groups, Kac-Moody August 20 – 24, 2001 groups, and more generally, by gauge groups on Org. : Ian Hambleton (McMaster), Ronnie Lee (Yale) manifolds of arbitrary dimension. The successes Recently there have been important in the study of these groups have been breakthroughs in the study of the topology of immensely fruitful both in low-dimensional manifolds and related topics on group actions, geometry and topology and in quantum field especially in the area of 3-and 4-dimensional theory. Infinite-dimensional Lie groups are also manifolds with new input from the Seiberg- fundamental in the theory of integrable systems Witten theory and symplectic topology. One of and their hierarchies. In this context, their action the main objects of this workshop is to describe becomes quite explicit on spaces of pseudo- these new advances on the subject. differential and Fourier integral operators. The In addition, there also have been important purpose of this mini-programme will be to developments in other areas. For example, there review some of the significant recent are the study of discrete group actions on developments in the above areas and to explore Euclidean space using controlled surgery theory, some of the important open problems. the generalization of Casson invariants from • Introductory Lectures V. Guillemin (MIT) & A.A. Kirillov (Pennsylvania) SU(2) to SU(3), the study of Torelli group actions October 29– November 1, 2001 on the cohomology of moduli spaces, the • Workshop on the Geometry of Infinite- classification of topological group actions on 4- Dimensional Lie Groups manifolds, just to name a few. Not concentrated November 2 – 6, 2001 completely on 4-dimensions, our programme Participants will include: P. Deift (Pennsylvania), P. Etingof will also present these topics for the case of high- (MIT), V. Fock (ITEP), V. Guillemin (MIT), L. Jeffrey dimensional manifolds and related subjects. In (Toronto), M. Kapranov (Toronto), A.A. Kirillov (Pennsylvania) , F. Lalonde (Montréal), J. Leslie (Howard), P. fact, it is the design of the conference to bring Michor (Vienna), E. Meinrenken (Toronto), P. Olver about formal and informal discussion between (Minnesota), H. Omori (Tokyo), V. Ovsienko (CNRS- different perspectives, to compare questions, Luminy), T. Ratiu (EPFL Lausanne), T. Robart (Howard), P. Slodowy (Hamburg), I. Zakharevich (Ohio State). methods and applications. The list of participants includes: R. Cohen (Stanford), S. Cappell (Courant Institute), J. Davis GROUPS AND ALGEBRAIC GEOMETRY (Indiana), A. Edmonds (Indiana), T. Farrell (SUNY at January - June 2002 Binghamton), P. Feehan (Max-Planck-Institute für Mathematik, Bonn), R. Fintushel (Michigan State) K. The importance of algebraic geometry in Froyshov (Harvard), R. Gompf (Texas at Austin), C. Herald representation theory, has grown enormously (Nevada at Reno), R. Kirby (UC Berkeley), T. Leness (Florida during the past decades, with the arrival of such International), T. Li (Princeton), M. Marcolli (Max-Planck- Institut für Mathematik, Bonn), M. McCooey (McMaster), E. techniques as D-modules and perverse sheaves. Miller (Polytechnic University of New York), J. Morgan Geometry intervenes in a crucial fashion in the (Columbia), L. Nicolaescu (Notre Dame), P. Ozsvath proof of such results as the Kazhdan-Lusztig (Michigan State), E. Pedersen (SUNY at Binghamton), F. Quinn (Virginia Polytech Inst & State University), D. conjecture, the construction of canonical bases Ruberman (Brandeis), R. Schultz (UCR), D. Wilczynski (Utah for representations, and the work of Beilinson- State University at Logan), B. Williams (Notre Dame). Drinfeld on the Geometric Langlands programme. A number of deep connections have arisen between the algebraic geometry and

44 Annual Report 2000 - 2001 CRM C o m i n g E v e n t s

Schwarz (Brandeis), D. Wright (Washington), M. Zaidenberg algebraic combinatorics, whose ramifications (Grenoble), D. Zhang (Singapore). extend all the way to mathematical physics and * To be confirmed topology. A special emphasis of the programme will be in graduate training, and a variety of short courses will be organized, as well as Invariant Theory April 8 – 19, 2002, Queen's University, Kingston, Ontario graduate courses of a more introductory nature. Org. : D. Wehlau (Queen’s), E. Campbell (Queen’s) Funding is available for graduate students wishing to attend. The first week will be devoted to introductory lectures aimed at graduate students by Aisenstadt Chairs Professors P. Fleischmann (Kent), H. Kraft June 2002 (Basel), G. W. Schwarz (Brandeis), and Harm There will be three series of lectures delivered Dersksen (MIT). The second week will be under the auspices of the Aisenstadt chair, by E. devoted to a workshop on Invariant Theory. The list of invited speaker includes: M. Brion*, B. Broer, C. Frenkel (Berkeley), L. Lafforgue (IHES), and G. De Concini*, L. Helminck , M. Hunziker, G. Kemper, N. Lusztig (MIT). Kechagias, F. Knop, P. Littelmann , L. Moser-Jauslin, V. Popov, Y. Sanderson, R J. Shank, N. Thiery, W. van der Graduate courses Kallen*, E. Vinberg*. January - April 2002 *To be confirmed Abram Broer (Montréal) Hilbert Schemes of Points and their Applications Concentration Period on the Langlands Henri Darmon (McGill) Programme for Function Fields Automorphic Forms April - May 2002 Org. : H. Darmon (McGill), J. Hurtubise (CRM) Eyal Goren (McGill) Curves, Vector Bundles on Curves and their Moduli The last few years have seen spectacular new Yvan Saint-Aubin (Montréal) results in the Langlands programme over Kac-Moody Algebras function fields, both in characteristic zero and in characteristic p. The aim of this period is to Winter School on Computations in Coxeter provide an overview of some essential Groups techniques in the area, as well as new results. January 21 – 28, 2002 April 2002 Org. : W. Casselman (UBC), R. Bédard (UQAM), F. du Cloux (Lyon I) Short courses for graduate students on topics including the classical Hitchin systems, étale and These short courses are designed to show how l-adic sheaves, as well as a survey of the number techniques from computer algebra can be theoretic Langlands programme. applied to effective computation in Coxeter groups. The course will be held in the The Langlands Programme for Function Laurentians, outside Montréal. Fields April 30 - May 17, 2002 Group Actions on Rational Varieties February 27 - March 3, 2002 A three-week extended workshop, with the first Org. : P. Russell (McGill) two weeks devoted to survey lectures for The workshop will focus on recent graduate students: developments in automorphisms of affine spaces Week 1: Survey lectures on preliminary material: and related algebraic varieties with simple stacks, chtoucas, perverse sheaves and D- topology, in particular exotic affine spaces modules, opers. Lectures by D. Ben Zvi (algebraic varieties homeomorphic to an affine (Chicago), D. Goss (Ohio State), A. Polischuk space). (Boston), C. Sorger (Nantes), K. Vilonen The list of invited speakers includes: T. Asanuma (Toyama), (Northwestern). T. Bandman (Bar-Ilan), D. Daigle (Ottawa), A. Van den Week 2: Aisenstadt lectures given by L. Essen* (Nijmegen), G. Freudenburg (Southern Indiana), M. Lafforgue (IHES) and E. Frenkel (Berkeley), Gizatullin (UTFSM), R. Gurjar* (Tata), I. Dolgachev* (Michigan), J. Winkelmann* (Bochum), S. Kaliman (Miami), covering recent results in the Langlands K. Masuda (Himeji), F. Knop* (Rutgers), M. Koras, H. Kraft programme over function fields, in both (Basel), L. Makar-Limanov (Wayne State), L. Moser-Jauslin* (Bourgogne), M. Miyanishi (Osaka), P. Cassou-Nogues characteristic 0 and characteristic p. During the (Bordeaux), V. Popov (MIEM), A. Sathaye (Kentucky), G.

CRM Annual Report 2000 - 2001 45 C o m i n g E v e n t s first two weeks, R. Langlands will also give a Algebraic Transformation Groups series of lectures. June 10 – 15, 2002 Week 3: The concentration period is to be Org. : A. Broer (Montréal), J. Carrell (UBC) followed by the 2002 Canadian Number Theory The purpose of the meeting is to bring together Association conference. experts in Algebraic Groups, Algebraic Geometry, Representation Theory and related Computational Lie Theory areas, especially those touching on: geometric May 27 - June 10, 2002 methods in representation theory using tools like Org. : W. Casselman (UBC), F. Knop (Rutgers) equivariant cohomology and perverse sheaves; This extended workshop is aimed at researchers the Hilbert scheme of points on a surface and its interested in explicit computations in Lie theory, connection with the n!-conjecture in algebraic in particular Coxeter groups. In addition to the combinatorics; equivariant versions of usual talks, there will also be several series of cohomology and Chow groups related to flag survey lectures, suitable for graduate students, manifolds and Schubert varieties; quantum by M. Brion (Grenoble), M. Geck (Lyon), F. Knop cohomology and Schubert calculus. (Rutgers), P. Littelmann (Wuppertal), G. The list of participants includes: A. Bertram (Utah), M. Brion Olshanskii* (IITP), J. Stembridge (Michigan). (Grenoble), C. De Concini (Rome), W. Fulton (Michigan), V. Ginzburg (Chicago), M. Haiman (UCSD), M. Kapranov Professor G. Lusztig (MIT) will be delivering (Toronto), A. Knutson (Berkeley), B. Kostant (MIT), S. Kumar some of his Aisenstadt lectures during the (North Carolina), L. Manivel (Grenoble), E. Meinrenken (Toronto), I. Mirkovic (Massachusetts), H. Nakajima (Kyoto), period of the conference. D. Peterson* (UBC), C. Procesi* (Rome), E. Vasserot* (Cergy- * To be confirmed Pontoise), C. Woodward (Rutgers). Invited participants include: D. L. Alvis (Indiana), A. * To be confirmed Anatolievich Klyachko (Bilkent), R. Bédard (UQAM), R. Bezrukavnikov (Chicago), S. Billey (MIT), M. Brion (Joseph Fourier), I. Cherednik (North Carolina), F. du Cloux (Lyon I), M. J. Dyer (Notre Dame), W. Fulton (Michigan), M. Geck (Lyon), M. Haiman (California, San Diego), G. J. Heckman (Nijmegen), A. G. Helminck (North Carolina State), F. Knop (Rutgers), S. Kumar (North Carolina at Chapel Hill), P. Littelman (Bergische), R. MacPherson (IAS), J. McKay (Concordia), M. Noumi (Kobe), A. Okounkov (Berkeley), G. Olshanski (Moscow), E. M. Opdam (Amsterdam), A. Ram (Wisconsin), Y. B. Sanderson (William Paterson) T. A. Springer (Utrech), J. R. Stembridge (Michigan), B. Sturmfels (Berkeley), P. Trapa (Harvard), J. F. van Diejen (Chile), M. van Leeuwen (Poitiers), D. A. Jr Vogan (MIT), N. R. Wallach (California, San Diego), G. Saunders Warrington (Harvard), A. Zelevinski (Northeastern). * To be confirmed

46 Annual Report 2000 - 2001 CRM C o m i n g E v e n t s

General Programme 2001-2002

Second Canadian Journal of Statistics mathematicians, together with applications in Read Paper Session finance, stochastic systems, image processing, June 7, 2001, Simon Fraser University, Burnaby, British solid mechanics, electrodynamics, combustion, Columbia Org. : Christian Genest (Laval), Richard Lockhart (Simon matrix calculation, etc. In-depth coverage of each Fraser) theme (including discussion of both numerical, During the Annual Meeting of the Statistical modelling and theoretical issues specific to each Society of Canada, a major scientific contribution application) along with hands-on computer will be read and discussed publicly. The paper is experiments will be offered at this SMS 2001. Flexible Regression Modeling with Adaptive Logistic The speakers will be Anne Bourlioux and Basis Functions of Peter Hooper (Alberta). The Panagiotis Souganidis, Numerical Combustion : paper will be discussed by Mary Lindstrom Modelling and Computing Turbulent Flamelets; (Wisconsin), Jim Ramsay (McGill), Nancy Gene H. Golub and C. Bai, Matrices, Moments, Heckman (UBC), and Hugh Chipman and Hong and Quadratures; Gundolf Haase and Ulrich Gu (Waterloo). The comments of the selected Langer, Multigrid Methods: Theory, Algorithms, discussants will be published along with the Implementation, Parallelization; Laurence Halpern paper in the September 2001 issue of the One-way Operators, Absorbing Boundary Canadian Journal of Statistics and presented orally Conditions, and Domain Decomposition for during this session. Evolution Operators; Anthony Humphries and Andrew Stuart, Computational Aspects of Eighth Canadian Undergraduate Deterministic and Random Dynamical Systems; Mathematics Conference Karol Mikula and James A. Sethian, Level-set and June 12 – 17, 2001, Université Laval, Québec Diffusion Methods in Image Processing; Frédéric Org. : Pier-André Bouchard St-Amant (Laval), Jean- Nataf, Optimized Domain Decomposition Methods; Philippe Boulet (Laval), Sylvain Hallé (Laval), Jean- François Plante (Laval) George Papanicolaou, Asymptotic Analysis of Stochastic Differential Equations and Applications; This annual conference is aimed at Canadian and Ronnie Sircar, Stochastic Volatility Modelling. undergraduate students whose programme of study involves mathematics. The participants Statistics 2001 Canada: The Fourth are encouraged to present a 20 or 50-minute talk Canadian Conference in Applied on a mathematical subject of their choice. Statistics Furthermore, five invited speakers will enrich July 6 – 8, 2001, Université Concordia, Montréal the participant's knowledge of current Org. : Y. Chaubey (Concordia), F. Nebebe (Concordia) mathematical research. This conference will feature plenary speakers, and contributed and invited papers, with Séminaire de mathématiques emphasis on applied statistics. Areas covered supérieures : Modern Methods in include Bayesian Methods, Biostatistics, Data Scientific Computing and Applications Mining, Demography, Econometrics, July 9 – 20, 2001, Université de Montréal Org. : G. Sabidussi (Montréal), K. Mikula (Slovak Multivariate Analysis, Operations Research, Technical University, Brátislává, Slovakia), A. Bourlioux Probability, Psychometrics, Sampling, Survival (Montréal), M. Gander (McGill), S. Lessard (Montréal), G. Analysis, and Time Series. C. Papanicolaou (Stanford), A. Stuart (Warwick) The conference follows a well-established The scientific computing approach to the tradition. The First Canadian Conference in solution of differential equations of all types, Applied Statistics was held in 1971 at Concordia associated with a variety of applications, is a University. Since then, the Department of multi-faceted technique that encompasses not Mathematics and Statistics has organized such a only numerical methods but also more formal conference every tenth year. analysis of the underlying equations, along with The plenary speakers are David Brillinger a good understanding of the practical (Berkeley), Christian Genest (Laval), John D. application being modelled. Recent Kalbfleisch (Waterloo), Jerry Lawless (Waterloo), achievements of this multi-disciplinary approach will be presented by expert applied

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Jim Ramsay (McGill), C. R. Rao (Penn State), J. Spectral Statistics and High Energy N. K. Rao (Carleton), P. K. Sen (North Carolina). Eigenstates August 25 - September 2, 2001, CRM FUSION 2001: 4th International Org. : Dmitry Jakobson (McGill), John Toth (McGill) Invited speakers: P. Bleher (IUPUI), A. Bourget (McGill), W. Conference on Information Fusion Craig (McMaster), H. Donnelly (Perdue), E. Duenez August 7 – 10, 2001, Montréal (American Institute of Mathematics), B. Eynard (CRM, Org. : E. Shahbazian (Lockheed Martin & CRM) Montréal), V. Jaksic (Ottawa), J. Harnad (CRM, Montréal), L. Ma (Tsinghua), K. McLaughlin (Arizona), M. Min-Oo This conference will provide a forum for the (McMaster), Y. Petridis (McGill), I. Rivin (Temple), Z. presentation of research and technological Rudnick (Tel Aviv), P. Sarnak (Princeton), U. Smilansky advances by scientists and engineers working in (Weizman Institute), K. Soundararajan (IAS), R. Speicher (Queens), T. Tate (Johns Hopkins), A.Uribe (Michigan), I. all aspects of information and data fusion Vardi (Le Bois-Marie), H. Widom (UC Santa Cruz), S. techniques and systems. It will also feature Zelditch (Johns Hopkins). keynote speeches and plenary talks. Topics The idea of the workshop is to bring together include various aspects of theoretical and mathematicians and physicists working on technical advances in information fusion, issues related to asymptotic eigenstate algorithms and systems, as well as applications. properties, especially as they relate to classical limits and chaos. There are various subjects to be Second Gilles Fournier Memorial investigated. These include the asymptotic Conference behaviour of individual eigenstates, the role and August 13 – 15, 2001, Université de Sherbrooke Org. : Marlène Frigon (Montréal), Andrzej Granas utility of random matrix theory in the prediction (Montréal), Tomasz Kaczynski (Sherbrooke) of eigenvalue statistics for the Laplace-Beltrami Les thèmes principaux de cette seconde operator and the role of periodic orbits and conférence dédiée à la mémoire de Gilles scars. Fournier seront la théorie des points fixes et la théorie de points critiques ainsi que leurs Histoires de structures et de catégories applications aux équations différentielles et aux September 2001, CRM Org. : Luc Bélair (UQAM) & Liliane Beaulieu (CRM) systèmes dynamiques. À cette occasion, des Invited speakers: L. Beaulieu (CRM), M. Bunge (McGill), C. développements récents de ces domaines seront Houzel (Paris), A. Joyal (UQAM), J. Lambek (McGill), M. présentés par des experts canadiens et étrangers Makkai (McGîll), C. McLarty (Case Western), G. Reyes afin de stimuler les échanges entre eux et les (Montréal). étudiants des cycles supérieurs qui Cet atelier, qui réunit mathématiciens, historiens participeront. et philosophes des mathématiques, s’est donné pour objectif de faire le point sur les histoires des La conférence sera composée de conférences structures et de la théorie des catégories. Il principales de 50 minutes, conférences invitées s’agira aussi de combler certaines lacunes d’une de 40 minutes et quelques exposés de 30 minutes historiographie qui a négligé de montrer les liens données par de jeunes mathématiciens. La entre les développements de différentes participation d'étudiants de cycles supérieurs branches des mathématiques et la quête pour sera fortement encouragée. cerner, d’un point de vue strictement mathématique ou d’un point de vue Les conférenciers principaux seront Massimo métamathématique, le principe collectivisant des Furi (Florence), Kazimierz Geba (Gdansk), structures ou des catégories. Comme l’an passé, la Andrez Granas (Montréal), Antonio Marino parole sera également donnée aux protagonistes (Pise), Mario Martelli (Cal St. Fullerton), Jean de ces histoires. Mawhin (Université Catholique de Louvain) et Michel Willem (Université Catholique de Constance van Eeden's Conference: Louvain). Les conférenciers invités seront A. Mathematical Statistics 2002 Abbondandolo (Pise), S. Alama (McMaster), H. May 24 – 25, 2002, CRM Org. : Marc Moore (École Polytechnique), Sorana Froda Ben-El-Mechaiekh (Brock), P. Deguire (UQAM), Christian Léger (Montréal and CRM) (Moncton), M. Lassonde (Université des Antilles et de la Guyane) et H. Steinlein (Munich.) This conference will recognize the extraordinary services of Professor Constance van Eeden to the Canadian statistical community, and to the Université de Montréal in particular. It will feature invited talks by Roelof Helmers (CWI,

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Amsterdam), Chris A.J. Klaassen (University of There will be a banquet on Friday night. This Amsterdam), Denis Larocque (HEC), Louis-Paul conference will precede the Annual Meeting of Rivest (Université Laval), Bill Strawderman the Statistical Society of Canada which will be (Rutgers University), and Jim Zidek (UBC). held in Hamilton.

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Theme Year 2002-2003: Mathematical Methods of Computer Science

Organizing Committee physical reality for information processing David Avis (McGill), Yoshua Bengio (Montréal), purposes. For instance, quantum mechanics Gilles Brassard (Montréal), Luc Devroye allows for unbreakable cryptographic codes and (McGill), Pierre L'Ecuyer (Montréal), Pierre such a high level of parallelism in computation McKenzie (Montréal), Prakash Panangaden that a classical computer the size of the universe (McGill), Bruce Reed (McGill), Denis Thérien would be left behind. The goal of this school is to (McGill.) make the field of quantum information processing accessible to a general audience of Overview mathematicians and computer scientists who have little or no familiarity with quantum The field of computation, formally born only last mechanics. century but with roots that stretch back to Euclid, is now a mathematical discipline in its AISENSTADT CHAIR LECTURE SERIES own right, with solid theoretical foundations on which are based its spectacular development. There will be three series of conferences The CRM special year in the mathematics of associated with the Aisenstadt Chairs by Manuel computer science proposes to explore in depth a Blum (Carnegie Mellon), Laszlo Lovasz significant spectrum of the many sub-areas that (Microsoft Research), and Endre Szemeredi are core foundational material for modern (Rutgers University). computer science, that exhibit significant and new mathematical content, and that have indeed CONCENTRATION PERIODS influenced the development of mathematics. Complexity theory, analysis of algorithms May-June 2002 Mathematically, the areas with the earliest Org.: Pierre McKenzie (Montréal), Denis Thérien (McGill) influence on computer science were logic and discrete mathematics. Since then, the theoretical In May 2002, the CRM will host two of the most foundations of computer science have important international conferences in blossomed, and ideas from the area (like theoretical Computer Science, namely the ACM effectiveness, complexity and tractability) have Symposium on Theory of Computing and the grown to occupy an ever more important role in IEEE Conference on Computational Complexity. mathematics. More recently, a recurrent theme In addition, there will be several 1-week in many of the domains examined are workshops on topics that lie at the core of the probabilistic methods; these have permeated the theory of computing. Each workshop will bring whole of computer science, and so particular together a number of leading scientists who will emphasis will be placed on the utilisation of present both expository lectures and state-of-the- these techniques, both in theoretical areas and in art research. more applied ones such as simulation and machine learning. Lecture series on branching programs May 13-17, 2002 Org.: Ingo Wegener (Dortmund) Summer School on Quantum Information Processing ACM Symposium on Theory of Computing (STOC) July 15-19, 2002 May 19-21, 2002 Org.: Gilles Brassard (Montréal) IEEE Conference on Computational Complexity Lecturers: A. Ambainis, C.H. Bennett, G. Brassard, H. May 21-24, 2002 Buhrman, R. Cleve, C. Crépeau, *N. Gisin, P. Høyer, R. Laflamme, M. Mosca, A. Tapp, J. Watrous Randomness in Branching program *to be confirmed May 27-31, 2002 Random techniques play an important role in Classical information theory is firmly rooted in computer science, through algorithms which the classical physics of Newton and Einstein. give an efficient solution to problems for which But the world is quantum mechanical. This has no good deterministic solution is known, or prevented us from tapping the full potential of through the probabilistic study of complexity. A

50 Annual Report 2000 - 2001 CRM C o m i n g E v e n t s week will be devoted to this theme, starting with Combinatorics, probability and the links between probabilistic methods and algorithms branching programs. May 2003 Org.: David Avis (McGill), Luc Devroye (McGill), Bruce A. Reed (McGill) Verification and model-checking June 3-7, 2002 Leave nothing to chance. This cliché embodies In the past ten years, theoretical work in the area the common belief that randomness has no place of verification has started to bear fruit. The in well-planned methodologies, every i should workshop will cover the major areas of this be dotted and every t should be crossed. In development, in particular those linked to discrete mathematics, at least, nothing could be model-checking. further from the truth. Introducing random choices into algorithms can improve their Descriptive complexity performance. The application of probabilistic June 10-14, 2002 tools has led to the resolution of combinatorial Invited speakers for the one-week workshops include: M. problems which have resisted attack for decades. Ajtai, D. Barrington, P. Beame, P.L. Crescenzi, R. Gavalda, N. Immerman, K.J. Lange, P. Pudlak, M. Sachs, R. Raz, P. A month-long concentration period will take Schnoebelen. place around this general theme. Lecturers at the An area that has come to the fore in recent years, school will introduce participants to a number of descriptive complexity gives a tool that weapons, mostly from the probabilistic arsenal, complements more classical approaches to and their applications in combinatorics and in complexity theory. After a survey of the area, the the study of algorithms. We anticipate a workshop will concentrate on links between significant amount of collaboration between branching programs and algebraic structures. participants at the school during the month. There will be 5 hour mini-courses given by: N. Quantum Foundations in the Light of Alon (Technion), V. Chvatal (Rutgers), A. Frieze Quantum Information (Carnegie-Mellon), L. Lovasz, (Microsoft), C. October 13 – November 2, 2002 McDiarmid (Oxford), M. Molloy (Toronto), J. Org.: Gilles Brassard (Montréal), Christopher A. Fuchs (Los Pach (City College New York and Hungarian Alamos National Laboratory) Academy of Sciences). Invited speakers include: H. Barnum, G. Brassard, H. Briegel, J. Bub, A. Cabello, C. Caves, *R. Cleve, C. Fuchs, N. Gisin, *D. Greenberger, L. Hardy, P. Hayden, A. Holevo (*), R. Jozsa, A. INTERNATIONAL ANNUAL MEETINGS Kent, D. Mayers, D. Mermin, *T. Mor, M. Nielsen, A. Peres, I. Pitowsky, R. Schack, B. Schumacher, J. Smolin, R. Spekkens, ACM Symposium on Theory of *A. Steane, D. Wallace, W. Wootters, A. Zajonc. Computing (STOC) * to be confirmed May 19-21, 2002 Rolf Landauer's best-known aphorism is "information is physical". This workshop is IEEE Conference on Computational centred around the belief that "physics is Complexity informational"! Our long-term purpose is to May 21-24, 2002 reformulate the foundations of quantum Org.: Pierre McKenzie (Montréal), Denis Thérien (McGill) mechanics in the light of quantum information These two conferences are part of the theory. Rather than being counterintuitive, could concentration period on Complexity theory, it be that quantum mechanics was inevitable for analysis of algorithms. information to behave as we understand it now? For instance, what can we derive from the fact Mathematical Foundations of that unconditionally secure cryptographic key Programming Semantics (MFPS) March 17-22, 2003 distribution is possible but bit commitment is Org.: Prakash Panangaden (McGill) not? Conferences and workshops in this series, held annually since 1985, aim to provide a forum for researchers in all areas surrounding semantics to present their latest research results, and to improve communication and interactions between mathematicians and computer scientists who work in these areas. The areas of relevance

CRM Annual Report 2000 - 2001 51 C o m i n g E v e n t s include category theory, domain theory, logic terms of diversification, systems of interest now and topology on the mathematics side, and type include stochastic systems, real-time systems theory, semantics, and the design and and hybrid systems, that is, systems where the implementation of programming languages on state space is partly discrete and partly the computer science side. continuous. Applications include flight management systems for aircraft, process control IEEE Symposium on Logic in Computer systems, telecommunication systems and battle Science (LICS) management systems. In all of these one has to June 20-26, 2003 deal with continuous time evolution and usually Org.: Amy P. Felty (Ottawa), Philip Scott (Ottawa) with probabilistic aspects as well. Perhaps the To be held at the University of Ottawa in 2003, most successful mathematical technique for the IEEE Symposium on Logic in Computer dealing with these problems - now almost 20 Science (LICS) is an annual international forum years old - is model checking. This is now being on theoretical and practical topics in computer extended to probabilistic systems and the theory science that relate to logic in a broad sense. The has advanced to the point where tools have been CRM will be sponsoring four satellite workshops designed and built. In terms of the general for this conference. mathematical theory co-inductive techniques, like bisimulation, have proved their value WORKSHOPS repeatedly. Random number generation and highly The workshop would have two main speakers, uniform point sets who will each give five lectures: Prof. Marta June 17-28, 2002 Kwiatkowska, U. Birmingham “Probabilistic Org.: Pierre L'Ecuyer (Montréal) Model Checking” and Dr. Jan Rutten, CWI Invited speakers : G. Chaitin, C. Crépeau, L. Devroye, M. Evans, B.L. Fox, M. Fushimi, J. Gentle, P. Hellekalek, S. Amsterdam “Coinductive Calculus”. Heinrich, W. Hormann, A. Keller, G. Larcher, P. L'Ecuyer, J. Leydold, C. Lemieux, M. Mascagni, M. Matsumoto, S. Finite Model Theory Ninomiya, T.Nishimura, A.B. Owen, G. Pirsic, W. Schmid, I. March 2-9, 2003 Sloan, S. Tezuka, H. Wozniakowski, C. Xing. Org.: Denis Thérien (McGill) This workshop will bring together the world This workshop will focus on the expressive leaders in the theoretical and practical aspects of power of logics and on the deep relationship random number generation by computer and the between logic and computational complexity. design of highly-uniform point sets for quasi- The principal speaker will be Phokion Kolaitis Monte Carlo integration. The general theme is (U.C. Santa Cruz). The workshop will be held at the development of practical random number the Bellairs Research Institute of McGill generation software for various classes of University. applications, such as simulation, statistics, numerical analysis, computer games, lotteries, Semigroups and Automata cryptology, etc. In simulation, highly-uniform March 9-16, 2003 (or low-discrepancy) point sets can often Org.: Denis Thérien (McGill) advantageously replace the traditional random This workshop will discuss recent developments numbers. Their construction and analysis can be in the theory of automata and semigroups, in based on ideas and tools that are very similar to particular some dealing with long-standing open those used for random number generators and problems such as decidability of the dot-depth we want to strengthen this connection. hierarchy and decidability of Rhodes complexity. Mathematical Models and Techniques for Analysing Systems Cryptographic reduction of quantum and September 30-October 4, 2002 Org. : Prakash Panangaden (McGill) classical protocols April 28 - May 2, 2003 Invited speakers: R. Alur, P. Caines, L. deAlfaro, R. Org.: Claude Crépeau (McGill) Jagadeesan, D.Precup, R. Segala, F. van Breugel and M. Vardi. Invited speakers: D. Beaver, *C. Cachin, R. Cramer, C. Crépeau, I. Damgaard, P. Dumais, D. Gottesman, J. van de The analysis of systems has both diversified and Graaf, *R. Impagliazzo, J. Kilian, D. Mayers, *M. Naor, *S. deepened tremendously in the last few years. In Rudich, L. Salvail, A. Smith, A. Tapp, S. Wolf, M. Yung. *to be confirmed

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Cryptographic protocols have been studied for SEMINAR two decades in the classical scenario under There will be a year-long seminar on the various computational assumptions. Such mathematics of computing. protocols as Bit Commitment, Oblivious Transfer and Multiparty Computations have COURSES been implemented and reduced to each other. The Montreal universities offer a variety of Over the last few years, similar results are now courses in the area of the year. The list can be achieved in the context of adversaries equipped consulted at : with quantum computers. This workshop will http://www.iro.umontreal.ca/cours/ bring together specialists of both classical and http://www.cs.mcgill.ca/acadpages/grad/cour quantum cryptographic protocols who will se-grad.html present the state of the art in this fascinating area http://www.cs.concordia.ca/programs/grad/c of research. ourses.html http://www.info.uqam.ca/dinfo/coursdepfram Advances in Machine Learning e.html June 2-13, 2003 Org.: Yoshua Bengio (Montréal), Balázs Kégl (Montréal), Doina Precup (McGill) 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. Probabilities are at the core of recent advances in the theory and practice of machine learning algorithms. The workshop will focus on three broad areas where these advances are crucial: statistical learning theory, learning algorithms, and reinforcement learning. The workshop will therefore bring together experts from each of these three important domains. Among the sub - topics that will be covered, we note: variational methods, graphical models, the curse of dimensionality, empirical methods to take advantage of theories of generalization error, and some of the applications of these new methods.

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General Programme 2002-2003 Joint IMA-CRM Workshop on increase their scale, as well as change their Computational Methods for Large nature; goods purchased over the internet must Scale Integer Programs be delivered; also, they often get returned. October 14-19, 2002, Minnesota Related to these questions is the rich field of Org. : William Cook (Rice University), Martin W.P. network design problems, which arise in Savelsbergh (Georgia Institute of Technology), George particular in transportation logistics and in Nemhauser (Georgia Institute of Technology) telecommunications planning. In the past decade there have been significant The theory of location is evolving, with theoretical and computational advances in the questions such as competitive location or the field of integer programming. As a result there location of non-punctual or structured objects has been a greatly increased use of integer being studied; in routing, the advent of better communication devices and increased programming software in industry. However, computational power make real-time dynamic the need to solve even larger and more complex routing a possibility. These changes imply that problems continues to grow. In this workshop, new problems with different mathematical we will bring together experts in various areas of properties must be tackled and new algorithmic integer programming and its applications. strategies devised. Theoretical and methodological topics included This workshop will include a series of ten in the workshop are approximation algorithms surveys, covering both the more traditional and for large scale linear programs, stochastic integer the newer subject areas, with additional programming, branch-and-cut and branch-and- contributions by conference participants. Areas price, algebraic and combinatorial methods, covered include routing; location; economic decomposition, constraint programming and aspects, pricing, e-commerce; fleet management; parallel implementation. Application areas telecommunications; network design. include supply chain design and management, telecommunications, manufacturing, Quantum Control: Mathematical and transportation, scheduling, and finance. The Numerical Challenges workshop will be of interest to mathematicians October 7-11, 2002 Org.: André Bandrauk (Canada Research Chair, Chemistry, and operations researchers working in discrete U. de Sherbrooke, FRSC),Michel Delfour (CRM and DMS, and combinatorial optimization, computational U. de Montreal, FRSC) scientists working in parallel computing, search, Sponsors: NSERC and CRM and constraint programming. Goals of the This workshop will concentrate on advanced workshop include building a research agenda numerical methods and new mathematical and for the next decade, defining new areas of control and optimization approaches and tools application, and stimulating cooperation among for the quantum control of matter at the the different disciplines that contribute to the molecular level using current advanced laser field. technology. An entire new branch of science now known as Joint IMA-CRM Workshop on "Coherent Control of Molecular Processes" Distribution systems: location and following the pioneering work of theoretical vehicle routing chemists such as Paul Brumer (Toronto), Moshe December 2-6, 2002, Montréal Shapiro (Weizmann Institute), Stuart A. Rice Org. : Michel Gendreau (CRT, Montréal) and Gilbert Laporte (CRT, HEC) (Chicago), and other international and Canadian Invited participants: G. Laporte, A. Corberan, J.J. Salazar, D. distinguished scientists is steadily making an Vigo, M. Salomon, S. Nickel, T.Lowe, P. Hansen, O. Berman, impact on the experimental and technological G. Wesolowsky, J. Thisse, P. Marcotte, B. Gavish, M. Gendreau, M. Savelsbergh, J.Y. Potvin, A. Balakrishnan, M. world. O. Ball, B. Jaumard, M. Labbé, C. Colbourn, T. Crainic, T. This new field of research is dedicated to "using Magnanti current state of the art laser technology to The questions surrounding distribution systems control and manipulate the quantum behaviour are of prime economic importance. The scale of and motion of matter at the molecular level". The these systems is increasing at a fast rate because of the growth of international commerce and basis of this new science is the encoding and travel. The advent of e-commerce will only control of quantum information at the molecular level in order to control the time evolution of

54 Annual Report 2000 - 2001 CRM C o m i n g E v e n t s molecular processes, such as guiding the final Main themes: output of a reaction to a desired target. Most of Molecular and Electron Control Theoretical: Andre D. Bandrauk (Sherbrooke), Paul the research in this area has been numerical and Brumer (Toronto), Ronnie Kosloff (Hebrew University), theoretical, involving multidimensional time- Herschel Rabitz (Princeton). dependent Schroedinger equations, TDSE's. Experimental: Hideo Mabuchi (Caltech), Philip Howard Coupling these molecular processes to the laser Bucksbaum (Michigan) . field equations, Maxwell's equations, results in coupled parabolic (TDES's) and hyperbolic Quantum Control - Mathematical (Maxwell) partial differential equations. There Problems & Theories Org.: Roger Brockett (Harvard), Goong Chen (Texas A & are outstanding problems, both numerical and M), Michel Delfour (Montréal), Claude Le Bris (CERMICS, mathematical, which this workshop will address ENPC, Paris), Roberto Triggiani (Virginia), Jean-Paul by bringing together mathematicans, theoretical Zolesio (CNRS and INRIA, France), Enrique Zuazua (Complutense, Madrid, Spain). chemists and physicists working in the area of control and optimization of systems subject to Quantum Computing quantum laws. Org.: Daniel Liedar (Toronto), Serge Lacelle (Sherbrooke), The workshop will involve 20-30 international MIvanov (NRC-Ottawa), Raymond Laflamme (Waterloo), Richard E. Cleve (Calgary) experts in laser molecule interactions, optimization, theory and control of molecular Numerical Methods dynamics. It will emphasize participation of Org.: Robert Wyatt Texas), Tucker Carrington (Montréal), graduate students in applied mathematics, Michel Fortin (Laval), Anthony Peirce (UBC), Gene H. theoretical chemistry and physics. Golub (Stanford U), William Hager (Gainesville), Claude Le Bris (CERMICS, ENPC, Paris), G. Turinici (INRIA- Rocquencourt)

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Theme Year 2003-2004: Geometric and Spectral Analysis

Scientific Committee courses are listed in the detailed program given E. Bierstone (Toronto), W. Craig (McMaster), below. F. Finster (MPI), P. Gauthier (Montreal), D. Jakobson (MCGill),V. Jaksic (McGill), Aisenstadt Chair Lecture Series N. Kamran (McGill), R. Melrose (MIT), There will be two chairholders for the year. P. Milman (Toronto), J. Toth (McGill). SPECTRAL ANALYSIS Overview Contact geometry and analysis Analysis has traditionally stood at the center of July 2003 gravity of much of the research activity in Org.: R. Melrose, D. Auroux mathematics. In particular, the fields of In the vigorous development of contact geometric and spectral analysis have played a geometry, which has taken place over the past 10 fundamental role in shaping the major themes of years or so, the notion of a tight (or conversely current research in differential geometry and an overtwisted) contact structure has proved to mathematical physics, and they stand indeed at be central, with many deep and important the core of several of the deepest and most applications to three-dimensional topology. On spectacular advances in these fields. There is the analytic side, the notion of the quantization now, for example a much deeper understanding of a contact manifold, that is the existence of a of the eigenvalues and eigenfunctions of generalized Szegö projection, has come to play a manifolds than there was even five years ago. central role in developments related to the The thematic year in geometric and spectral algebra of pseudodifferential operators of analysis will focus on a number of themes in Heisenberg type and related homological which this interaction has been particularly questions. Both endeavors are related to fruitful. The year is organized around two embedding, or fillability, questions which interconnected themes: the first, whose different remain substantially open, especially in the three subthemes cover the whole year, is principally dimensional case. It seems likely that there are centered on various questions in spectral important relationships between these various analysis; it comprises what is in essence two notions and structures, with probable short programs, one on contact geometry and consequences on each side It is hoped that by the other on analysis on singular space, and a bringing this group together they will be able to more extended period on spectral analysis in understand these relationships and their mathematical physics and number theory. The repercussions. two short programs have a particularly strong The format is one of informal lecture series over emphasis on developing new connections to two weeks, on subjects such as Contact Floer other areas of mathematics. The second theme homology and symplectic field theory, relates to the analysis of the Einstein equations, a Approximate holomorphic geometry, Gauge subject on which there has been spectacular theory and symplectic fillings, Heisenberg progress in recent years. It is concentrated in the algebras, Toeplitz quantization, Powers of circle fall of 2003. bundles. These themes have been chosen so as to have a balance between the geometric and spectral Analysis and Resolution of components of the scientific program, and also Singularities with the objective of highlighting some of the August 2003 most interesting current applications of analytic Org.: E. Bierstone (Toronto), P. Milman (Toronto), D.H. ideas to physics. Phong (Columbia) There will be a strong emphasis on training Effective methods in resolution of singularities through the short courses which will precede the are becoming central to a modern generation of proposed workshops, as well as through the problems from analysis and geometry - for coordination of the graduate course offerings in example, spectral theory and Hodge theorem for analysis and geometry in the Montreal algebraic varities, stability of oscillating universities. In particular, a minimum of eight integrals, existence of Kähler-Einstein metrics, short courses is being planned in connection sharp forms of Moser-Trudinger inequalities. with the various workshops. Some of these short The diversity of the problems and their very

56 Annual Report 2000 - 2001 CRM C o m i n g E v e n t s different origins and aims have led to a lack of Spectral analysis in mathematical communication among researchers on these and physics and number theory related topics. This program, bringing together November 2003-May 2004 leading experts in resolution of singularities, complex differential geometry, and real analysis Integrable and near-integrable and partial differential equations, may have Hamiltonian PDEs. ground-breaking impact. November 2003 Week 1. Workshop on oscillatory integrals and Org.: W. Craig (McMaster), P. Deift (Pennsylvania), H. critical integrability exponents Flaschka (Arizona), S. Kuskin (Heriot-Watt), P. Olver(Minnesota), P. Winternitz (CRM) Topics include degeneracy of holomorphic functions in several variables, Legendre This workshop will provide a cross-section of distributions and multiplier ideal sheaves. the most significant current activity in the field of Hamiltonian pdes, including integrability, Week 2 Short courses . asymptotics in the small dispersion limit, KAM Three short courses to be accessible to graduate theory, and Arnol'd stability. This workshop is students in analysis, given by the organizers or organized in conjunction with the special year other participants. in analysis at the Fields Institute. • Effective methods in resolution of singularities – ideas involved in Spectral theory of Schrödinger operators desingularization algorithms, concrete January 2004 examples with a view to applications in Org.: V. Jaksic (McGill), Y. Last (Hebrew) analysis and geometry. The spectral theory of Schrödinger operators has • Stability questions in real and complex been the stage of spectacular developments over analysis; for example, stable forms of the the last ten years. The emphasis has shifted to method of stationary phase, stability of the problems involving semiclassical limits and critical integrability exponents, ascending limits of large numbers of particles (e.g. atomic chain conditions, stability problems for Hamiltonians) and to the problems involving degenerate Fourier integral operators. quasi-peridic and random structures. The goal of • Real and complex blow up, resolution of the workshop is to bring together the world metrics, configuration spaces and Lie leading experts, young researchers and the algebras of vector fields - leading to a graduate students in this fast developing field. description of harmonic forms and L2 The state of the art research and results will be cohomology of various singular spaces. described in an accessible way, and the new directions of research will be pointed out. Week 3 Workshop on resolution of singularities, Short course lecturers: Barry Simon (Caltech), Bernard metrics and the Laplacian Helffer (Paris), Jan Phillip Solovaj (Copenhagen), Christian The Hodge theorem, describing the harmonic Gerard (Paris), Stanislav Molchanov (North Carolina), forms on a smooth algebraic variety and relating Wilhelm Schlag (Caltech) them to its cohomology, has had wide impact on differential and algebraic geometry, and Dynamics in statistical mechanics differential analysis. In the more general case of February 2004 Org.: V. Jaksic (McGill), C.-A. Pillet (Toulon) a singular projective variety, a description of the harmonic forms remains largely open, although The past ten years have witnessed some major there are substantial conjectures. An approach new developments in the field of non- through resolution of singularities depends on equilibrium statistical mechanics, owing to an understanding the structure of the Fubini-Study influx of fresh ideas from probability theory and metric lifted to a resolution. The workshop will C*-algebras. This progress is complemented by bring together researchers in geometric, the study of concrete, physically relevent models algebraic and analytic areas related to these of infinite particle systems, for which the zeroth questions. and the second law have been now rigorously established. The goal of the workshop is to bring together the world's leading experts in the field. Short course lecturers: Jurg Frohlich (ETH), David Ruelle (IHES), Kuksin (Edinborough), Jan Derezinski (Warsaw), Jean-Piere Eckmann (Geneva), Varadhan (Courant)

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Toeplitz operators, Riemann-Hilbert researchers in this rich and important area of problems and random matrices. mathematics, which lies at the boundary of March 2004 analysis and number theory. Org.: D. Jakobson (McGill), J. Toth (McGill). Short course lecturers: H. Iwaniec (Rutgers), A. Zaharescu In the last decade, a number of deep connections (Illinois) have been established between random matrix theory, orthogonal polynomials, integrable ANALYSIS OF THE EINSTEIN EQUATIONS systems of pdes of the Painleve and KP types, September-October 2003 the Riemann-Hilbert problem, combinatorics, Workshop on the Cauchy problem for the representation theory and statistical mechanics. Einstein equations. By considering Toeplitz matrices, one can study September 2003 eigenvalue statistics for quantizations of very Org.: F. Finster, N. Kamran. general Hamiltonian systems on Kähler A number of major advances have been achieved manifolds. This workshop will provide a unique over the past few years in the analysis of the opportunity for bringing together a number of Cauchy problem in general relativity. These key contributors to these developments. include the proof of the non-linear stability of Short course lecturers: A. Its (Indiana), K. McLaughlin (North Minkowski space, the proof of the Riemannian Carolina) Penrose conjecture and the rigorous description of the asymptotic behavior at infinity of the Semi-classical theory of eigenfunctions admissible Cauchy data. This workshop will and pdes bring together some of the key players who have April 2004, (to be held at the fields Institute) been involved in these developments, and will Org.: D. Jakobson (McGill), J. Toth (McGill) provide an opportunity for exploring some of Many questions in quantum chaos are motivated the remaining open problems. by the correspondence principle in quantum mechanics. These include asymptotic bounds for Workshop on the interaction of gravity the eigenfunctions, integrated and pointwise with external fields Weyl error terms, and scarring. Another October 2003 fundamental question concerns the local and Org.: F. Finster, N. Kamran. global statistical properties of the eigenfunctions, The interaction of gravity with external fields is their nodal sets and critical points. These governed by highly coupled systems of partial questions will from the main theme of the differential equations on manifolds. The analysis workshop. of these systems has lead to surprising results on Short course lecturers: V. Guillemin (MIT), N. Nadirashvili the role of external fields in the dynamics of (Chicago) gravitational collapse and singularity formation. These results include, in the spherically Spectral theory and automorphic forms symmetric case, the existence of stable particle- Org.:Y. Petridis (CRM/McGill), J. Toth (McGill) like solutions of the Einstein-Yang Mills Analytic questions about families of L-functions equations, and the non-existence of black hole include the distribution of zeros and the solutions when the gravitational field is coupled generalized Riemann hypothesis, value to a Dirac spinor field. One of the objectives of distribution, special values as well as the workshop will be to review these connections with arithmetical questions such as developments, and to discuss some of the the distribution of primes, size of class gropups, directions for future research. analytic ranks and elliptic curves. This workshop Short courses: H. Friedrich (MPI), F. Finster (MPI), J. Smoller will bring together some of the most active (Michigan)

58 Annual Report 2000 - 2001 CRM Collaborations

Within its general mandate of promoting Programme, described in the next section. mathematical research, the CRM maintains a Another one is the CRM-FI prize awarded in wide network of collaborations at the local, recognition of outstanding accomplishments in national, and international levels. the mathematical sciences in Canada. It was created in 1994. This year's winner is W.T.Tutte of the University of Waterloo. The A NATIONAL INSTITUTE administrative responsibility in this matter The CRM is strongly committed to its national alternates each year between the CRM and the mission. The CRM takes measures to ensure that FI. Scientific collaboration continues between the the largest possible number of scientists across FI and the CRM, with a joint workshop in Canada benefits from its activities and become symplectic geometry and topology, during the involved in their planning. For instance, it spring of 2001. appoints to its Advisory Committee eminent Canadian scientists from various parts of the NATIONAL PROGRAMME COMMITTEE country; it is present at all important forums The three Canadian Institutes in the where the future directions of the Canadian Mathematical Sciences, CRM, Fields, and PIms, mathematical sciences are discussed; it urges its have initiated a new programme for the support organisers to make efforts to ensure the of joint activities of a national stature in the participation of the Canadian specialists in their mathematical sciences. This programme, funded activities; it organises and supports scientific to the tune of $100,000 per year, is administered events across the country; it collaborates with by a National Programme Committee of Canadian institutes, societies and associations. A members from the three institutes which makes specific budget is set aside each year for the recommendations to the three directors. The participation of Canadian graduate students in programme has many mandates, the first being its programmes. The CRM is the only national to fund conferences and workshops in the institute which operates in the two official mathematical sciences across Canada. These languages of Canada and it is highly visible on funds are essentially allocated to activities that the international scene. In keeping with its fall outside the main purview of the three national role, it co-ordinates its activities with institutes, or that would benefit from joint the Fields Institute, PIms, the Canadian institute funding. The programme also aims to Mathematical Society (CMS), the Canadian support activities that are held at the meetings of Applied and Industrial Mathematics Society the three mathematical science societies: CMS, (CAIMS), the Statistical Society of Canada (SSC), CAIMS, and SSC, as well as to support the the Canadian Association of Physicists (CAP), participation of graduate students at these and other societies as well as with other scientific meetings. Finally, it coordinates institutes abroad. international programmes and other ventures where it is advantageous for the three institutes THE FIELDS INSTITUTE (FI) AND THE to act as a whole. PACIFIC INSTITUTE FOR THE Here is the list of the activities sponsored by MATHEMATICAL SCIENCES (PIms) the National Programme in 2000-2001: Since the early 1990’s two other research institutes have joined the CRM on the Canadian Approximation, Complex Analysis and scene: Toronto’s Fields Institute (FI), and the Potential Theory July 3-7, 2000 Pacific Institute for Mathematical Sciences Université de Montréal, Montréal (PIms). As well as co-ordinating their scientific Org.: A. Daigneault (Montréal), Norair Arakelian, (Institute activities, the three institutes have worked of Mathematics, National Academy of Science of Armenia). closely on a variety of initiatives, the most Supported by the National Program Committee (CRM, important of which has been the Mathematics of Fields, PIMS), Université de Montréal, NSERC and NATO Information Technology and Complex Systems, There were a total of 68 participants. of which more is described elsewhere in this report. This NATO Advanced Study Institute, which was the 39th Session of the Séminaire de There are several other initiatives worthy of mathématiques supérieures at the Université de mention. One of these is the National

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Montréal, focused on the interplay between predominantly from the provinces of Manitoba complex analysis and potential theory. and Saskatchewan. The principal speakers were Alano Ancona, The participants developed solutions to three (Orsay) Norair Arakelian (Armenian Academy problems that were brought to the meeting by of Sciences), David H. Armitage (Queen's representatives of industry and government: Dr University of Belfast), Thomas Bagby (Indiana), Norman Corbett, Department of National Mario Bonk (Michigan), Huaihui Chen (Nanjing Defence (in Winnipeg), Dr. Darryl Dormuth, Normal University), David Drasin (Purdue), Atomic Energy of Canada Limited (in Pinawa), Stephen Gardiner (University College Dublin), and Dr. Graeme Strathdee, Potash Corporation Paul M. Gauthier (Université de Montréal) of Saskatchewen (in Saskatoon). This was Thomas Ransford(Laval), Arne Stray (Bergen). followed by three days of intensive work by the The proceedings of the conference, participants. The problem sessions were assisted Approximation, Complex Analysis, and by three experts: Bob Blakely of Texas A & M Potential Theory, will be published by Kluwer University facilitated the AECL problem, Chris Academic Publishers. Budd of the University of Bath facilitated the DND problem, and Tim Myers of Cranfield 12th Canadian Conference on University facilitated the Potash Corporation Computational Geometry problem. Each working group presented a August 16-19, 2000 summary and recommendations of their work to Fredericton, New Brunswick the full group. These summaries are currently Org.: David Bremner, (New Brunswick) being written into reports which will be Supported by the National Program Committee (CRM, Fields, PIMS) and the University of New Brunswick, and published in a proceedings volume in the near sponsored by AARMS future, in both English and French. The reports Computational Geometry is concerned with will also be available on the web at algorithms, software, and mathematical www.math.brandonu.ca/workshopmath. foundations for the treatment of geometric data by computer The Canadian Conference on APICS-AARMS: October 2000 Computational Geometry (CCCG) reflects this Atlantic Association for Research in the diversity of interest, with invited speakers and Mathematical Sciences (AARMS) and Atlantic contributed papers on topics ranging from Provinces Council on the Sciences (APICS) geometric applications in industry to the Annual Meeting frontiers of pure mathematics. There were 75 October 20-22, 2000 Dalhousie University, Halifax participants at the conference from 1 0 countries. Org.: A. Coley, S. Ruan & R. Wood, Dalhousie University The plenary speakers were Gil Kalai, (Paul Erdos Supported by the National Program Committee (CRM, Memorial Lecture), Jerusalem; Naoki Katoh, Fields, PIMS), CMS / CMS Students Committee, Dalhousie Kyoto; and Colin Ware, New Hampshire. University, Nelson Canada, Pearson Education Canada, John Wiley & Sons, McGraw-Hill Ryerson, MathResources A special issue of Computational Geometry: Inc., Waterloo Maple, Inc. Theory and Applications devoted to papers from There were 3 plenary lectures, by Joachim this conference will appear in October 2001. Lambek (Blundon Lecture), McGill; Morven Gentleman, Dalhousie; and Larry Bretthorst, First Prairie Industrial Problem Solving Washington University, St. Louis. Workshop August 7-11, 2000 The annual Undergraduate Mathematics Brandon, Manitoba Competition was held on Friday, with a team of Org.: Lynn Batten (Deakin), John Brewster (Manitoba), two students from each university member of Doug Pickering, (Brandon) & Michael Tsatsomeros (Regina). APICS. And special student sessions were held, Supported by the National Program Committee (CRM, in which students presented the results of their Fields, PIMS), Brandon University, the University of honor theses or summer projects. Manitoba, University of Regina, the Institute of Industrial Mathematical Sciences and Western Economic A special APICS session on Applied Diversification Canada Mathematics & Numerical Analysis was held on The First Prairie Mathematics and Industry Saturday, with the goal of bringing together Problem Solving Workshop attracted 45 faculty, researchers from Atlantic Canada to students and industry representatives, communicate their research work and encourage possible collaboration.

60 Annual Report 2000 - 2001 CRM C o l l a b o r a t i o n s

Two AARMS special research sessions were held Black Holes III: Theory and Mathematical on Sunday, in category theory and Bayesian Aspects statistics. May 19-23, 2001 Kananaskis inn and Conference Center, Kananaskis, Alberta CMS Winter Meeting Org.: V Frolov (Alberta) December 10-1 2, 2000 Supported by the National Program Committee (CRM, Vancouver, Vancouver, B.C. Fields, PIMS), The Canadian Institute for Advanced Supported by the National Program Committee (CRM, Research (CIAR), The Canadian Institute for Theoretical Fields, PIMS), the University of British Columbia, Simon Astrophysics (CITA) and the University of Alberta Fraser University, The Vancouver Institute, the University Black Holes III was a research-related conference of Calgary, The Centre for Experimental and Constructive Mathematics (CECM MITACS, University of focusing on the latest advances in the theoretical Saskatchewan, University of Alberta, The Royal Society of and mathematical aspects of black hole physics. Canada Meeting Director: Dale Rolfsen, UBC It paid special attention to such mathematically Local Arrangements Co-Chairs: Afton Cayford and John oriented problems as the string and M theory Fournier, UBC approach to black holes, numerical studies of The meeting was attended by 286 participants. black hole collisions and critical gravitational The plenary speakers were Patrick Dehornoy collapse, and exact solutions of Einstein's (Caen), Richard Durrett (Cornell), Roger Howe equations in higher and lower dimensions. (Yale), Izabella Laba (UBC), Stanley Pliska (UI Chicago) Paul Roberts (Utah), Peter Sarnak Groups, Rings, Lie and Hopf Algebras (Princeton). The Coxeter-James Lecture was May 28-June 1, 2001 Memorial University given by Damien Roy (Ottawa), the CMS Org.:Y. Bahturin, E. Goodaire, M. Parmenter & Y Zhou Doctoral Prize lecture by Stephen Astels (Memorial Univ.) (Georgia). Bernard Couteau, Sherbrooke was Supported by the National Program Committee (CRM, Fields, PIMS), and the Memorial University of presented with the Adrien-Pouliot Award and Newfoundland Arthur Sherk (Toronto) received the CMS Distinguished Service Award. Yuri Bahturin, with help from Edgar Goodaire, Michael Parmenter and Yiqiang Zhou of There were special sessions in Algebraic Memorial University, ran a highly successful Geometry, Classical and Computational International Workshop on Groups, Rings, Lie Analysis, Financial Mathematics, History of and Hopf Algebras, sponsored by AARMS (the Mathematics, Mathematical Education, Number Atlantic Association for Research in the Theory, Operator Algebras, Ordered Groups, Mathematical Sciences) and Memorial's Partial Differential Equations, and Probability Department of Mathematics and Statistics. The and its Applications. workshop attracted 40 researchers from 10 countries, from Russia to Japan and Belgium to Canadian Annual Symposium on Operator Brazil. Professor Susan Montgomery of the Algebras April 26-May 2, 2001 University of Southern California was named Mathematical Sciences Research Institute (MSRI) the first AARMS Distinguished Lecturer, and gave (Berkeley) two talks on Finite-dimensional Semisimple Hopf Supported by the National Program Committee (CRM, algebras. Fields, PIMS) Co-Chairs: G. Elliott, University of Toronto and I. F. In addition to a plenary talk, Lie algebras over Putnam, University of Victoria rings of differential operators, Fields medalist Efim This meeting was joint for the first two days Zelmanov delivered a well-attended public with the MSRI workshop on Quantization and address entitled Abstract Algebra in the 20th Noncommutative Geometry, and during the Century, on the first evening of the meeting. three-day period April 29 - May 1 it functioned More information and the schedule of the as a closing conference for the 2000-01 MSRI meeting may be found at program on Operator Algebras. http://www.math.mun.ca/- yuri/GRLHA/default.htm

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CMS Summer Meeting graduate students and postdoctoral fellows. First June 2-4, 2001 prize was awarded to Ricardo Carretero- University of Saskatchewan Org.: C. Soteros, M. Bremner, Y. Cuttle & F.-V. Kuhlmann, Gonzalez of Simon Fraser University, with (Saskatchewan) honorable mentions going to Gustavo Carrero of Supported by the National Program Committee (CRM, the University of Alberta, and Chee Tiong Ong. Fields, PIMS), and the University of Saskatchewan Meeting Director: K. Taylor, University of Saskatchewan 29th Annual Meeting of the Statistical The 2001 Summer Meeting of the Canadian Society of Canada (SSC) Mathematical Society was both a scientific and June 10-14, 2001 organizational success. There are relatively few Western North American Region of the International Biometric Society (WNAR) and the Institute for mathematicians who live within easy traveling Mathematical Statistics (IMS) on the campus of Simon distance of Saskatoon, so the total of 279 Fraser University (SFU) in Burnaby, B.C, registered participants exceeded most Supported by the National Program Committee (CRM, expectations and seems to be a record for a Fields, PIMS) and Simon Fraser University regular summer meeting. The meeting was a grand success with The CMS Jeffery-Williams Lecture was given by approximately 500 registered participants. David Boyd, University of British Columbia, and Four workshops were held: the CMS Krieger-Nelson Lecture by Lisa Jeffrey, • Inferences from Genetic Data on Pedigrees by E. University of Toronto. The plenary lecturers Thompson, U. Washington; were Georgia Benkart, Wisconson-Madison; Zoe • The Analysis of Sample Survey Data by J. Chatzidakis, Paris; Geoffrey Grimmett, Eltinge, U.S. Bureau of Labor Statistics and Cambridge; and Barry Simon, Cal Tech. Texas A&M; • There were also ten well-attended special Data Mining by H. Chipman, U. Waterloo; • sessions in Abstract Harmonic Analysis, Beyond MCMC: Monte Carlo Methods in Geometric Topology, Graph Theory, Infinite Bayesian Computation, by J. Ibrahim, Harvard Dimensional Lie Theory and Representation School of Public Health and M. Chen, Theory, Mathematical Education: Cognition in Worcester Polytechnic Institute. Mathematics, Matrix Analysis, Model Theoretic There were 55 sessions in total ranging from Algebra, Number Theory - in Honor of David sessions on Genetics and Forestry to Discrete Boyd, Rigorous Studies in the Statistical Probability and Combinatorics, with a range of Mechanics of Lattice Models, and Scattering internationally known speakers and sessions Theory and Integrable Systems. aimed at graduate students. The complete program is available on the web at CAIMS http://www.math.sfu.ca/-tim/sscmtg.html. June 7-9, 2001 University of Victoria, B.C. Supported by the University of Victoria, PIMS, The Fields CANADIAN ASSOCIATIONS AND Institute, CRM, MITACS and the Laboratory for PROFESSIONAL SOCIETIES Automation Communications and Information Systems Research (University of Victoria) The CRM maintains close ties with the different Scientific Committee Chair: Florin Diacu, University of professional societies in the mathematical Victoria Local organizers: R. Edwards and D. Leeming, sciences: CMS, CAIMS, SSC, and CAP. The University of Victoria president of the CMS is an ex-officio member of About 120 participants enjoyed 6 thematic the CRM advisory committee, and together with sessions plus a poster session. The sessions were: the other institutes, the CRM organises special sessions at CMS meetings. The SSC meetings Applied Dynamical Systems (plenary speaker, have been funded through the national Jerrold Marsden), Data Compression (plenary programme; as well, the CRM gives out a prize speaker, Bin Yu), Fluid Dynamics (plenary each year jointly with the SSC; similarly, speaker, Grae Worster), Computational Biology together with CAP, it awards a prize each year (plenary speaker, Tandy Warnow), in mathematical and theoretical physics. There Mathematical Biology (plenary speaker, Hal is a section on this year’s prize-winners Smith), and Neural Networks and Neural elsewhere in this report. Dynamics (plenary speaker, Nancy Kopell). A panel of five judges evaluated the contributed presentations (both posters and short talks) by

62 Annual Report 2000 - 2001 CRM C o l l a b o r a t i o n s

INTERNATIONAL COLLABORATION release with the other Montréal universities, The CRM has exchange protocols with Osaka bringing the equivalent of another two positions University, with Seoul's Asia-Pacific Center for to the CRM each year. On an ad-hoc basis linked Theoretical Physics, with the Institute of to the theme programme, the CRM has also been Mathematical Sciences at Nankai University, arranging release of research personnel from with the Technical University of Prague and the nearby universities such as Laval, Sherbrooke, University of Rome. Queen’s and Ottawa; some of these arrangements are being put on a more In its publications, the CRM is continuing its permanent footing. The partnerships of the CRM partnership with the American Mathematical with the other research institutes in the Montreal Society, in particular with its two series of joint area have been very profitable. More will be said publications, the CRM Monograph series and about these in the next section. the CRM Proceedings and Lecture Notes. It also has two series with Springer-Verlag, in statistics INSTITUT DES SCIENCES and in mathematical physics. It has publications exchange agreements with Fields Institute, PIms MATHÉMATIQUES (Pacific Institute for the Mathematical Sciences), One important vehicle for collaboration with the M.S.R.I. (Mathematical Sciences Research Québec universities is the Institut des sciences Institute), the Institute for Mathematics and its mathématiques. This institute, which Applications, École Normale Supérieure encompasses most of Québec’s universities, is (France), and Isaac Newton Institute. principally concerned with co-ordinating graduate training. The links with research are A SOLID REGIONAL BASE obvious, and indeed, the CRM and the ISM have a long-standing partnership, in particular in All this activity rests on a solid base of offering postdoctoral fellowships, in organising cooperation with universities in the region, in the CRM-ISM colloquium, and in organising particular the Montréal universities, and most special courses for the CRM’s thematic particularly the Université de Montréal, whose programmes. support for the CRM has been indefatigable. The Université de Montréal releases each year five of its faculty members to work at the CRM, and the support of these faculty members is an essential asset for the CRM's scientific activities. There is in addition a regular programme of teaching

CRM Annual Report 2000 - 2001 63 Industrial Mathematics

The main vehicle for the CRM’s efforts in this • Analyse du risque des flottes de véhicules area is the research networks to which it Georges Dionne, CRT belongs. There are two of these, one the Network • Modèles à noyaux et modèles probabilistes for Computing and Mathematical Modelling pour l’extraction d’informations utiles de (ncm2), involving seven research centres in the grandes bases de données Montreal area in a multi-disciplinary Yoshua Bengio, CRM consortium, and MITACS, a national network. In • Nowcasting and Decision Making addition, it has concentrated its efforts in a few for Environmental Problems chosen areas in which it can develop a Charles Lin, CERCA significant presence. • Image Segmentation and Characterization NETWORK FOR COMPUTING AND using Level Set-Based Curve and Surface

MATHEMATICAL MODELLING (ncm2) Evolution, Boundary Detection and Lie Groups The CRM serves as the organisational centre for Jiri Patera, the Network for Computing and Mathematical CRM • Modelling, ncm2 (in French: Réseau de calcul et Tarification et gestion du revenu en transport de modélisation mathématique, rcm2), a aérien. collaboration which allows the network to Patrice Marcotte, CRT & Gilles Savard, respond to the needs of industry in a large GERAD number of fields related to a common area of • Design et contrôle optimal de dispositifs computing and mathematical modelling, mostly médicaux. around five major themes: (1) risk management, Dominique Pelletier, CERCA (2) information processing, imaging and parallel • Algorithme d’optimisation pour les problèmes computing, and (3) transport and de tournées et d’horaires. telecommunications, (4) health and (5) electronic François Soumis, GERAD commerce. • Quality of Service Mapping as an The other centres of the network at the time of Optimization Problem creation were the Centre for Research on Odile Marcotte, GERAD & Brigitte Computation and its Applications (CERCA), the Kerhervé, UQAM Centre for Interuniversity Research and Analysis • on Organizations (CIRANO), the Centre for Approche hiérarchique et multi-échelles pour Research on Transportation (CRT), and the la localisation des sources d’activité en Group for Research in Decision Analysis MEG/EEG. (GERAD). Since then, two new members joined Bernard Goulard, CRM the network: the Centre de Recherche Overall, the projects have involved the Informatique de Montréal (CRIM) and the participation of 55 researchers in the network Institut National de la Recherche Scientifique- centres, and 76 postdoctoral fellows and Télécommunications (INRS-Télécommunica- graduate students. The total value of the tions). contributions of our partners in 2000-2001 was $737K cash and $423K in kind. The industrial v NSERC-funded research projects partenaires involved at some point with ncm2's research projects are : AD OPTTechnologies Inc., The ncm2 has completed the fourth year of a 5-year NSERC grant with an average of ANIQ R&D Inc., Banque nationale du Canada, $600K per year. Centre de sécurité civile du Québec, CHUM (Centre hospitalier de l’Université de Montréal), The year 2000-2001 saw the consolidation of a CLSC Côte-des-Neiges, Consultants INRO Inc., set of projects started in 2000, and funded as Environnement Canada, Bombardier, Prévost part of two-year cycle, as well as the launch Car Inc., ADS Groupe Composites Inc., Groupe of a series of new projects. The network Québec-Cartier, Hydro-Québec, HydroSoft, Bell funded the following 9 projects during 2000- Mobilité, Assurance AXA, HMS Énergie, 2001: Insurance Bureau of Canada, Microcell, Société de l’assurance automobile du Québec, Silicon

64 Annual Report 2000 - 2001 CRM I n d u s t r i a l M a t h e m a t i c s

Graphics Inc., Insurance Company of British endow chairs and to finance a research Columbia, Air Canada, Ultramar, Hôpital Royal infrastructure. The laboratory has two locations, Victoria, Lockheed Martin Electronic Systems the main one being in downtown Montréal, next Canada, Montreal Jewish General Hospital, to CIRANO. As well as offices, it contains a Urgences Santé, Centre universitaire de santé state-of-the-art simulation laboratory for McGill (MUHC), Société canadiennes des postes, electronic commerce and experimental Astra Zeneca, Boehringer-Ingelheim, Merck economics. The other component is located at Frosst, Biochem-Pharma, CCG. the Université de Montréal, and is devoted to multi-media research. v Network activities A dozen research projects were funded during

The ncm2 organises various networking 2000-2001. Of these, 5 were affiliated with the activities. One popular item is its Grandes CRM. They are Yoshua Bengio’s Datamining, Conférences series, which had two lectures in Rachida Dssouli’s Service Creation Environment: A 2000-2001: Quality Driven Service Engineering Methodology, Designing Telecommunication Network: Modeling Bernard Goulard’s M3Int: Multi-Media Issues, Mathematical Problems, and some Solutions Mathematical Imaging on the Net, and Jiri Patera’s 25 September 2000 Development of the Aperiodic Encryption Method Martin Grötschel, (Konrad-Zuse-Zentrum für Informationstechnik und Technische Universität, Berlin.) and Evaluation and Demonstration of a New Family of Cryptographic Systems. Training products of experts by maximizing contrastive likelihood LABORATOIRE UNIVERSITAIRE SUR 23 October 2000 Geoffrey Hinton, (Univ. College London) LE TEMPS EXTRÊME (LUTE) m In addition, there was a workshop whose The summer of 2001 saw the birth of a new nc 2 purpose was to reinforce networking between laboratory, the Laboratoire Universitaire sur le the CRM and some French partners in brain Temps Extrême (LUTE). The laboratory involves imaging: a contribution of $300K per year from Environment Canada, a significant contribution Plasticité cérébrale et modélisation mathématique 5-6 March 2001 ($1M) in computer time, as well as the presence Bernard Goulard (CRM, Univ. de Montréal) & Habib Benali in the university environment of a good number (CHU Pitié-Salpêtrière & CRM) of Environment Canada’s researchers. The laboratory will involve not only meteorological LABORATOIRES UNIVERSITAIRES research but also an extensive study into impacts BELL as well as mitigating measures.

The CRM is an active participant in the ncm2’s Laboratoires universitaires Bell, part of a joint INSTITUTE FOR MATHEMATICS AND project between the ncm2 and Bell. The ITS APPLICATIONS laboratories aim at creating innovations in the The ncm2 has arranged for an exchange program field of multimedia research and applications with the Institute for Mathematics and its (mainly interactive applications aimed at the Applications in Minnesota. This institute is the general public, electronic commerce applications US’s major research institute in Applied and new generations of evolved networks) as Mathematics. As part of the IMA’s 2002 well as at promoting the training of a highly programme, the ncm2 will be hosting a qualified, international calibre workforce in workshop on distribution networks in the fall of these areas. 2002. As well, the IMA will host a certain The guiding principles of the Bell University number of ncm2 post-doctoral fellows during the Laboratories are: a deep integration with the year. university environment; a balance between exploratory research, applied research and MITACS applications development; a multidisciplinary This network of centres of excellence on approach. Mathematics of Information Technology And These objectives and guiding principles are Complex Systems (MITACS) is one of 18 such made possible thanks to a $12M investment networks set up by the federal government. which is used to finance research projects, to MITACS was put together by the three Canadian

CRM Annual Report 2000 - 2001 65 I n d u s t r i a l M a t h e m a t i c s mathematical institutes (CRM, Fields, PIms) in conferences) linked to the MITACS projects. The 1998, and research began in the spring of 1999. following activities were organized by CRM: The MITACS network covers the whole country, New Methods in Financial Risk Management with the participation of 26 universities, 200 October 13, 2000 researchers, 150 students, and more than 75 Invited speakers: Frank Diebold (University of Pennsylvania and NBER), John Galbraith (McGill University and companies. The research areas (essentially in CIRANO), Victor Chernozhukov (MIT), Simone Manganelli applied mathematics) also cover a large (European Central Bank). spectrum. The industrial partners of the CRM- Estimation of Diffusions centred research projects are: Ad-Opt November 3, 2000 Technologies, Air Canada, Heart & Stroke Invited speakers: Yacine Ait-Sahalia (Princeton University), Ola Elerian (Nuffield College, Oxford University), Michael Foundation, Hydro-Québec, Laboratoires Johannes (Columbia University). Universitaires Bell, National Bank of Canada, and. Procter & Gamble. Volatility Modeling and Financial Applications The second general annual meeting of the December 1, 2000 network was held in May 2001 in Montreal. This Invited speakers: Andrew Matytsin (Merrill Lynch), Eric large-scale event with over 200 participants Jacquier (Boston College University & CIRANO), Marc- André Lewis (CIRANO). brought together most of the researchers in the network, a large number of students (whose New Approaches for Volatility Modeling travel fees were mostly paid by MITACS), and February 23, 2001 Invited speakers: Robert Engle (Stern Business School, New many of the industrial collaborators. At the York University), Neil Shephard (Nuffield College, Oxford conference, results from the research groups University), Nour Meddahi (Université de Montréal, CRDE were presented, but there were also very and CIRANO). interesting presentations from scientists in Finance Day on Option Pricing industry exhibiting their specific needs in the April 6, 2001 areas of applied mathematics covered by the Invited speakers: David Bates (University of Iowa), Jin- Chuan Duan (University of Toronto and Hong Kong MITACS researchers, and displaying the links University of Science & Technology), Stylianos Perrakis that have been established between MITACS (Concordia University), Éric Renault (Université de groups and private partners. Students and Montréal, CRDE and CIRANO). postdoctoral fellows played a very important May 4, 2001 Invited speakers: Nikolay Gospodinov (Concordia), Silvia role at the conference, with a poster session and Gonçalves ((Université de Montréal), Gordon Fisher a study group on the industrial applications of ((Concordia). mathematics held before the main sessions. A Corporate Finance panel selected the best poster presentations. May 11, 2001 These meetings are essential to create new links Invited speakers: Randall Morck (University of Alberta), Denis Gromb (MIT), Anup Agrawal (University of and maintain cohesion between the different Alabama), Martin Boyer (HEC and CIRANO). researchers of the network, which work on quite First varied aspects of applied mathematics: One of the highlights of the year was the “ ever CRM-MITACS Spring School on biomedical research, commercial and industrial Optimisation applications, information technology, ”. Montreal has a very strong school manufacturing, and mathematical finance. Each in optimisation, and it was natural to organise a MITACS project belongs to one of these themes, school on the subject. The event was very well and theme leaders have annual theme meetings attended, with over one hundred participants. where technical details of the research can be There were eight series of four lectures, given discussed more easily than in the general by: meeting. The CRM hosted the following two • John Dennis, Rice meetings : Pattern Search in Optimization • Biomedical applications • Jacques Desrosiers, HEC, Montréal 4-5 November 2000 Column Generation Org.: Robert Muira, Univ. of British Columbia • Michel Gendreau, Univ. de Montréal • Finance Metaheuristics 9-10 February 2001 Org. : René Garcia, Univ. de Montréal-CIRANO • Pavol Hell, Simon Fraser Finally, each of the institutes has organized Graph Partitioning special events (workshops, seminars, • Martine Labbé, Univ. Libre de Bruxelles

66 Annual Report 2000 - 2001 CRM I n d u s t r i a l M a t h e m a t i c s

Design of Telecommunication Networks IMAGING • Maurice Queyranne, Univ. of British The CRM has developed over the last few years Columbia Submodular Optimization a considerable expertise in the area of imaging, • Stefan Scholtes, Cambridge Univ. in particular brain imaging, with a particular Bilevel optimization emphasis on the area of the statistical analysis of images. This has lead to several important • Paul Tseng, Univ. of Washington at Seattle research links with laboratories working in the Semidefinite complementarity area of brain imaging, most notably McGill’s, • David Williamson, IBM Almaden Research Brain Imaging Centre (BIC) and the laboratory of Center, Approximation algorithms brain imaging at the Pitié-Salpétrière in Paris. On the research side, among the projects linked The CRM has participate in two large inter- to the CRM, let us note a few results. For institutional initiatives to obtain imaging and example the group led by B. Jaumard (Poly) has computing equipment: the first as part of the developed new and more powerful optimization MCBIR consortium centred at the BIC, which algorithms for communication channels was awarded 23M by the Canadian Foundation allocation, taking advantage of Montréal's for Innovation (CFI), and another as part of a expertise in operations research applied to University of Montreal-based consortium, which telecommunications networks. The group led by is still under adjudication. In parallel, it was the L. Glass (McGill) has created new atrial lead institution in setting up a Valorisation fibrillation models, allowing classifying and Recherche Québec proposal called detecting different types of atrial fibrillations. Mathématiques et Technologie de l’Imagerie The group led by J. Detemple (McGill) and R. Cérébrale (MITIC), which if successful, will Garcia (UdeM) has produced an impressive equip the community with some of the research number of published results showing progress personnel to run all the large machines. The in the areas of asset allocation, statistical models proposal is still under adjudication. of financial time-series, and statistical inference on these series. The group led by F. Soumis (Poly) has created a new version of the GENCOL software for mathematical programming based on column generation, and the new system, delivered to AD OPT and GIRO, speeds up the solution (up to a factor of 10) of scheduling problems. The group led by Y. Bengio (UdeM) has created a successful new paradigm for statistical language modelling which beats the performance of models which have dominated this area for almost 20 years, thanks to the computation power delivered by the super- computers of the Réseau Québécois de Calcul de Haute Performance. New learning algorithms for data-mining of large data sets, which interest Bell Canada, have also been designed.

CRM Annual Report 2000 - 2001 67 Awards, Distinctions, and Landmarks Researchers play a key role in a research centre such as ours and we are particularly proud of the group that we have assembled. Their scientific and academic influence is outstanding. Here is a short list of the main prizes and awards that they have received in the last year.

André Bandrauk professor in the chemistry François Lalonde of Université de Montréal department, Université de Sherbrooke and on was awarded a Canada Research Chair in sabbatical leave at CRM in 2000-2001 has been differential geometry and topology. awarded the prestigious 2001 John-Polanyi prize. The award ceremony took place during Robert Langlands received on November 27 the 84th conference of the Canadian chemical 2000, the Grande Médaille d'or de l'Académie des society in Montréal, March 2001. This prize was sciences (2000) from the Institut de France. created in honour of John C. Polanyi, recipient of the 1986 Nobel Prize in chemistry Jean LeTourneux took part in a Université de Montréal round-table on culture and the Nantel Bergeron of York University has university: mission impossible? He was also a received a Premier's Research Excellence Award participant in the television show Découvertes on (PREA) from the Ontario Government for the quantum mechanics and its beginnings, in years 2000 through 2005. These prizes are December 2000 on SRC. awarded to the best young researchers in Ontario. He also received a Canada Research John McKay of Concordia University was Chair in Mathematics for the years 2000 through named a Fellow of the Royal Society of Canada 2006 (CRC). 2000. He also received the Faculty Award of Excellence 2001 Francis Clarke was appointed a senior member of the Institut universitaire de France (September Christiane Rousseau has been appointed to 2001) become the president-elect of the Canadian Mathematics Society, starting June 1, 2001. In Stéphane Durand of Collège Édouard- June 2002, she will then become its President for Montpetit was awarded the first prize of the a two-year term. World Mathematical Year 2000 Poster Competition of the European Mathematical Ronald Stern of Concordia University was Society. These posters can be seen at awarded the Ulam Chair at the University of http://www.crm.umontreal.ca/math2000/table Colorado at Boulder for the academic year 2000- au.html 2001.

Bernard Goulard of Université de Montréal Keith Worsley of McGill University gave the took part in the Radio-Canada television show Statistical Society of Canada Presidential Invited Découvertes on quantum mechanics on Address at the Joint Meetings of the Statistical 5/11/2000. He was also a participant in the Society of Canada, the Western North American radio news of Nouvelles Radio-Canada, RDI, on Region of the International Biometric Society the Kursk submarine tragedy, 18/08/2000. and the Institute of Mathematical Statistics in Vancouver last June. Entitled The Geometry of Michel Grundland, of Université du Québec à Random Images in Astrophysics and Brain Mapping, Trois-Rivières was awarded for the Alan it surveyed his pathbreaking work in applying Richards Fellowship at the University Durham. sophisticated statistical and probabilistic tools to the study of brain mapping and astrophysical Niky Kamran of McGill University was the images. principal lecturer of a series of ten CBMS-NSF Lectures in Pure Mathematics, Washington D.C., 2000.

68 Annual Report 2000 - 2001 CRM Research Programmes Research reports appear in their original language.

Twareque Ali de l’intégration. Ce travail d’historien s’appuie Square-integrable Group Representations, sur une abondante documentation inédite Wavelets, and Wigner Transforms (écrite, orale et photographique) dont une partie Twareque Ali's research during the last couple fera l’objet d’une publication sous la forme of years was centred around the theory of d’une base de données, portée sur CD-ROM. Le square-integrable group representations and the chercheur a aussi mis sur pied un atelier relationship of square-integrability with the consacré à l’histoire de la théorie des catégories ; Plancherel transform. It has been demonstrated une première rencontre, organisée en that the Plancherel transform for Type I groups collaboration avec Michael Barr (McGill) a eu is the unifying link between square-integrability, lieu au CRM en août 2000 ; la deuxième the wavelet transform, and the generalized rencontre, organisée en collaboration avec Luc Wigner function. This connection has far- Belair (UQAM), aura lieu au CRM en septembre reaching consequences, in the sense that it can be 2001. used to generate large classes of Wigner functions for Type I groups. From the point of Jacques Bélair view of physical applications, Wigner functions Équations différentielles non linéaires are quasi-probability distributions on classical retardées et modélisation physiologique phase spaces (coadjoint orbits of the groups in La dynamique non linéaire fournit une question), corresponding to quantum interprétation de changements complexes du mechanical states, and hence they can be used to rythme physiologique comme bifurcations study the physical states of atomic and lorsque les valeurs des paramètres de contrôle quantum-optical systems. They can also be sont modifiées. La théorie mène à des interpreted as characteristic signatures of signals prédictions pour les comportements possibles in image analyses. In this way, the use of the dans un environnement expérimental et permet Plancherel transform in connection with square- une explication unifiée des divers régimes. Le integrability unifies the theories of signal travail de Bélair est concentré sur le feedback analysis, wavelet transforms, and quantum non linéaire à retard en contrôle, dans les tomography. On the computational side, a large systèmes d’oscillations hormonales et number of generalized Wigner distributions neuromusculaires, en insistant sur le rôle du have been computed for a special class of group délai, des boucles multiples de feedback et des semidirect products admitting open free orbits délais variables dans la génération de under the coadjoint action. These distributions comportements périodiques (oscillatoires) ou have been used extensively in atomic and irréguliers. quantum optical calculations. En collaboration avec J. Mahaffy, M. Mackey et M. Santillan, on a développé un modèle de Liliane Beaulieu thrombopoièse qui inclut un mécanisme de Bourbaki en son temps destruction à taux constant. Ce travail incorpore L’objectif central de cette étude est de les découvertes les plus récentes sur la reconstituer l’histoire de la formation du groupe thrombopoeitine, et permet de suggérer des de mathématiciens N(icolas) Bourbaki, dans les mécanismes d’induction d’oscillation dans le années trente, de sa survie durant les années de niveau des plaquettes sanguines en circulation. guerre et d’occupation, de la restauration de Avec M. Mackey, ce travail est intégré dans le l’équipe à la fin des années quarante et de son développement d’un modèle général institutionnalisation dans les années cinquante. d’hématopièse pour identifier l’origine Au plan mathématique, il s’agit de retracer les physiologique des oscillations dans la changements de cap pris par Bourbaki dans ses neutropénie. choix théoriques et de les situer dans le contexte Une collaboration avec des chercheurs en des mathématiques qui étaient en train de se pharmacie a mené à une co-supervision développer, notamment en théorie des d’étudiant, afin de construire des modèles qui ensembles, en algèbre, en analyse et en théorie

CRM Annual Report 2000 - 2001 69 R e s e a r c h P r o g r a m m e s incorporent des régimes transients pour la où nous n’avons pas assez de connaissances sur représentation de mécanismes d’absorption de un problème pour directement énoncer une relaxant neuromusculaires, et aboutissant à la solution sous la forme d’un programme, mais où mise au point d’un modèle original. Une autre nous avons des exemples illustrant la tâche à collaboration vise à développer un modèle basé effectuer. Le problème de l’apprentissage peut sur des principes physico-chimiques pour s’exprimer comme le choix d’une fonction parmi expliquer les profils observés dans un ensemble de fonctions selon l’espérance d’un l’administration de médicaments à l’aide de critère (la qualité de la solution choisie par microsphères. l’ordinateur pour un exemple particulier.) Enfin, un étudiant a travaillé dans le cadre du Cependant, comme la véritable distribution des réseau MITACS, sur le raffinement d’un modèle exemples est inconnue, cette espérance ne peut ionique de myocyte auriculaire. pas être calculée, seulement estimée par sa valeur empirique sur les données observées. La Habib Benali véritable difficulté de l’apprentissage est donc de Modélisation en imagerie neurofonctionnelle généraliser ou de pouvoir transférer l’information existante dans les exemples Notre projet de recherche consiste à développer disponibles à de nouveaux exemples. Les une méthodologie de quantification fiable des recherches de Yoshua Bengio se concentrent sur processus physiologiques cérébraux à partir de certains types d’algorithmes d’apprentissage (en séquences d'images médicales multimodalité en particulier les réseaux de neurones artificiels et IRM fonctionnelle, IRM anatomique, MEG et les modèles de Markov cachés) et leurs EEG. Les approches utilisées relèvent des applications (en reconnaissance de formes, techniques statistiques multidimensionnelles reconnaissance de la parole, vision par ainsi que l'apport des méthodes hiérarchiques et ordinateur, analyse de processus industriels, et multi-échelles pour la localisation des la prédiction et prise de décision à partir de activations en IRMf et des sources d'activations séries chronologiques financières.) Cette année en EEG/MEG. Nos applications cognitives et des résultats très importants ont été obtenus cliniques ont pour objectifs de: dans le domaine de la modélisation statistique • Caractériser les circuits neuronaux des du langage, battant les systèmes qui dominent ce processus cognitifs correspondant à des problème depuis vingt ans. ensembles distribués au niveau du cerveau et liés transitoirement pour exécuter une Nantel Bergeron tâche. Les liens dynamiques entre ces Structure combinatoire et algébrique ensembles seront examinés à l'aide des modalités d'imagerie IRMf et EEG/MEG. Nous nous intéressons à l’étude de structures algébriques en utilisant la combinatoire. De • Caractériser les invariants anatomiques et grandes lignes de recherche se découpent dans fonctionnels de ces ensembles neuronaux. nos travaux. Dans des études longitudinales, ces invariants seront corrélés au processus de L’étude d’espaces de polynômes quasi- réorganisation fonctionnelle de l'activité harmoniques associés à des diagrammes. cérébrale. L'étude de la plasticité cérébrale Les algèbres de Hopf associés à des réseaux. chez des patients opérés de Gliomes bas L’étude des fonctions quasi-symétriques et grades guidera nos développements symétriques non-commutatives. méthodologiques. En ce qui concerne (a), nous avons émis l’hypothèse que ces espaces sont hautement Yoshua Bengio symétriques et leur étude a suscité beaucoup Algorithmes d’apprentissage d’intérêt dans la communauté mathématique et Les algorithmes d’apprentissage automatique physique. Nous savons maintenant que certains permettent à l’ordinateur d’apprendre à partir de ces espaces sont liés à des solutions de d’exemples. Ce champ de recherche est à modèles en physique quantique. l’intersection de l’intelligence artificielle, En ce qui concerne (b), nous avons remarqué que l’inférence statistique, et l’optimisation pour plusieurs algèbres, les constantes de numérique. Les algorithmes d’apprentissage structure multiplicative sont liées à sont particulièrement utiles dans les situations l’énumération de chemins dans des réseaux.

70 Annual Report 2000 - 2001 CRM R e s e a r c h P r o g r a m m e s

Nous développons présentement une théorie qui Ces dernières années, il a étudié en particulier la nous permet de mieux comprendre ce lien et structure des variétés de décomposition des d’unifier les constructions existantes. algèbres de Lie semi-simples, avec des Pour (C), nous lions (A) et (B) par une étude applications dans la théorie des arrangements exhaustive de ces fonctions. d’hyperplans associés aux groupes de réflexion.

Steven Boyer Robert Brunet Studies in Low-dimensional Topology Applications des mathématiques au domaine biomédical His research efforts over the last few years focused on the topology of low-dimensional Mes recherches actuelles portent sur les manifolds, particularly knot theory, and the domaines suivants : • geometric representation theory of 3-manifold les risques toxicologiques chez l’humain dus groups. His primary interest in the first of these à la présence de matières toxiques dans research areas is to study exceptional l'environnement • phenomena, which arise from the geometric l'épidémiologie théorique. operation of Dehn surgery on knots. Together En toxicologie, je collabore depuis 7 ans avec le with his collaborator Xingru Zhang (SUNY at Dr Gaétan Carrier de la Faculté de Médecine. Buffalo) they were able to prove definitive L'approche que nous avons développée fait results in several cases they studied. The intervenir des systèmes d'équations methods they employed involved the interplay différentielles (linéaires et non-linéaires) et des between the topology of 3-dimensional outils statistiques pour modéliser l'absorption, la manifolds and the representation theory of their distribution, la métabolisation et l'élimination de fundamental groups. In particular they made substances toxiques absorbées par les humains important theoretical advances in this latter area et les animaux. Chaque substance porte ses which led to other applications in surgery propres mécanismes biologiques et physiques theory. This year he and Zhang have qui doivent être incorporer dans un modèle collaborated with Cameron Gordon to study spécifique. Nos travaux publiés jusqu'ici Dehn fillings of large hyperbolic 3-manifolds touchent les intoxications par les and with Marc Culler and Peter Shalen to dioxines/furannes, le pyrène, l'azimphosméthyl investigate new applications of the Jaco-Shalen- (un insecticide), le méthyl-mercure absorbé par Johannson theory of characteristic sub- la consommation d'aliments, le méthanol et le manifolds. Also he began a collaboration with formaldéhyde présents en milieu industriel. Dale Rolfsen (UBC) and Bert Wiest (Rennes) En épidémiologie théorique, mes recherches se centered on the orderability of the fundamental poursuivent en collaboration avec le Dr Claudio groups of 3-manifolds. Struchiner de la Fundaçao Oswaldo Cruz au Brésil. Elles visent la reconstruction, à partir de Abraham Broer données épidémiologiques accessibles, de Les groupes algébriques de transformation et variables qui ne sont pas accessibles directement la théorie des invariants. mais qui sont toutefois importantes pour prédire Présentement, il s’intéresse aux variétés le développement des maladies infectieuses. Les algébriques qui sont liées à la théorie des principales mathématiques utilisées sont les représentations des groupes de Lie semi- systèmes d'équations aux dérivées partielles et simples. Les liens entre la théorie des des méthodes de régularisation statistique. représentations et la géométrie algébrique sont profonds et très intéressants. Francis Clarke Quelques exemples typiques de telles variétés Stabilisation d’un système contrôle par retour sont les variétés nilpotentes dans une algèbre de d’état Lie, les variétés de décompositions et le fibré Depuis quelques années, les recherches de cotangent d’une variété de drapeaux. Pour Francis Clarke portent surtout sur la théorie du l’étude de ces variétés, on a besoin de la contrôle. Les points forts récents sont les géométrie algébrique, de la topologie algébrique suivants: et la théorie des invariants. • Nouvelle approche aux fonctions Lyapounov pour la stabilité.

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• Méthode originale de construction de retour structures, control of the drag by small changes d'état optimal en théorie de la commande. in the shape of the wing of an aircraft, etc... • Résolution d'un problème classique en There is an urgent need for theory and directions contrôle, en montrant qu'un système est to understand and interpret the increasing commandable vers l'origine si et seulement number of computational results and the si l'on peut le stabiliser par un retour d'état modeling issues encountered in applications. (feedback.) The programme concentrates on the following • Élaboration d'un nouveau concept de retour five intertwined projects: d'état éventuellement discontinu; étude de • the mathematical analysis, differential robustesse. calculus, and optimization for shapes and geometries, Henri Darmon • the development of appropriate intrinsic Complex Multiplication for real quadratic methods for the differential calculus and fields functional analysis on submanifolds of the Last year I was led me to introduce the notion of Euclidean space, modular forms of weight (2,2) on the product of • the intrinsic modelling and analysis of thin a p-adic and Poincare upper half-plane and to and asymptotic shells for C1,1 midsurfaces or define p-adic periods associated to such forms. curves, This clarifies the relation between the • the design of solid vibrating gyroscopes exceptional zero conjectures of Mazur, Tate and (Bryan effect), Teitelbaum and my study with Bertolini of the • the stabilization and control of partial anticyclotomic case. Most significantly perhaps, differential equations on submanifolds when this provides a conjectural p-adic analytic the underlying geometry is an integral part construction of global points on elliptic curves, of the control process (non-cylindrical points which are defined over ring class fields of problems, shells). certain real quadratic fields. This is intriguing, This work has had an impact on the Canadian insofar as it suggests that the theory of complex Space Programme for the design of thermal multiplication should extend (at least diffusers and radiators to condition the thermal conjecturally) to real quadratic fields. It is still an environment of satellites and on the positioning open question (known as Hilbert's 12th problem, of sensors and actuators for satellites of the third or Kronecker's Jugendtraum) to supply analytic generation. The fundamental results of the constructions of the class fields of real quadratic research are also used on current projects on the fields (or of more general number fields) along design of planned NEV to be built by the lines of what is accomplished by the theory Bombardier and the design of medical devices of complex multiplication for imaginary (stents for cardiac surgery). quadratic fields. Daniel Dufresne Michel Delfour Stochastic Processes in Finance Modeling, Design, and Control of Physical and Technological Systems with Respect to Shapes The project concerns the Mathematics of Finance. The pricing of financial derivatives is The theme of this programme is the study of the based on no-arbitrage arguments, in a partial theoretical and numerical aspects of shapes and equilibrium model of the economy. The model is geometries as variables in the modeling, design, expressed in probabilistic terms. In many cases, and control of physical and technological prices are shown to be expected values. The systems. This area of research is becoming very computation of those expected values requires broad, rich and fascinating with an extremely various mathematical tools: stochastic processes, important potential for applications in many series expansions, partial differential equations, different areas: optimal design of mechanical and so on. In particular, the project deals with parts for the automotive industry, positioning of the distribution of functionals of Brownian sensors and actuators, control of the position of motion. the free boundary in material sciences, active control of noise, image processing, free and moving boundary problems, design of biomedical devices, design and control of thin

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Stéphane Durand des relations d'évolution entre les espèces. Fractional Generalization of the KdV Equation L'approche génomique consiste à comparer Using supersymmetry it is possible to generalize l'ordre des gènes dans deux génomes différents. in a non-trivial way the Korteweg-de-Vries Le domaine lié aux réarrangements de gènes equation (KdV) to an integrable system of two date du début des années 90, et son champs coupled differential equations (Mathieu). d'utilisation devient de plus en plus important. Knowing that the supersymmetry can itself be En effet, une multitude de génomes sont extended (parasupersymmetry and fractional maintenant complètement séquencés, et il supersymmetry [Durand, Vinet]), it is natural to devient possible d'inférer des relations look for generalizations to integrable systems of d'évolution à partir de la totalité du matériel several coupled differential equations. The génétique des espèces. Différents problèmes formalism of fractional superspace introduced peuvent être abordés dépendant du type de by Durand allows such a generalization in a mutations, du phénomène d'évolution, et de la natural way. This result is reached using the complexité biologique considérée. Ces fractional extension of supersymmetry, the problèmes donnent lieu à des études Hamiltonian structure of the fractional pseudo- combinatoires, algorithmiques et de théorie des classical mechanics and the fractional graphes variés et complexes. Nous avons generalization of a superextension of a Virasoro contribué à différents aspects de ces problèmes. algebra (and/or its q-deformations). En particulier, nous avons développé un outil qui permet de rechercher le scénario d'évolution Nadia El-Mabrouk le plus parcimonieux entre deux espèces, en Réarrangements génomiques et recherche de considérant des inversions pondérées. motifs d'ARN Richard Fournier Ma recherche s'oriente sur deux axes de la Quelques problèmes d’analyse complexe bioinformatique. Le premier concerne la recherche de structures d'ARN dans les Le domaine de recherche de Richard Fournier séquences génomiques. Étant donné une famille est l'analyse complexe, en particulier la théorie particulière de motifs biologiques structurés géométrique des fonctions d'une variable (motifs d'ARN de transfert, d'ARN complexe. Ce chercheur s'intéresse plus ribosomiques, d'introns auto-catalytiques...), le spécialement à certains problèmes sur les problème général est de localiser dans le génome transformations conformes, les classes spéciales tous les motifs qui sont susceptibles d'appartenir de fonctions univalentes et l'extension au plan à une telle famille. Les motifs sont définis par de certaines inégalités classiques (par exemple un certain nombre de contraintes liées à leurs l'inégalité entre les moyennes arithmétique et structures primaire (1D), secondaire (2D) géométrique.) L'analyse complexe est un sujet (hélices, triple-hélices, pseudo-noeuds) et même classique qui s'est récemment renouvelé grâce à tertiaire. Alors que plusieurs méthodes efficaces l'étude des fractals et de la dynamique des existent pour la recherche de séquences, il fonctions méromorphes ou entières. n'existe aucune méthode efficace pour la recherche de structures secondaires conservées. Marlène Frigon Nous avons développé un algorithme de Théorie des points critiques pour des recherche très flexible et relativement rapide fonctionnelles multivoques pour la recherche de toutes sortes d'hélices. Les recherches de Marlène Frigon portent Notre objectif est d'améliorer cet algorithme du principalement sur l'existence de solutions aux point de vue de sa complexité en temps, mais équations et inclusions différentielles avec ou aussi de la souplesse de la représentation d'une sans impulsions. Les méthodes utilisées sont structure secondaire. Notre but est également de topologiques et variationnelles. Dans ce dernier transformer le prototype en un logiciel domaine, elle a apporté une contribution professionnel facile à utiliser, comportant une originale sur l'application de ces méthodes aux interface graphique appropriée et un moyen équations aux dérivées partielles et elle a interactif d'agir sur la représentation des hélices. contribué directement au développement de la Mon deuxième axe de recherche concerne la théorie des points critiques en élaborant comparaison de génomes, dans le but d'inférer quelques aspects d'une théorie des points critiques pour des fonctionnelles multivoques.

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Les recherches de Marlène Frigon portent ever-higher levels of detail and realism in such également sur la théorie des points fixes. Elle a simulations requires enormous computational récemment généralisé à des systèmes infinis des capacity, and has provided the impetus for résultats classiques en théorie des équations dramatic breakthroughs in computer algorithms différentielles à savoir les théorèmes de Picard et and architectures. Parallel computers have de Peano. Aussi, comme mentionné proved to be the only tools with the necessary précédemment, ses travaux portent sur les capacity to satisfy current demands in research équations différentielles avec impulsions. Ces and industry. But the development of parallel problèmes sont particulièrement difficiles algorithms specialized for the underlying lorsque les impulsions se produisent à des problems are lagging behind. This is my current moments variables. Avec D. O'Regan, elle a main area of research. obtenu plusieurs résultats dans ce domaine. Paul Gauthier Langis Gagnon Analyse Traitement et analyse d’images haute Gauthier et ses collaborateurs et étudiants résolution continuent leurs recherches en approximation et Les travaux du Dr Langis Gagnon, membre ont amorcé une étude des rapports avec le associé au CRM et responsable de l’équipe problème principal des mathématiques pures – Vision et Imagerie du Centre de Recherche celui de trouver les zéros de la fonction zeta de Informatique de Montréal (CRIM), portent, entre Riemann. autres, sur le traitement et l’analyse de scènes terrestres dans les images satellites haute Pawal Gora résolution (optiques, multi-spectrales et radars.) Absolutely continuous invariant measures in Les thèmes étudiés incluent le filtrage one and higher dimensions. multirésolution du chatoiement dans les images The theory of one and higher dimensional RADARSAT, la caractérisation texturale des piecewise expanding transformations is a images IKONOS pour des fins de segmentation beautiful, important and challenging subject for des boisés, le raffinement de résolution des research. Methods ranging from theory of images multispectrales, la segmentation des numbers and elementary geometry to measure zones hydriques dans l'imagerie radar par theory and functional analysis are used. In turn contours actifs géométriques, la détection de these transformations find application in many réseau routier, etc. Ces travaux sont physical and biological problems. subventionnés par le CRSNG et le CRIM avec une contribution en bourses d’études du CRM. A very useful in applications generalization is so Un autre domaine principal de recherche porte called "random map", a process that on each step sur l’analyse des images ophtalmiques et est applies a map from some family according to a supporté en partie par une subvention given set of probabilities. One of the applications d’infrastructure du FCI. Tous les étudiants is a model of the superposition of quantum supervisés par le Dr Gagnon bénéficient d’une states in alternative (based on theory of fractal bourse du programme de bourse d’études space-time) approach to quantum physics. supérieures en milieu de pratique du fond We want to continue our study of one and FCAR. higher dimensional maps and random maps, and explore the properties of their invariant Martin Gander measures. Another problem is the global control Parallel Algorithms for High Performance of higher dimensional systems using methods Computing related to acims. One and two-dimensional Computation is now regarded as an equal and results are very promising. Still another field we indispensable partner, along with theory and plan to explore are applications of dynamical experiment, in the advance of scientific systems to biology and medicine. We have some knowledge and engineering practice. Numerical results in this direction and will continue our simulation enables the study of complex systems work. In particular, in collaboration with and natural phenomena that would be too medical specialists, we will work on the expensive or dangerous, or even impossible, to dynamics of 6-MP metabolism when the drug is study by direct experimentation. The quest for

74 Annual Report 2000 - 2001 CRM R e s e a r c h P r o g r a m m e s used in the Inflammatory Bowel Disease nous fournit de nouveaux outils pour aborder treatment. les phénomènes non-linéaires en physique, spécialement ceux décrits par des systèmes Bernard Goulard multidimensionnels d’équations aux dérivées Méthodes statistiques et imagerie partielles (EDP) et qui n’ont pu être résolus par Le traitement d'une image revient de plus en d’autres méthodes (par exemple la diffusion plus à reconstruire au mieux un objet à partir inverse.) Le programme de recherche est d'informations incomplètes et souvent bruitées, constitué des quatre projets suivants: • ce qui amène l'utilisation de connaissances " a Symétries conditionnelles pour les systèmes priori " et de méthodes statistiques. B. Goulard, d’équations aux dérivées partielles non- J.M. Lina et D. Clonda procèdent à une linéaires. • modélisation statistique des images à traiter Une comparaison entre les différentes basée sur les propriétés des ondelettes de méthodes de groupe de Lie servant à Daubechies complexes. Leur caractérisation des solutionner les équations aux dérivées images passe par une modélisation de la partielles • distribution des coefficients en ondelettes par le Solutions invariantes et partiellement biais d'un modèle en arbre pour un processus de invariantes des équations de la dynamique Markov caché. Ce modèle a été perfectionné et des fluides. • appliqué à différents problèmes de traitement Les ondes de Riemann multiples pour les du signal. Ces études sont en phase avec les systèmes quasilinéaires d’équations aux travaux menés dans le cadre d'une collaboration dérivées partielles et les relations avec la avec le groupe de Pitié-Salpêtrière (Paris) dans méthode de réduction par symétries. l'analyse des mesures de magnétoencéphalographie (cf J. M. Lina.) Les John Harnad premiers résultats ont été présentés. Systèmes intégrables, déformations isomonodromiques et applications Par ailleurs, dans un projet subventionné par Bell-Lub, B.Goulard, J.M.Lina et F. Nekka Pendant l’année passée (2000-20001), les projets travaillent en collaboration avec B. Johnston suivants ont été développés: (INRS Telecom) à la mise en oeuvre d'un La relation entre deux approches aux systèmes système basé sur la technologie intemet. hamiltoniens complètement intégrables a été L'objectif est de faire circuler des images mise au point : l’une est fondée sur les flots médicales et des logiciels d'analyse entre des hamiltoniens isospectraux dans les groupes et lieux (hôpitaux, instituts,..) éloignés les algèbres de lacets, générées par les invariants géographiquement et ce, dans des conditions spectraux avec une structure de Poisson qui maximales de confidentialité, intégrité et provient d’une matrice R classique; l’autre, disponibilité des données. Ce travail implique l’approche développée par Magri et ses notamment une intégration d'analyse des images collaborateurs, est fondée sur la notion de et de leur circulation sur le réseau. Un premier structures multi-hamiltoniennes On a démontré prototype de serveur a été mis en œuvre et testé que, dans le contexte de flots isospectraux dans avec des images de fond de l’œil et des les algèbres et les groupes de lacets, tous les opérateurs très simples. résultats de la seconde approche (c’est à dire : l’existence des structures multihamiltoniennes, Michel Grundland les invariants commutatifs provenant du Symétries et solutions des systèmes non- théorème de Gel’fand-Zakharevich et les linéaires en physique coordonnées séparatrices associées aux vecteurs Au cours des dernières années, les recherches de propres du tenseur de Nijenhuis) découlent de la Michel Grundland portent sur les méthodes de théorie des matrices R associées aux structures réduction par symétries (MRS) ainsi que sur la de Poisson holomorphe sur les surfaces méthode des invariants de Riemann (MRI) et complexes. Cette approche a été étendue leurs applications aux équations de la théorie également aux cas des structures de matrices R des champs non-linéaires, à la physique de la classiques quadratiques, et aux cas matière condensée ainsi qu’à la dynamique des trigonométriques et elliptiques. fluides. Le développement de ces méthodes

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Un nouveau projet, développé conjointement This researcher is also studying the spectra of avec Marco Bertola et Bertrand Eynard, concerne elements of group rings and certain questions in les modèles multi-matriciels aléatoires et les extremal & spectral graph theory. polynômes bi-orthogonaux. Nous avons démontré que les systèmes d’équations de Niky Kamran récurrences satisfont par les polynômes Géométrie des équations aux dérivées biorthogonaux par rapport aux mesures de la partielles/ Groupes de Lie de dimension forme d’exponentielles d’un polynôme, les infinie/ Équations d’onde en relativité générale systèmes différentiels et les systèmes de Le programme de recherches de Niky Kamran déformations induites par des changements comporte trois axes principaux. D’une part, il dans la mesure sont compatible, et ainsi la vise à étudier les rapports géométriques qui monodromie des systèmes différentiels est existent entre les diverses propriétés invariante par rapport aux déformations. Une d’intégrabilité géométrique et l’existence de lois généralisation du théorème classique de de conservation pour les équations aux dérivées Christoffel-Darboux sur les sommes des partielles en dimensions m ≥ 3. D’autre part, il polynômes orthogonaux a été déduite pour le porte sur l’étude (en collaboration avec P. Olver cas biorthogonal. Nous avons également et T. Robart) des structures de groupe de Lie de démontré un théorème de « dualité » spectrale dimension infinie qui sont adaptées à la théorie qui dit que les courbes spectrales associées aux des pseudogroupes de Lie analytiques de type couples duaux de systèmes d’équations infini. Enfin, il a pour but d’étudier le différentiels sont égales. comportement global des solutions d’équations d’onde telles que l’équation de Dirac dans les Jacques Hurtubise variétés pseudo-riemanniennes correspondant Systèmes intégrables aux solutions exactes de type trou noir des Les travaux de J. Hurtubise ont porté sur les équations d’Einstein, un des objectifs étant de systèmes intégrables. Deux articles, un sur les démontrer la non-existence de fermions en systèmes de Hitchin, et l’autre sur les modules configuration stable au voisinage d’un trou noir de fibrés paraboliques sont parus. Un autre, en rotation. Ces travaux sont réalisés en portant sur la séparation de variables pour les systèmes de Sklyanin a été soumis. Cet article a collaboration avec F. Finster, J. Smoller et S. T. donné lieu à un projet majeur sur la Yau. généralisation de ces systèmes à des groupes réductifs arbitraires présentement en voie avec Paul Koosis E. Markman. Amélioration de l’estimation harmonique Jusqu’à récemment l’estimation harmonique Dmitry Jakobson (c'est-à-dire l’emploi de la formule généralisée Semiclassical Asymptotics in Spectral de Jensen) a été l’un des procédés les plus Geometry puissants pour trouver des bornes pour une The main interests of this researcher lie in the fonction analytique dont le comportement précis area of analysis, especially the properties of est inconnu. Il est très important en analyse de eigenvalues and eigenfunctions of Laplace pouvoir établir ces bornes, car elles nous operators on Riemannian manifolds. The permettent d’augmenter notre connaissance de correspondence principle in quantum mechanics la fonction en question. Mais l’estimation predicts that in the high-energy limit. Those harmonique n’est pas un outil universel et ne properties would depend on the geodesic flow s’applique pas dans certaines situations; il serait on the manifold, and this researcher is involved donc intéressant de trouver une méthode qui va in a detailed study of this correspondence, other plus loin. areas of interest include the study of Lp norms On peut parfois obtenir les bornes qu’on cherche of eigenfunctions, their nodal sets and critical pourvu que les intégrales figurant dans points. l’estimation harmonique puissent être Another project concerns the study the statistics remplacées par des sommes de forme semblable, of zeroes of generalized lame harmonics in prises sur un ensemble discret de points, et on a various regimes (semiclassical, thermodynamic vu dernièrement que ce remplacement est etc.) and their complex analogues. parfois possible. Pour cela la plus petite majorante

76 Annual Report 2000 - 2001 CRM R e s e a r c h P r o g r a m m e s surharmonique est employée. Le but de ce projet de ce que les physiciens appellent la théorie des est de comprendre le rôle, encore mystérieux, super-cordes. Son développement a attiré joué par cet objet dans ce genre de question; on l'attention des physiciens (Witten, Vafa, espère pouvoir de cette façon parvenir à une Aspinwall, Greene,...) aussi bien que celle des méthode générale. De nouveaux résultats ont été mathématiciens dont les méthodes ont suivi une obtenus. évolution rapide depuis vingt ans. La plupart des travaux portent sur les aspects Dimitry Korotkin dits hard de la topologie symplectique et des Riemann-Hilbert problems and tau-functions systèmes hamiltoniens, en se servant de in integrable gravity models techniques topologiques, géométriques et During the 2000-2001 year the research went in analytiques, en particulier les méthodes the following main directions. First, it was d'équations aux dérivées partielles elliptiques et analysis of a class of matrix Riemann-Hilbert la cohomologie quantique. Ces méthodes sont problems solvable via the objects associated to fondées sur l'étude du comportement des compact Riemann surfaces. espaces de modules de courbes Riemann-Hilbert problems of that kind arise in pseudoholomorphes, qui sont solutions des relationship with conformal field theory, as well équations de Cauchy-Riemann généralisées as in the theory of exact solutions of Einstein's associées à une structure presque complexe. Les equations. The main result in this direction was résultats que nous avons obtenus au cours des the solution of arbitrary Riemann-Hilbert deux dernières années incluent l'application de problem with quasi-permutation monodromy la cohomologie quantique à l'étude de la matrices in terms of Szego kernel on an auxiliary dynamique hamiltonienne qui a mis en évidence Riemann surface. It was established explicit link les propriétés de stabilité et de rigidité des between Malgrange divisor of the Riemann- systèmes hamiltoniens. Ils contiennent aussi une Hilbert problem and theta-divisor on the forte généralisation des travaux de Kirwan et Jacobian of the auxiliary algebraic curve. d'Atiyah-Bott sur les fibrations symplectiques ou Another problem was the application of algebro- algébriques, à partir de méthodes tout à fait geometric solutions of Einstein's equations nouvelles. Je poursuis également l’étude des (found by the author 12 years ago) to realistic groupes de difféomorphismes symplectiques de physical systems, in particular to rotating dust certaines variétés rationnelles qui conduit à une discs interacting with central black hole. connaissance du type d’homotopie rationnelle Some preliminary results were obtained in this de l’espace des plongements symplectiques de la direction; in particular, the stationary axially boule standard. symmetric Einstein's equations were derived from Fay's trisecant identity. Robert Langlands, Marc-André Lewis et Yvan Saint-Aubin François Lalonde The Ising Model in Domains with Boundary Topologie symplectique et systèmes In order to describe the critical behaviour of the hamiltoniens two-dimensional Ising model, this group of Les travaux les plus récents se rapportent à la researchers has introduced a field similar to that topologie symplectique, à la théorie de jauge et of the free boson whose jump lines delimit the aux systèmes hamiltoniens, sujets qui ont fait constant spin clusters. The statistical l'objet d'un intense développement depuis une distribution of this field has been studied by quinzaine d'années. Monte-Carlo simulations. It satisfies the two La topologie (ou géométrie) symplectique est hypotheses of universality and conformal l'étude mathématique des espaces courbes, de invariance. Crossings on clusters of positive dimension paire arbitraire, munis d'une forme spins have also been investigated and some of symplectique, analogue anti-symétrique d'une their properties are similar to those of crossings métrique riemannienne, qui donne à ces espaces in percolation models. la structure qu'il faut pour donner un sens aux lois de la physique aussi bien qu'aux procédés de quantification (passage du classique au quantique.) Ce sujet est le versant mathématique

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Christian Léger Le projet est au tout début de son cycle de Resampling Methods and Tuning Parameter maturité et des algorithmes de détection de Selection micro événements sont présentement étudiés. Christian Léger’s research is on the use of L'étape suivante sera la validation de ces resampling methods in statistics. These methods algorithmes en utilisant plusieurs nuits de use the power of the computer to approximate sommeil. the distribution of an estimator to construct, for instance, a confidence interval for an unknown Sabin Lessard parameter. To validate these methods, Analysis of Population Genetic Models asymptotic theory as well as computer Sabin Lessard's research interests include a wide simulations are used. In the last few years, Léger variety of population genetic models and the has constructed confidence intervals which take concomitant evolutionary dynamics. His into account the data driven selection of the ultimate goals are: a) to explain the maintenance model in multiple linear regression when the of variability in biological populations, b) to model is chosen using the data. By using the develop mathematical and statistical techniques bootstrap or subsampling to create new data sets to analyse population genetic structures, c) to and by rechoosing the model on each of them, it deduce general evolutionary principles, and d) is possible to construct confidence intervals to study populations with complex interactions which reflect the uncertainty in the model between individuals. selection step. Jean LeTourneux Frédéric Lesage q-fonctions spéciales Détection automatique des micro événements La plupart des fonctions spéciales de la physique dans les EEG du sommeil mathématique possèdent des q-analogues, c’est- Les domaines multi-disciplinaires sont devenus à-dire des déformations faisant intervenir un part intégrante de l'activité de recherche en paramètre q. De même que les algèbres de Lie mathématique. Parmi celles-ci, l'utilisation de fournissent un cadre unificateur pour l’étude des techniques mathématiques modernes pour fonctions spéciales, les q-déformations de ces l'analyse d'images médicales et la reconnaissance algèbres en fournissent un pour celle des q- de formes. fonctions spéciales. En collaboration avec Luc Le présent projet, fait en collaboration avec le Vinet (CRM) et Roberto Floreanini (Trieste), Jean centre du sommeil de l'hôpital Sacré-Coeur, LeTourneux étudie systématiquement consiste à étudier le problème des EEG du l’interprétation algébrique des q-polynômes sommeil. Ces signaux sont à la base de l'analyse spéciaux contenus dans la hiérarchie des du sommeil et sont pris à partir d'électrodes polynômes d’Askey-Wilson. positionnées sur le cerveau lors du sommeil. L'analyse elle-même se fait en interprétant les Jean-Marc Lina signaux enregistrés pour toute une nuit à partir Ondelettes, statistique et processus complexes de critères bien établis permettant de spécifier L'activité scientifique de JM Lina est les différents stades du sommeil de même que principalement consacrée à la modélisation certains événements ponctuels. statistique de certains processus reliés à l'imagerie médicale à des fins d’aide au Un des problèmes rencontrés lors de ces diagnostic ou de compréhension au niveau analyses est le temps pris par un humain pour fonctionnel. On s’intéresse ici aux situations où analyser une nuit de sommeil. Ici, des méthodes ces processus ne sont pas directement mesurés mathématiques d'analyse du signal cherchent à ou observés: associés ou non à une reproduire ce travail de façon automatique et représentation particulière du signal, ils sont reconnaître la présence de micro-événements "cachés". L’objectif de cette modélisation est dans les signaux EEG. À plus long terme, ces d’expliquer, de façon quantitative, les méthodes pourraient ouvrir la porte à une observations via le comportement de ces nouvelle forme d'analyse où des marqueurs variables. Ce cadre méthodologique correspond aux approches Markoviennes en imagerie qui mathématiques cachés, invisibles à l'analyste sont de plus en plus utilisées en traitement de humain, seraient découverts. l’information. On s’interesse à deux aspects mathématiques. D’une part, la représentation

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des observations qui permet d’exhiber des related to the Monster, Baby, and F24 as Schur propriétés ou des comportements typiques dans multipliers. les données. Dans ce volet, la représentation hiérarchique (comme celle fournie par la Jean Meunier représentation multi-échelle en ondelettes) est Traitements numériques d'images médicales principalement étudiée. D’autre part, la modélisation statistique qui fait intervenir des Mes travaux de recherche portent sur variables explicatives à partir desquelles on peut l'estimation du mouvement tridimensionnel, le répondre au problème posé. Ces deux sujets sont recalage, la comparaison de données volumiques étudiés dans deux domaines de l’imagerie et sur la construction d'atlas (modèle) médicale. En mammographie, il s’agit de numérique avec applications en imagerie déterminer la présence de régions cancéreuses médicale dans le but de faciliter une analyse en mesurant la « rugosité » locale de l’image, particulièrement autour des foyers de tridimensionnelle de ces images par le médecin. microcalcifications. L’étude et la modélisation Ces travaux se font avec la collaboration des statistique des coefficients en ondelettes pour ce grands hôpitaux universitaires montréalais et de type de données constituent le cœur de ce thème l'Institut de génie biomédical de l'Université de de recherche. En imagerie cérébrale, on Montréal et de l'École Polytechnique. s’intéresse à la MEG qui consiste à déterminer Plus particulièrement, en cinéangiographie les sources d’activation cérébrale à partir des biplan (séquences de radiographies obtenues mesures de magnéto-encéphalographie. La selon deux vues) nous avons développé une variable d’activation n’étant pas directement mesurée, nous étudions un modèle statistique de approche d'autocalibrage des caméras qui ne type Markov caché. Finalement, modélisation requiert pas d'objet de calibrage (cube ou autres) multi-échelle et inférence statistique en contrairement aux autres méthodes classiques résolution de problèmes inverses font l’objet ceci afin de récupérer la forme et le mouvement d’un travail de recherche en imagerie cérébrale. 3D d'un objet comme le réseau coronarien. Cette Celui-ci repose sur le formalisme de Maximum méthode réduit considérablement la complexité d’Entropie en moyenne. Ces deux thèmes de du protocole d'acquisition des images puisqu'on recherche font l’objet de collaborations n'a pas à utiliser de cube de calibrage après internationales (A. Arnéodo, CNRS, Fr. et H. chaque examen d'un patient. Nous travaillons Benali, INSERM, Fr.) aussi au développement d'une méthode de reconstruction 3D à partir d'une seule vue John McKay (vision monoculaire) en se basant sur des Moonshine and its Haupt Modules and ADE connaissances a priori sur le réseau coronarien. We investigate the consequences of the relation Nous avons aussi développé une méthode pour between the Monster sporadic finite group, and construire un atlas numérique (modèle moyen the Haupt modules which describe its avec les variations normales) du cerveau humain representations. This research was started in en utilisant un ensemble d'images de résonance 1979 by the author and is known as Monstrous magnétique obtenues chez des sujets sains. Ce Moonshine. Designated by John Thompson modèle (atlas) possède deux importantes (Fields medallist) as a ‘problem for the next propriétés généralement absentes century’ it has recently been explained by simultanément dans les autres atlas Richard Borchards for which he was awarded a électroniques : une intensité moyenne et une Fields medal in 1998 at Berlin. By using forme moyenne des tissus du cerveau; il sera recurrence relations for the Fourier coefficients particulièrement utile pour aider à porter un of the Haupt modules, and the devices of diagnostic ou pour classifier des images. Nous symmetrization and desymmetrization, we travaillons présentement à étendre cette believe we have a complete list. A consequence approche à la construction d'un atlas spatio- of this is the description of many hundreds of temporel du réseau coronarien du cœur en integrable systems attached to the Haupt mouvement, à la modélisation géométrique de la modules, generalizing the work of Halphen in cornée humaine et à l'imagerie SPECT (Single 1881 on the reduction of self-dual Yang-Mills. Photon Emission Computed Tomography The ADE problem, now called the McKay utilisée en médecine nucléaire.) correspondence, involves the remarkable fact that the fundamental groups of type E8, E7, E6 are

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Fahima Nekka the gradings of classical simple Lie algebras over Vers une nouvelle méthode de classification et the real number field. Most important among the modélisation pharmaco-cinétique des effets applications is the grading preserving spatiaux des médicaments à action rapide. deformations of the algebras. En géométrie fractale, il est bien connu qu’on Study of properties and applications of the cut peut définir différentes dimensions pour le and project point sets ("quasicrystals"). même objet, ce qui a suscité beaucoup de Completion of a small monograph where the recherche autour de la définition et du calcul des properties of the 1-dimensional sets are brought dimensions fractales. Il est aussi possible together, proven, and explained. d’associer la même dimension fractale, voire le Specific applications of image processing and même spectre de dimensions, à différents objets. data fusion motivated mainly by our Ce dernier point est d’importance centrale dans collaboration with Lockheed Martin, Canada. la caractérisation des structures et leur Most intensive efforts will be invested in the comparaison en vue de classification. C’est dans application of "quasicrystals" in cryptography, ce but que nous avons entamé notre recherche and in the exploration of the many possibilities, sur un des indices les plus popularisés par evaluation of demonstration models, and the Mandelbrot, qui néanmoins a bénéficié de peu security questions. d’études. Nous avons été menés ainsi à étudier un aspect de l’écart par rapport à l’invariance François Perron par translation. On a démontré que la mesure Inférence statistique, simulations MCMC (de Hausdorff) générée par l’intersection des Les intérêts de recherche de F. Perron sont liés à ensembles étudiés avec leurs translatés vérifie la statistique et portent plus particulièrement sur une loi de conservation de masse avec les les sujets suivants : théorie de la décision, échelles. Nous avons aussi trouvé que le spectre analyse multidimensionnelle, statistique de mesures associé à ces intersections pouvait bayésienne et simulations par MCMC (chaînes servir de nouvel outil de classification entre de Markov avec Monte-Carlo.) Les problèmes deux structures distinctes mais ayant la même liés à la théorie de la décision visent à améliorer dimension. Nous mettons actuellement au point les estimateurs existants. L’approche privilégiée l’algorithme de calcul de ce spectre de mesure consiste à produire de meilleurs estimateurs afin de le valider et de l’adapter à des structures minimax, l’estimateur minimax étant celui qui réelles. performe le mieux dans le pire des cas. Un Les bloqueurs neuromusculaires sont utilisés estimateur est meilleur qu’un autre s’il fait comme agents anesthésiants à action rapide. Il toujours au moins aussi bien que l’autre en est donc important de bien modéliser la phase faisant parfois mieux. Dans l’article ‘On a initiale afin de bien évaluer les paramètres Conjecture of Krishnamoorthy and Gupta’ on remet pharmacocinétiques et pharmacodynamiques. en question la conjecture qui prétend qu’un Les modèles classiques s’avèrent inadéquats certain algorithme améliore plusieurs pour la description de la circulation non- estimateurs minimax. Dans un autre contexte, homogène de ces médicaments. Dans ce celui de l’estimation d’une moyenne pour une deuxième projet, nous avons développé un distribution de loi normale en plusieurs modèle basé sur l’équation de diffusion qui dimensions, on sait que lorsque la dimension incorpore l’hétérogénéité spatiale par une excède deux, on peut améliorer l’estimateur meilleure compréhension physiologique de la donné par la moyenne échantillonnale. Dans circulation et nous l’avons validé sur une variété l’article ‘Improving on the MLE of a Bounded de données cliniques. Normal Mean’ on montre que le même phénomène se produit en dimension 1 et 2 Jiri Patera lorsque la moyenne est tronquée. De façon Lie Theory, Quasicrystals, and Image générale, on favorise l’approche bayésienne. On Processing y parvient plus facilement avec l’aide de l’ordinateur en effectuant d’intenses calculs Following is a list of the research interests being numériques. Ceci nous amène à raffiner les pursued by Jiri Patera. méthodes de simulation existantes. Dans l’article Application of Lie theory. Exploitation of our "Beyond Accept-Reject Sampling" on perfectionne most recent results, namely the classification of la méthode d’acceptation-rejet. Un projet en

80 Annual Report 2000 - 2001 CRM R e s e a r c h P r o g r a m m e s cours est de la rendre encore plus sophistiquée Christiane Rousseau en y incorporant des chaînes de Markov. Étude qualitative et bifurcations dans les équations différentielles ordinaires Colin Rogers Un premier aspect de la recherche de C. Deformation of Isothermic Surfaces and K- Rousseau porte sur les problèmes de finitude Nets in Membrane Theory and Nonlinear des cycles limites (cyclicité finie) dans les Elasticity : Application of Solitonic Methods bifurcations des champs de vecteurs du plan Solitonic pulses with their novel survival avec applications aux bifurcations génériques de properties following interaction have major champs de vecteurs ainsi qu’à la partie finitude technological applications to optimal du 16e problème de Hilbert pour les systèmes communication and semi-conducting devices. quadratiques, laquelle découle de la cyclicité Materials which allow solitonic propagation are finie de 121 graphiques du plan. Des progrès très of paramount practical importance in nonlinear significatifs ont été accomplis: le premier avec optics. This project will provide model les applications de la thèse de H. Zhu permettant constitutive laws for smart materials which de montrer la cyclicité finie de graphiques admit soliton transmission. In a parallel génériques ayant un point nilpotent de type investigation, solitonic methods will be used in elliptique ou selle, le deuxième avec F. the engineering design of elastic membrane Dumortier et Y. Ilyashenko où un principe de structures. « prolongement analytique » permet de montrer We also investigate the synthesis of materials aisément la cyclicité finie de graphiques science. Here, recent advances in materials apparaissant dans des familles continues de design and soliton theory are brought together graphiques. to synthesize smart solitonic materials. Un deuxième aspect porte sur les critères d’intégrabilité et de linéarisabilité d’un champ Ivo Rosenberg de vecteurs polynomial au voisinage d’un point Clones and Relations de selle. Des travaux préliminaires montrent une Universal algebra. The main topic is the study of organisation remarquable des strates de champs clones, on a finite universe A, which are intégrables et linéarisables. Le travail se poursuit composition closed sets of operations on A. This pour expliquer ce phénomène. La démarche is a basic problem for finite algebras. Ideals, consiste à regarder l’influence des invariants de congruence kernels and discriminator algebras Martinet-Ramis pour la classification analytique were also studied. Algebraic duality, an des points de selle résonants et des col-nœuds extension of Stone’s duality for boolean algebras, lorsqu’on perturbe les valeurs propres. Dans ce allows topological representations of algebras. It projet C. Rousseau collabore avec C. Christopher was shown that dualizability is invariant under (Plymouth, UK), P. Mardesic et R. Roussarie nilpotent shifts. (Dijon.) The very complex problem of local completeness Roch Roy and of locally maximal clones on infinite On Time Series Analysis and Modelling universes was reduced to a few more Roch Roy’s main research interest is time series manageable cases. The completeness problem analysis and modelling. Time series analysis for uniformly delayed circuits over a finite at- continues to be a major field of interest in least-four-letter alphabet was advanced. The statistical research as almost scientific discipline simplicity of the lattice of clones and the is concerned with data collected over time. His description of all Mal’tsev clones on a finite at- recent research was mostly concentrated on the least-three-element universe was studied. following projects: Hyperalgebras. A hyperalgebra on A is an Tests for independence of two possibly algebraic structure with values in the set P of nonstationnary multivariate time series and nonvoid subsets of A. I. Rosenberg studied them application in economic and finance; as C-isotone algebras on P which allowed a Goodness of fit tests for multivariate time series universal algebra approach to hyperalgebras and models; lead to interesting problems on C-isotone clones Study of the properties of a class of generalized on P. In particular, hypergroups on A can be linear regression models with latent variables for studied as C-isotone monoids on P.

CRM Annual Report 2000 - 2001 81 R e s e a r c h P r o g r a m m e s describing time series of counts and application Elisa Shahbazian in epidemiology; Data Fusion Modelling of nonlinear time series using weak Elisa Shahbazian’s main area of expertise is Data ARMA representations. Fusion architectures, and how the data fusion During the past year, with the Ph.D. student capabilities should be integrated within large Pierre Duchesne, he has developed a class of systems. robust tests for the hypothesis of independence Since 1994, she has been responsible for of two univariate ARMA time series against the conception, prioritization, and coordination of alternative of serial correlation of an arbitrary all R&D activities at Lockheed Martin Canada. form between the two series. These activities involve development of intelligent decision support technologies for C4I David Sankoff applications (Data Fusion – levels 1, 2, 3 & 4, Biomathématique et sociolinguistique Resource Management, Imaging, etc.), and the David Sankoff’s research involves the engineering infrastructure for the establishment formulation of mathematical models and the of these technologies on board the naval and development of analytical methods in the airborne platforms of Canada, and sciences and humanities. This includes the diversification of these capabilities into design of algorithms for problems in commercial applications such as Intelligent computational biology, applied probability for Transportation and Remote Sensing. phylogenetic analysis of evolution, and statistical methodology for studying Ronald Stern grammatical variation and change in speech Nonsmooth Analysis: Theory and Applications communities. Recent work has focused on the R.J. Stern’s general area of interest is nonsmooth evolution of genomes as the result of analysis and control theory. A general goal in chromosomal rearrangement processes and on control problems is to design a feedback law, formal models for bilingual syntax. which achieves some desired behaviour. Examples include problems of stabilization in a Dana Schlomiuk dynamical system, steering a trajectory to a Études locales et globales de champs de target set in minimal time, or minimizing a cost vecteurs analytiques functional subject to some dynamic constraints. Les travaux de Dana Schlomiuk portent sur des Even in some very simple models of such problèmes locaux (problème de centre) ainsi que problems, however, there is generally no sur la géométrie globale de certaines familles de classical (e.g., continuous or smooth) feedback champs de vecteurs polynomiaux ou analytiques synthesis. The root cause of this is the fact that dans le plan. Ces travaux visent en particulier à in optimal control, the value function is donner une base conceptuelle nouvelle pour les generally nonsmooth, while in problems of champs de vecteurs polynomiaux dans le plan, stabilization, one only has a generalized permettant d’en dégager des traits (nonsmooth) Lyapunov function available. Dr. caractéristiques de la dynamique doublement Stern’s present research interests involve globale (on s’intéresse aux champs dans toute applying the methods of nonsmooth analysis to l’étendue du plan et cela pour des familles such feedback design problems, in order to dépendant de paramètres) afin d’unifier des obtain solutions in a generalized framework. résultats épars de la littérature et d’en obtenir des nouveaux. Un trait caractéristique de ces John Toth travaux est l’usage des méthodes Spectral Asymptotics multidisciplinaires : analytiques, algébriques, I am interested in questions related to spectral géométriques (plus particulièrement algébro- statistics of quantum Hamiltonians and in géométriques.) Un autre volet du projet en cours problems of quantum chaos for integrable e porte sur la partie finitude du 16 problème de systems. Hilbert concernant les cycles limites. With Alain Bourget we have determined the asymptotic level-spacings distribution for the zeroes of the Lamé eigenfunctions and are currently working on the corresponding result

82 Annual Report 2000 - 2001 CRM R e s e a r c h P r o g r a m m e s for more general quantum integrable spin des modèles superintégrables sur des espaces à chains. courbure constante. In joint work with Yiannis Petredis, we have proved that the Hardy bound is attained for the Pavel Winternitz Weyl counting function in a probabilistic sense, Group Theoretical Methods in Physics and by averaging over the moduli space of flat Non-linear Phenomena in Physics metrics on tori. We also have analogous results Field of research: Mathematical physics, for Heisenberg manifolds. symmetries and non-linear phenomena. • Applications of Lie groups to the study of Pierre Valin difference equations. Fusion de données par raisonnement évidentiel • Exact solutions of non-linear differential Toute application de fusion de données doit equations, especially those coming from contenir 4 fonctions séquentielles : non-linear optics. • l’enregistrement spatio-temporel, • Lie algebra contractions and the separation • un mécanisme d’association pour corréler of variables. les nouvelles données avec des objets • Classification of Lie algebras and their existants, subalgebras. • l’estimation de l’identification (ID) (ou fusion d’attributs) obtenue par un Keith Worsley raisonnement évidentiel de tous les attributs. The Geometry of Random Images in Medicine • les attributs peuvent provenir d’images, de and Astrophysics capteurs de type radar, de senseurs The Euler characteristic of the excursion set of a intelligents, ou d’algorithmes. random filed is a tool that has been used over La présente recherche se concentre sur la the last decade to analyze positron emission troisième fonction la plus importante, celle de tomography (PET) images, functional magnetic l’estimation de l’identité, à travers classifieurs resonance images (fMRI), galaxy density maps (Bayes, réseaux de neurones, etc.) et la logique and the cosmic microwave background, thought de Dempster-Shafer. to originate from the creation of the universe. These images are modeled as a Gaussian Luc Vinet random field, and the excursion set is the set of Physique théorique et combinatoire algébrique points where the field exceeds some fixed Les objectifs principaux des projets de recherche threshold value. The Euler characteristic, which de Luc Vinet sont: counts the number of connected components of • de développer les outils théoriques the excursion set minus the number of “holes”, nécessaires à la résolution des modèles is the basis of a proposed estimator of the importants de la physique des systèmes number of “signals” in the image. I have quantiques à plusieurs corps; extended the theory developed by Adler (1981), • d’étendre la théorie algébrique des fonctions The Geometry of Random Fields, to: a) include a spéciales. boundary correction for the expected Euler characteristic, which leads to a highly accurate P Deux résultats dignes de mention ont été -value for the field maximum; b) c2, t and F obtenus par Luc Vinet et ses collaborateurs en fields; c) searching over smoothing kernel width 1999-2000. Il a montré en utilisant les as well as location, so we can estimate the extent transformations de Darboux qu’une classe of the signal (joint work with David Siegmund); importante de polynômes de Koornwinder avec d) knots in the excursion set. a b δ δ fonction de poids w(x) = x (1-x) +M0 (x) + M1 (1-x) obéissent à des équations différentielles de Jean-Paul Zolézio rang élevé. Contrôle de problèmes d’évolution non Il a aussi examiné certains aspects des cylindrique polynômes de Krall-Sheffer. Il s’agit de On considère des systèmes dynamiques issus de polynômes à deux variables qui généralisent les la mécanique des milieux continus dans lesquels polynômes orthogonaux classiques à une le domaine géométrique (occupé par le milieu variable. Luc Vinet a montré avec ses continu) est lui-même dynamique. Le collaborateurs que ces polynômes sont reliés à mouvement des frontières et des interfaces est

CRM Annual Report 2000 - 2001 83 R e s e a r c h P r o g r a m m e s lui-même un des paramètres de contrôle. La régime quasi statique. L’élasticité et les codes nécessité de travailler en régularité minimale et électromagnétique en géométrie pilotée. d’utiliser des formulations intrinsèques amène à Le concept important est celui du champ revisiter les modèles EDP des systèmes transverse Z intervenant par une nouvelle mécaniques eux-mêmes. équation d’état « pilotée » par le crochet de Lie Les exemples principaux abordés concernant [Z, V] où V est un champ dont le flux gouverne d’une part les fluides newtoniens visqueux avec l’évolution des géométries. possiblement des frontières libres et des Parmi les applications citons les travaux en cours couplages fluides structures en grande avec Michel Delfour concernant la dynamique déformation. Les fluides non newtoniens en artérielle utilisant également les modèles intrinsèques de coques élastiques.

84 Annual Report 2000 - 2001 CRM Publications The CRM publishes monographs, lecture notes, proceedings, software, videos and research reports. It has several collections. The in-house collection Les Publications CRM offers many titles in both English and French. The CRM also has publishing agreements with the American Mathematical Society (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 CRM Proceedings and Lecture Notes. Springer-Verlag publishes the CRM Series in Mathematical Physics and the CRM Subseries of the Springer Lecture Notes in Statistics. The following list of Recent Titles contains books that have appeared during the year 2000 –2001 or that will be published soon. Recent Titles

AMS: CRM Monograph Series and Darboux Transformations: The Geometry of • Spencer J. Bloch, Higher Regulators, Algebraic Soliton, vol. 29 (to appear, October 2001). K-Theory, and Zeta Functions of Elliptic Curves, • John McKay & Abdellah Sebbar (eds.), vol. 11, 2000. Proceedings on Moonshine and Related Topics, • Masayoshi Miyanishi, Open Algebraic vol. 30 (to appear, November 2001). Surfaces, vol. 12, 2001. • Alexander R. Its & John Harnad (eds.), • Michael Baake & Robert V. Moody (eds.), Isomonodromic Deformations and Applications, Directions in Mathematical Quasicrystals, vol. vol. 31 (to appear). 13, 2000. • Joel Feldman, Horst Knörrer & Eugene Springer-Verlag: CRM Series in Trubowitz, Fermionic Functional Integrals and Mathematical Physics the Renormalization Group. • Yvan Saint-Aubin & Luc Vinet (eds.), • Eyal Z. Goren, Lectures on Hilbert Modular Algebraic Methods in Physics - A Symposium Varieties and Modular Forms, vol. 14 (to for the 60th Birthday of Jíri Patera and Pavel appear, October 2001) . Winternitz, 2000. • Jose I. Burgos, The Regulators of Beilinson and • Yvan Saint-Aubin & Luc Vinet (eds.), Borel, vol.15 (to appear, November, 2001). Theoretical Physics at the End of the XXth Century. Lecture Notes of the CRM Summer AMS: CRM Proceedings & Lecture Notes School, June 27-July 10, 1999, Banff, Alberta, • B. Brent Gordon, James D. Lewis, Stefan Canada, (to appear). Müller-Stach, Shuji Saito & Noriko Yui • Roman Jackiw, (A Particle Field Theorist’s) (eds.), The Arithmetic and Geometry of Lecture on (Supersymmetric, Non-Abelian) Algebraic Cycles, vol. 24, 2000. Fluid Mechanics (and d-Branes), (to appear). • Decio Levi & Orlando Ragnisco (eds.), SIDE III - Symmetry and Integrability of Difference CRM Subseries of the Springer-Verlag Equations, vol. 25, 2000. Series: Lecture Notes in Statistics • John Harnad, Gert Sabidussi & Pavel • S.Ejaz Ahmed & Nancy Reid (eds.), Empirical Winternitz (eds.), Integrable Systems: From Bayes and Likelihood Inference, 2001. Classical to Quantum, vol. 26, 2000. • Marc Moore (ed.), Spatial Statistics, 2001. • Israel M. Sigal & Catherine Sulem, Nonlinear Dynamics and Renormalization Group, vol. 27, Les Publications CRM 2001. • James G. Huard & Kenneth S. Williams • J.C. Taylor (ed.), Topics in Probability and Lie (eds.), The Collected Papers of Sarvadaman Groups: Boundary Theory, vol. 28. Chowla, I, II, III, 2000. • Alan Coley, Decio Levi, Robert Milson, Colin • Nadia El-Mabrouk, Thomas Lengauer & Rogers & Pavel Winternitz (eds.), Bäcklund David Sankoff (eds.), Currents in Computational Molecular Biology 2001.

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Previous Titles

AMS: CRM Monograph Series • John Harnad & Alex Kasman (eds.), The • James D. Lewis, A Survey of the Hodge Bispectral Problem (Montréal, 1997), vol. 14, Conjecture, 2e Édition (with an appendix by 1998. B. Brent Gordon), vol. 10, 1999. • Michel Delfour (ed.), Boundaries, Interfaces • Yves Meyer, Wavelets, Vibrations and Scaling, and Transitions (Banff, 1995), vol. 13, 1998. vol. 9, 1997. • Peter G. Greiner, Victor Ivrii, Luis A. Seco & • Ioannis Karatzas, Lectures on Mathematics of Catherine Sulem (eds.), Partial Differential Finance, vol. 8, 1996. Equations and their Applications (Toronto, • John Milton, Dynamics of Small Neural 1995), vol. 12, 1997. Populations, vol. 7, 1996. • Luc Vinet (ed.), Advances in Mathematical • Eugene B. Dynkin, An Introduction to Sciences: CRM’s 25 Years (Montréal, 1994), Branching Measure-Valued Processes, vol. 6, vol. 11, 1997. 1994. • Donald E. Knuth, Stable Marriage and its • Andrew M. Bruckner, Differentiation of Real Relation to Other Combinatorial Problems. An Functions, vol. 5, 1994. Introduction to the Mathematical Analysis of • David Ruelle, Dynamical Zeta Functions for Algorithms, vol. 10, 1996. Piecewise Monotone Maps of the Interval, vol. 4, • Decio Levi, Luc Vinet, & Pavel Winternitz 1994. (eds.), Symmetries and Integrability of • V. Kumar Murty, Introduction to Abelian Difference Equations (Estérel, 1994), vol. 9, Varieties, vol. 3, 1993. 1995. • Maximilian Ya. Antimirov, Andrei A. • Joel S. Feldman, Richard Froese, & Lon M. Kolyshkin, & Rémi Vaillancourt, Applied Rosen (eds.), Mathematical Quantum Theory Integral Transforms, vol. 2, 1993. II: Schrödinger Operator (Vancouver, 1993), • Dan V. Voiculescu, Kenneth J. Dykema, & vol. 8, 1995. Alexandru Nica, Free Random Variables, vol. • Joel S. Feldman, Richard Froese, & Lon M. 1, 1992. Rosen (eds.), Mathematical Quantum Theory I: Many-Body Theory and Group Theory AMS: CRM Proceedings & Lecture Notes (Vancouver, 1993), vol. 7, 1994. • Pierre Hansen & Odile Marcotte (eds.), • Guido Mislin (ed.), The Hilton Symposium Graph Colouring and Applications, vol. 23, 1993 : Topics in Topology and Group Theory 1999. (Montréal, 1993), vol. 6, 1994. • Jan Felipe van Diejen & Luc Vinet (eds.), • Donald A. Dawson (ed.), Measure-valued Algebraic Methods and q-Special Functions, vol. Processes, Stochastic Partial Differential 22, 1999. Equations and Interacting Systems (Montréal, • Michel Fortin (ed.), Plates and Shells, vol. 21, 1992), vol. 5, 1994. 1999. • Hershy Kisilevsky & M. Ram Murty (eds.), • Katie Coughlin (ed.), Semi-Analytic Methods Elliptic Curves and Related Topics (Sainte- for the Navier-Stokes Equations, vol. 20, 1999. Adèle, 1992), vol. 4, 1994. • Rajiv Gupta & Kenneth S. Williams (eds.), • Andrei L. Smirnov & Rémi Vaillancourt Number Theory, vol. 19, 1999. (eds.), Asymptotic Methods in Mechanics, vol. • Serge Dubuc & Gilles Deslauriers (eds.), 3, 1993. Spline Functions and the Theory of Wavelets, • Philip D. Loewen, Optimal Control via vol. 18, 1999 Nonsmooth Analysis, vol. 2, 1993. • Olga Karlampovich (ed.), Summer School in • M. Ram Murty (ed.), Theta Functions. From Group Theory (Banff, 1996), vol. 17, 1998. the Classical to the Modern, vol. 1, 1993. • Alain Vincent (ed.), Numerical Methods in Fluid Mechanics (Montréal, 1995), vol. 16, Springer-Verlag: CRM Series in 1998. Mathematical Physics • François Lalonde (ed.), Geometry, Topology • Jan Felipe van Diejen & Luc Vinet (eds.), and Dynamics, (Montréal, 1995), vol. 15, 1998. Calogero-Moser-Sutherland Models, 1999. • Robert Conte (ed.), The Painlevé Property: One Century Later, 1999

86 Annual Report 2000 - 2001 CRM P u b l i c a t i o n s

• Richard MacKenzie, Manu B. Paranjape & • Rudolf Beran & Gilles R. Ducharme, Wojciech J. M. Zakrzewski (eds.), Soliton: Asymptotic Theory for Bootstrap Methods in Properties, Dynamics, Interactions, Appli- Statistics, Montréal, 1991. cations, 1999 • James D. Lewis, A Survey of the Hodge • Luc Vinet & Gordon Semenoff (eds.), Conjecture, Montréal, 1991. Particles and Fields (Banff, 1994), CRM Series • David W. Rand & Tatiana Patera, Concorder: in Mathematical Physics, Springer, New Concordance Software for the Macintosh, York, 1998. Montréal, 1991 (software and user guide). • David W. Rand & Tatiana Patera, Le Les Publications CRM Concordeur: un logiciel de concordances pour le • Michael Barr & Charles Wells, Category Macintosh, Montréal, 1991 (software and user Theory for Computing Science, 1999 guide). • Maximilian Ya. Antimirov, Andrei A. • Véronique Hussin (ed.), Lie Theory, Kolyshkin & Rémi Vaillancourt, Differential Equations and Representation Mathematical Models for Eddy Current Testing, Theory (Montréal, 1989), Montréal, 1990. 1998. • John Harnad & Jerrold E. Marsden (eds.), • Xavier Fernique, Fonctions aléatoires Hamiltonian Systems, Transformation Groups gaussiennes, vecteurs aléatoires gaussiens, and Spectral Transform Methods (Montréal, Montréal, 1997. 1989), Montréal, 1990. • Faqir Khanna & Luc Vinet (eds.), Field • M. Ram Murty (ed.) Automorphic Forms and Theory, Integrable Systems and Symmetries, Analytic Number Theory (Montréal, 1989), Montréal, 1997. Montréal, 1990. • Paul Koosis, Leçons sur le théorème de Beurling • Wendy G. McKay, Jirí Patera & David W. at Malliavin, 1996. Rand, Tables of Representations of Simple Lie • David W. Rand, Concorder Version Three: Algebras. I. Ex-ceptional Simple Lie Algebras, Concordance Software for the Macintosh, Montréal, 1990. Montréal, 1996 (software and user guide). • Anthony W. Knapp, Representations of Real • Decio Levi, Curtis R. Menyuk, & Pavel Reduc-tive Groups, Montréal, 1990. Winternitz, Self-Similarity in Stimulated • Wendy G. McKay, Jirí Patera & David W. Raman Scattering (Montréal, 1993), Montréal, Rand, SimpLie User’s Manual–Macintosh 1994. Software for Representations of Simple Lie • Jacques Gauvin, Theory of Nonconvex Algebras, Montréal, 1990 (software and user Programming, Montréal, 1994. guide). • Rémi Vaillancourt, Compléments de • Francis H. Clarke, Optimization and mathématiques pour ingénieurs, Montréal, Nonsmooth Analysis, Montréal, 1989. 1993. • Hedy Attouch, Jean-Pierre Aubin, Francis • Robert P. Langlands & Dinakar Clarke & Ivar Ekeland (eds.), Analyse non Ramakrishnan (eds.), The Zeta Functions of linéaire (Perpignan, 1987), Montréal & Picard Modular Surfaces (Montréal, 1988), Gauthiers-Villars, Paris, 1989. Montréal, 1992. • Samuel Zaidman, Une introduction à la théorie • Florin N. Diacu, Singularities of the N-Body des équations aux dérivées partielles, Montréal, Problem, Montréal, 1992. 1989. • Jacques Gauvin, Théorie de la programmation • Lucien Le Cam, Notes on Asymptotic Methods mathématique non convexe, Montréal, 1992. in Statistical Decision Theory, Montréal, 1974. • Pierre Ferland, Claude Tricot, & Axel van de Walle, Analyse fractale: Application W indows AMS/International Press ™ 3.x d’initiation aux ensembles fractals, • Duong H. Phong, Luc Vinet & Shing-Tung Montréal, 1992 (software and user guide). Yau (eds.), Mirror Manifolds and Geometry, • Stéphane Baldo, Introduction à la topologie des AMS/IP Studies in Advanced Mathematics, ensembles fractals, 1991. Amer. Math. Soc., Providence, RI, Internat. • Robert Bédard, Groupes linéaires algébriques, Press, Cambridge, MA, & CRM, Montréal, Montréal, 1991. 1998(vol.10).

CRM Annual Report 2000 - 2001 87 P u b l i c a t i o n s

Aisenstadt Chair Collection • Robert Hermann, Physical Aspects of Lie • Yuri I. Manin, Quantum Groups and Group Theory, Presses de l’Université de Noncommutative Geometry, Les Publications Montréal, 1974. CRM, 1988. • Mark Kac, Quelques problèmes mathématiques • Laurent Schwartz, Semimartingales and Their en physique statistique, Presses de l’Université Stochastic Calculus on Manifolds, Presses de de Montréal, 1974. l’Université de Montréal, 1984. • Sybreen de Groot, La transformation de Weyl • Yuval Ne’eman, Symétries, jauges et variétés de et la fonction de Wigner: une forme alternative de groupe, Presses de l’Université de Montréal, la mécanique quantique, Presses de 1979. l’Université de Montréal, 1974. • R. Tyrrell Rockafellar, La théorie des sous- gradients et ses applications à l’optimisation, Miscellaneous fonctions convexes et non convexes, Presses de • Pierre Ferland, Claude Tricot, & Axel van de l’Université de Montréal, 1979. Walle, Fractal analysis user’s guide. • Jacques-Louis Lions, Sur quelques questions Introduction to fractal sets using Windows ™ d’analyse, de mécanique et de contrôle optimal, 3.x., Amer. Math. Soc., Providence, RI & Presses de l’Université de Montréal, 1976. Centre de recherches mathématiques, • Donald E. Knuth, Mariage stables et leurs Montréal, 1994. relations avec d’autres problèmes combinatoires, Presses de l’Université de Montréal, 1976.

88 Annual Report 2000 - 2001 CRM P u b l i c a t i o n s

Research Reports

[CRM-2678] D. J. Rowe, H. de Guise, and B. C. une infinité d'impulsions qui dépendent de l'état, Sanders, Asymptotic limits of SU(2) and SU(3) September 2000. Wigner functions, July 2000. [CRM-2693] A. El Boukili, A. Madrane, and [CRM-2679] A. Ramani, B. Grammaticos, S. Rémi Vaillancourt, Adaptive techniques for Lafortune, and Y. Ohta, Linearisable mappings and semiconductor equations with a Raviart-Thomas the low-growth criterion, July 2000. element, September 2000. [CRM-2680] L. Lapointe, A. Lascoux, and J. [CRM-2694] M. Bilodeau, Asymptotic distribution Morse, A filtration of the symmetric function space a of the largest eigenvalues for underlying elliptical refinement of the Macdonald positivity conjecture, distributions, October 2000. August 2000. [CRM-2695} D. Levi, S. Tremblay, and P. [CRM-2681] A. Ramani, B. Grammaticos, and S. Winternitz, Continuous symmetries of equations on Tremblay, Integrable systems without the Painlevé lattices, October 2000. property, August 2000. [CRM-2696} M. Bilodeau, Asymptotic distribution [CRM-2682] S. Tremblay, B. Grammaticos, and of the largest eigenvalue, November 2000. A. Ramani, Integrable lattice equations and their [CRM-2697] F. Dumortier, Y. Ilyashenko, and C. growth properties, August 2000. Rousseau, Normal forms near a saddle-node and [CRM-2683] D. Levi, S. Tremblay, and P. applications to finite cyclicity of graphics, October Winternitz, Lie point symmetries of difference 2000. equations and lattices, August 2000. [CRM-2698] B. Eynard, Asymptotics of skew [CRM-2684] D. Dryanov and R. Fournier, On orthogonal polynomials, December 2000. Visser's inequality, August 2000. [CRM-2699] J. Harnad, Dual isomonodromic tau [CRM-2685] Richard Fournier, Some remarks on functions and determinants of integrable Fredholm Jack's lemma, August 2000. operators, December 2000. [CRM-2686] A. Joffe, É. Marchand, F. Perron, [CRM-2700] C. Amblard, E. Lapalme, and J.-M. and P. Popadiuk, On a particular sum of dependent Lina, Biomagnetic cortical sources detection by {B}ernoulli and its relationship to a matching type maximum entropy on the mean, December 2000. problem, August 2000. [CRM-2701] Dana Schlomiuk and Nicolae Vulpe, [CRM-2687] C. Christopher, P. Mardesic, and C. Planar quadratic differential systems with Rousseau, Normalizable, integrable and linearizable invariant straight lines saddle points in complex quadratic systems in C2, [CRM-2702] F. H. Clarke, L. Rifford, and R. J. August 2000. Stern, Feedback in state constrained optimal control, [CRM-2688] M. B. Sheftel, P. Tempesta, and December 2000. Pavel Winternitz, Superintegrable systems in [CRM-2703] P. Duchesne and R. Roy, Consistent quantum mechanics and classical Lie theory, tests for independence against serial dependence of September 2000. unknown form in vector time series models, January [CRM-2689] R. {Hernandez Heredero}, D. Levi, 2001. and P. Winternitz, Relation between backlund [CRM-2704] M. Bilodeau and P. Duchesne, transformations and higher continuous symmetries of Robust estimation of the SUR model, January 2001. the Toda equation, September 2000. [CRM-2705] M. Bilodeau and P. Duchesne, [CRM-2690] C. Amblard and S. Girard, Symmetry Principal component analysis from multivariate and dependence properties within a semiparametric familial correlation matrix, January 2001. family of bivariate copulas, September 2000. [CRM-2706] F. Dubeau, A. Ouansafi, and A. [CRM-2691] A. Boivin, P. M. Gauthier, and P. V. Sakat, Approximation de la solution d'une équation Paramonov, Approximation on closed sets by différentielle ordinaire avec impulsions qui dépendent analytic or meromorphic solutions of elliptic de l'état, January 2001. equations and applications, September 2000. [CRM-2707] P. Bouchard, J.-F. Angers, and É. [CRM-2691a] Jamila Karrakchou, On output Bossé, A new fuzzy inference engine applied to stabilization of discrete linear delay systems, identify information fusion, January 2001. September 2000. [CRM-2708] F. Dumortier, A. Guzmán, and C. [CRM-2692] François Dubeau and Jamila Rousseau, Finite cyclicity of elementary graphics Karrakchou, Équations différentielles à retard avec surrounding a focus or center in quadratic systems, January 2001.

CRM Annual Report 2000 - 2001 89 P u b l i c a t i o n s

[CRM-2709] Bertrand Eynard, Random matrices, [CRM-2773] M. Bouchard, R. C. Brunet, P.-O. Saclay lecture notes, January 2001. Droz, and G. Carrier, A biologically-based dynamic [CRM-2710] B. Toni, Cyclicity of isochronous model for predicting the disposition of methanol and centers, February 2001. its metabolites in animals and humans, 2001 [CRM-2711] P.-L. Buono, J. S. W. Lamb, and M. [CRM-2774] M. Bouchard, R. C. Brunet, P.-O. Roberts, Steady-state bifurcations in reversible Droz, and G. Carrier, A biologically-based dynamic equivariant systems, February 2001. model for predicting the disposition of formaldehyde [CRM-2712] P. Arminjon, A. Madrane, and A. St- and its metabolites in animals, 2001 Cyr, Numerical simulation of 3D flows with a non- [CRM-2775] H. Darmon and P. Green, Elliptic oscillatory central scheme on unstructured curves and class fields of real quadratic fields: tetrahedral grids, February 2001. algorithms and evidence, 2001. × [CRM-2713] J. Hernàndez-Loreto and B. Toni, [CRM-2776] H. Darmon, Integration on Hp H and Ciclos límite de primer orden de una 1-forma arithmetic applications, 2000. linearizable, February 2001. [CRM-2777] M. Bertolini and H. Darmon, [CRM-2714] J. Hernàndez-Loreto and B. Toni, Iwasawa's main conjecture for elliptic curves over

Periodos críticos y clasificación de centros de un anticyclotomic Zp-extensions,2001. sistema cúbico, February 2001. [CRM-2778] M. Bertolini, H. Darmon, A. Iovita, [CRM-2715] B. Toni, Differential dynamics in terms and M. Spiess, Teitelbaum's exceptional zero of {J}acobian loops, February 2001. conjecture in the anticyclotomic setting, 2001. [CRM-2744] J. Chavarriga and D. Schlomiuk, [CRM-2779] D. Dufresne, On general class of risk Integrability criteria for differential equations on the models, 2001. projective plane, May 2001. [CRM-2780] N. El-Mabrouk and D. Sankoff, The [CRM-2745] S. Gravel and P. Thibault, reconstruction of doubled genomes, 2001. Integrability and linearizability of the Lotka-Volterra [CRM-2781] N. El-Mabrouk, Reconstructing an system with a saddle point with rational hyperbolicity ancestral genome using minimum segments ratio, November 2000. duplications and reversals, 2001. [CRM-2764] R. Collobert, S. Bengio, and Y. [CRM-2782] M. Frigon, Remarques sur Bengio, A parallel mixture of SVMs for very large l'enlacement en théorie des points critiques pour des scale problems, 2001. fonctionnelles continues, May 2001. [CRM-2765] P. Vincent and Y. Bengio, K-local [CRM-2783] M. J. Gander, F. Magoules and F. hyperplane and convex distance nearest neighbor Nataf, Optimized Schwarz methods without overlap algorithms, 2001. for the Helmholtz equation, April 2001. [CRM-2766] I. Takeuchi, Y. Bengio Y., and T. [CRM-2784] M. J. Gander and L. Halpern, Un Kanamori, Robust regression with asymmetric algorithme discret de décomposition de domaines pour heavy-tail noise, 2001. l’équation des ondes en dimension 1, 2001. [CRM-2767] N Chapados, Y. Bengio, P. Vincent, [CRM-2785] M.J. Gander and L. Halpern, J. Ghosn, C. Dugas, I. Takeuchi, and L. Meng, Méthodes de décomposition de domaines pour Estimating car insurance premia: a case study in l'équation des ondes en dimension 1, 2001. high-dimensional data inference, 2001. [CRM-2786] M. J. Gander, Optimized Schwarz [CRM-2768] Y. Bengio and N. Chapados, Methods for Helmholtz Problems, 2001 Extending metric-based model selection and [CRM-2787] D. S. Daoud and M. J. Gander, regularization in the absence of unlabeled data, 2001 Overlapping Schwarz Waveform Relaxation for [CRM-2769] F. Bergeron, N. Bergeron, and J.-C. Convection Reaction Diffusion Problems, 2001. Aval, lattice diagram polynomials in one set of [CRM-2788] M. J. Gander, L. Halpern, and C. variables, March 2001. Japhet, Optimized Schwarz algorithms for coupling [CRM-2770] S. Boyer, On the local structure of convection and convection-diffusion problems, 2001. SL(2, C)-character varieties at reducible characters, [CRM-2789] M. J. Gander and H. Zhao, 2001 Overlapping Schwarz waveform relaxation for the [CRM-2771] S. Boyer, E. Luft, and X. Zhang, On heat equation in n-dimensions, 2001. the algebraic components of the SL2(C)-character [CRM-2790] M. J. Gander, L. Halpern and F. varieties of knot exteriors, 2001. Nataf, Optimal Schwarz waveform relaxation for the [CRM-2772] R. C. Brunet, From population to one dimensional wave equation, 2001. proportion dynamics for epidemiological models with heterogeneity, 2001.

90 Annual Report 2000 - 2001 CRM P u b l i c a t i o n s

[CRM-2791] M. J. Gander and A. Ruehli, [CRM-2809] D. Jakobson and N. Nadirashvili,

Optimized waveform relaxation methods for diffusive Quasi-symmetry of Lp norms of eigenfunctions, 2001 type circuits, 2001. [CRM-2810] D. Jakobson and I. Rivin, Extremal [CRM-2792] D. S. Daoud and M. J. Gander, metrics on graphs, 2001 Overlapping Schwarz waveform relaxation for [CRM-2811] C. Klein, D. Korotkin, and V. convection reaction diffusion problems, 2001 Shramchenko, Ernst equation, Fay identities and [CRM-2793] M. J. Gander, Optimized Schwarz variational formulas on algebraic curves, 2001 Methods for Symmetric Positive Definite Problems, [CRM-2812] D. Korotkin, K. Korotkov, and B. 2001 Krylov, On classification of gas discharge images [CRM-2794] M. J. Gander and C. Rohde, around fingers and drops of liquid, 2001 Overlapping Schwarz waveform relaxation for [CRM-2813] D. Korotkin, On some integrable convection dominated dissipative conservation laws, system arising in differential geometry and general 2001 relativity, 2001. [CRM-2795] P. Gora, P. Bracken and A. [CRM-2814] F. Lalonde and M. Pinsonnault, Boyarsky, Deriving chaotic dynamical systems from Topology of the space of symplectic embeddings of the energy functionals, 2001 ball in a 4-dimensional rational manifold, 2001. [CRM-2796] P. Gora, P. Bracken and A. [CRM-2815] F. Lalonde and D. McDuff, Boyarsky, A minimum principle in chaotical Cohomological properties of ruled symplectic dynamical systems, 2001 manifolds, 2000 [CRM-2797] P. Gora and W. Bahsoun, Exact inner [CRM-2816] D. J. Ford and J. McKay, Monstrous functions, 2001 Moonshine—Problems arising I. Tate characters, [CRM-2798] P. Gora and A. Boyarsky, Absolutely 2001 continuous invariant measures for random maps with [CRM-2817] D. J. Ford and J.McKay, J., position dependent probabilities, November 2000 Monstrous Moonshine—Problems Arising II. The

[CRM-2799] P. Gora and N. Obeid, Absolutely Monster and affine E8 Dynkin data, 2001. continuous invariant measures for a class of [CRM-2818] L. Haddad, H. Machida, and I. G. meromorphic transformations, 2001 Rosenberg, Maximal and minimal partial clones, [CRM-2800] P. Gora and A. Boyarsky, On the 2000. discrete nature of time, 2000. [CRM-2819] L. Haddad, D. Lau, and I. G. [CRM-2801] P. Gora and A. Boyarsky, Chaotic Rosenberg, Intervals of partial clones containing maps derived from data, 2001 . maximal clones, 2000 [CRM-2802] P. Gora and A. Boyarsky, A [CRM-2820] A. A. Krokhin and I. G. Rosenberg, dynamical system interpretation of irreducible A monoidal interval of clones of autodual functions, complexity, 2001. 2001. [CRM-2803] P. Gora and A. Boyarsky, Control in [CRM-2821] F. H. Clarke and R. Stern, Hamilton- a class of chaotic unimodal maps, 2001. Jacobi characterization of the state constrained value, [CRM-2804] P. Gora and A. Boyarsky, 2001. Deterministic description of quantum mechanics, [CRM-2822] F. Gungor and P. Winternitz. 2001. Generalized Kadomtsev-Petviashvili equation with an [CRM-2805] Ph. Saint-Jean, J.-M. Lina, and B. inifinite dimensional symmetry algebra, 2001. Goulard, Irregular random fields, wavelets and [CRM-2823] G. S. Pogosyan and P. Winternitz. Euler characteristics, 2000. Separation of variables and subgroup bases on n- [CRM-2806] J.-M. Lina, D. Clonda, and B. dimensional hyperboloids, 2001. Goulard, Complex dyadic wavelets: statistical [CRM-2824] S. Frittelli, N, Kamran, T. Newman, modeling and image processing, 2001. Differential equations and conformal geometry, 2000. [CRM-2807] D. Clonda, J.-M Lina, and B. [CRM-2825] F. Finster, N. Kamran, J. Smoller Goulard, Mixed memory model for image processing and S.-T. Yau, The long-time dynamics of Dirac and modeling with complex Daubechies wavelets, particles in the Kerr-Newman black hole, 2001. 2000 [CRM-2826] F. Finster, N. Kamran, J. Smoller [CRM-2808] J. C. Hurtubise and E. Markman, and S.-T Yau, Decay rates and probability estimates Surfaces and the Sklyamin bracket, 2001. for Dirac particles in the Kerr-Newman geometry, 2001.

CRM Annual Report 2000 - 2001 91 Financial Report

The CRM benefits from several sources of ncm2: the Centre de recherche en calcul appliqué funding to sustain its various sectors of activity. (CERCA); the Centre interuniversitaire de This report distinguishes the amounts awarded recherche en analyse des organisations to the CRM from those awarded to the Centre’s (CIRANO); the Centre de recherche sur les researchers. transports (CRT); and the Groupe d’études et de recherche en analyse des décisions (GERAD). The Centre’s Funding As one of the three mathematics institutes in The various sources of funding are presented in Canada which jointly established the Table 1. In 2000-2001, the CRM received a second Mathematics of Information Technology and instalment of $874,650 of a four-year NSERC Complex Systems Network of Centres of institutes grant. This grant enables the Centre to Excellence (MITACS), the CRM supervises the fulfil its national mandate focussed on the activities of six of the Network’s research organization of scientific activities each year projects. It also promotes networking activities. (postdoctoral fellowships, student scholarships, The CRM received $125,000 in 2000-2001 for visiting researchers, thematic scientific program as well as a general program of scientific these tasks from the overall NCE funding activities, and research support personnel). (For provided to MITACS. In addition, the research more details, see below the section titled projects just mentioned received $660,000 in “Financial statements”.) NCE funding in 2000-2001 (see the note below The Comité d’étude et d’administration de la Table 3). recherche (CÉDAR) of the Université de The CRM also obtained grants for two Montréal provided an operating grant of postdoctoral fellowships from the Alfred P. $814,426 in 2000-2001. This budget is principally Sloan Foundation (US$50,000) and from the allocated for the remuneration of the scientific Heart & Stroke Foundation of Canada ($33,561). personnel of the Centre. The budget also covers A grant of $11,000 from the Ministère de la the release time of the faculty members who Culture et des Communications du Québec’s direct the CRM and a part of the salary of administrative staff as well as some operating programme assisting in the popularization of and computer expenses. The Université de science (Étalez votre science). The CRM’s André Montréal also contributed an additional $40,000 Aisenstadt endowment contributed revenues of for a visiting researcher. $55,037 in 2000-2001. These funds serve for the Centre’s scientific activities, particularly the The Fonds FCAR also supports the operations of annual André Aisenstadt Prize and Aisenstadt the CRM. The Centre received the second Chairs). instalment of $210,000 of a three-year operating grant in 2000-2001. This grant covers a part of Other contributions to the CRM’s funding from the salary expenditures for the research support universities and partner organizations, totalling personnel, the publications personnel, the $280,095, come from the Institut des sciences administrative personnel and operating costs. mathématiques (ISM) for joint CRM-ISM An annual amount of $14,000 from this grant is postdoctoral fellowships and the joint set aside for the research activities of two college colloquium series; from researchers of the (CEGEP) researchers on release time to the CRM. Montréal universities for joint postdoctoral fellowships and student scholarships; and from The CRM manages the collective scientific the Canadian Institute for Advanced Research activities and the general administration of the (CIAR). In addition, there were several Network for Computing and Mathematical contributions for the 2000-2001 thematic year: Modeling (ncm ). A budget of $70,894 was 2 $10,000 from CERCA for two symposiums allocated for these tasks in 2000-2001. In (NARI and MFRS); a $5,000 sponsorship from addition, the CRM received $80,000 from the Guidant for the workshop on Mapping and Network to finance the research projects of four Control of Complex Arrhythmias; and a of its members. These amounts come from the sponsorship of $500 from Boehringer Ingelheim Network’s annual NSERC grant of $648,894. The (Canada) Ltd for the NARI symposium. balance of this amount goes to the research projects of the four other founding centres of

92 Annual Report 2000 - 2001 CRM F i n a n c i a l R e p o r t

The CRM generated revenues of $66,487 from its Tableau 3 publishing programs (sales and royalties from Research partnerships: contracts and grants from industry, the CRM’s series with the American foundations, etc., CRM researchers, 2000-2001 Mathematical Society and Springer-Verlag New York, and from the CRM’s in-house collection) $ in and $60,167 from registration fees to scientific Account activities (thematic year, CRM summer school, Partner Number $ Amount at CRM CRM-MITACS spring school). Other funds came Bell University Laboratories 3 185,645 185,645 from compensation for services rendered and ncm2 (ANIQ, Lockheed Martin, 5 109,215 69,175 operating costs. A small revenue from the sale of partners of GIREF, Bell t-shirts, coffee cups and posters completes the University Laboratories, picture of the Centre’s income sources. Insurance Co. of B. C.) 2 Table 1 MITACS (Bell University 1 35,000 0 Laboratories) Main sources of funding of the CRM, 2000-2001 Lockheed Martin 1 11,000 11,000 $ Amount Total 10 340,860 265,820 NSERC (Institutes and Initiatives Program) 874,650 Université de Montréal (incl. CÉDAR) 854,426 1. These amounts are accounted in the Centre’s funding and FCAR (Research Centres Program) 210,000 the financial statements found in this annual report. NSERC (Research Network Program, ncm ) 150,894 2 2. The total amount of the NCE-MITACS funding awarded to National Centres of Excellence (MITACS) 125,000 the six projects supervised by the CRM is $660,000 (of which Contribution from universities & partners 280,095 $85,725 was awarded to members of the CRM). The industrial partners of these six MITACS projects contributed Other grants and revenue from endowments 173,648 $238,351 (of which $35,000 was obtained by researchers of Sales, Registration fees & other revenues 142,220 the CRM). Total 2,810,934 Financial Statements In these tables, amounts are rounded to the nearest dollar. The following financial statements present, on a cash accounting basis, the revenues and Funding for Research expenditures of the CRM for the fiscal year that In addition to the CRM’s grants, its researchers ended on May 31, 2001. The financial statements obtained $2,071,438 in research funding during do not include the research funding of the 2000-2001 fiscal year. The two following individual researchers. tables provide details on funding awarded by granting agency and by category of research Expenditures are divided in three broad partnerships. The last column in each table categories: Scientific Activities, Publications, and indicates the amount of funding that is managed Administration. directly by the CRM in its accounts at the The main line items under Scientific Activities are: Université de Montréal. • scientific personnel, that is, remuneration of Table 2 professors at the Université de Montréal Research grants (individual and team) CRM researchers, who undertake research on a full-time basis 2000-2001 at the CRM; expenses associated with the release of professors and researchers from $ in Account other institutions for prolonged periods so Granting agency Number $ Amount at CRM that they may work as invited researchers or NSERC 39 956,210 230,895 as members of the CRM; travel and NSERC-ncm 1 5 120,000 80,000 2 accommodation expenses of invited FCAR 9 232,952 37,000 researchers (this includes the Aisenstadt FCAR-Equipment 3 142,349 0 Chairs and the visiting researchers taking NCE-MITACS 2 4 85,725 5,000 part in the scientific activities of the Centre); NCE-IRIS 1 60,000 0 and postdoctoral fellowships and student Others 4 133,342 0 scholarships; Total 65 1,730,578 352,895 • scientific programmes, that is, the annual thematic program; the 2000 summer school; the general scientific program made up of

CRM Annual Report 2000 - 2001 93 F i n a n c i a l R e p o r t

contributions to off-site scientific activities The rubric Publications includes production costs and events, mini-programs on particular associated with the CRM’s publishing topics, colloquia organized jointly with the programmes (remuneration of personnel ISM, and expenses associated with the four preparing publications as well as direct costs prizes of excellence in the mathematical such as printing of in-house collection sciences (the André Aisenstadt Prize, the publications). CAP-CRM Prize in Theoretical and Finally, the rubric Administration covers the Mathematical Physics, the CRM-Fields remuneration of the CRM’s executive, the Institute Prize, and the CRM-SSC Prize in administrative personnel, the computer systems Statistics); and finally, the scientific analysts (who support the Centre’s network, programs (workshops, seminars, lectures, hardware and software used in its scientific, conferences) of the two networks, MITACS management, communications and administra- and ncm2; tive activities), and the communications • the personnel involved directly in the personnel (Web, newsletter and annual report), organization and management of the as well as expenses related to executive and scientific programs; and advisory business meetings, current operating • the research support personnel delivering costs, and computer equipment and computer services and electronic-publishing maintenance costs. services for the preparation of research The 2000-2001 year-end surplus is minimal. reports.

94 Annual Report 2000 - 2001 CRM