A Word from the Director...... 2 Presenting the CRM...... 4 Personnel 2001-2002...... 5 Scientific Personnel...... 6 Members 6 Postdoctoral Fellows 8 Visitors 10 Management...... 12 Bureau de direction 12 Advisory Committee 12 Computer Facilities 13 Homage to André Aisenstadt...... 14 Scientific Activities...... 16 Theme Year 2001-2002: Groups and Geometry 16 Aisenstadt Chair 24 General Program 2001-2002 26 CRM Prizes 31 National Program Committee 34 Members’ Seminars and Special Events 38 CRM-ISM Colloquium 44 Coming Activities ...... 45 Theme Year 2002-2003: Math in Computer Science 45 Theme Year 2003-2004: Geometric and Spectral Analysis 49 Theme Year 2004-2005: Mathematics of Complex Multiple-Scale Systems 52 Interdisciplinary and Industrial Program 54 General Program 56 CRM Collaborative Network ...... 58 AARMS/ACSMA...... 60 Industrial Collaborations ...... 61 Awards, Distinctions and Landmarks...... 64 Research Laboratories...... 65 CICMA 65 CIRGET 67 LACIM 69 Mathematical Analysis Laboratory 71 Applied Mathematics Laboratory 73 Mathematical Physics Laboratory 74 PhysNum 76 Statistics Laboratory 78 Publications ...... 80 Recent Titles 80 Previous Titles 81 Research Reports 84 Financial Report at 31 May 2002 ...... 87 Financial Statement 2001-2002 89
CRM Annual Report 2001 - 2002 1 A Word from the Director
Science first. It was an sur le Temps Extrême (LUTE). This laboratory, exceptionally rich year. with an important infusion in cash, personnel The thematic program in and computer time from Environment Canada, Groups and Geometry will work not only in the forecasting of extreme began with a remarkably weather, but also on modelling its impacts, in
vigorous three-week collaboration with the various ncm2 partners. A session in group theory first workshop is taking place in the fall of 2002 and low dimensional on extreme values, and is co-organized with the topology, with over one finance group. The year also saw the creation of hundred participants for a second spin-off company, in data-mining each of the three weeks. applied to insurance. The first, in imaging, won The workshops that followed were all great the Entrepreneurship prize of the École des successes, and I hesitate to name just a few, for Hautes Études Commerciales de Montréal. The fear of offending those left out; I will however CRM research group in imaging has continued thank in passing our colleagues in Kingston, building up a research network in brain- Eddy Campbell and David Wehlau, who put imaging. One of the group’s researchers, Jean- together a remarkable two-week session, with a Marc Lina, is now sharing his time with the large number of students and visitors. The Institut Universitaire de Gériatrie de Montréal, holders of the Aisenstadt Chair this year were and is now an associate researcher at INSERM three absolutely exceptional mathematicians: (France). This Montréal-Paris collaboration has Edward Frenkel, Laurent Lafforgue and George just been awarded an important grant from the Lusztig. Lafforgue went on to receive a Fields Ministère de la Recherche, de la Science et de la medal later in the year. Lafforgue and Frenkel Technologie. gave their lectures in tandem, and were accompanied by Robert Langlands, who also The development of science does rely on gave a series of talks. The year in all saw twenty continuous funding. This is an arduous or so lecture series, which had a considerable constraint and the year from this point of view impact (thanks once again to those who gave was exceptionally full. The CRM submitted last them). If one adds to this the seminars of the January a request for renewal to NSERC, as part various groups and laboratories attached to the of a reallocations process that included four CRM, the CRM-ISM Colloquium (my thanks to institutes and twenty or so grant selection the organizers, Dana Schlomiuk and Tadashi committees. It was a heavy task: choosing Tokieda), it all adds up to a rich scientific priorities, choosing programs, writing the atmosphere, unthinkable even ten years ago. proposal, organizing a site visit with over a hundred people to coordinate. Many of the CRM The 2001-2002 program was not even over yet researchers took part in the proceedings, and I when we started on the 2002-2003 program on thank them. The whole process was a great the Mathematics of Computer Science. The CRM success, with the CRM obtaining an 11% increase played host in May to two of the big conferences in funding, which puts it third in the in theoretical computer science, STOC and CCC. reallocations exercise and gives it the same There were a number of small satellite activities funding as the Fields Institute and PIMS. The organized around this, and in June, a workshop additional resources obtained will be used on random number generators, organized in mostly to increase funding of long-term visitors style by Pierre L’Écuyer. The summer also saw a and of postdoctoral fellows. school in quantum computing, directed by Gilles Brassard, with over eighty participants. On the provincial front, as these words are being written, the CRM has just submitted its As ever, the two industrial networks, MITACS application to FQRNT, the provincial research and ncm 2, had their share of events and agency, for increased funding. The exercise, if it developments. The main one was doubtless the is crowned with success, will fund a certain official opening on December 6, 2001, of the new number of laboratories associated to the CRM; it ncm2 laboratory, the Laboratoire Universitaire has already allowed the CRM to obtain
2 Annual Report 2000 - 2001 CRM A Word from the Director significant financial support from all the major large number of talented mathematicians that Québec universities, and this for the first time. are now in our universities, a large segment of them having just arrived. They will, I hope, have An additional satisfaction occurred in the the resources that they deserve. writing of the application, as I was listing the Jacques Hurtubise
CRM Annual Report 2001 - 2002 3 Presenting the CRM
The Centre de recherches mathématiques (CRM) project (Mathematics of Information was created in 1969 by the Université de Technology and Complex Systems Another). Montréal through a special grant from the example is the National Program National Research Council of Canada. It became Committee, which provides funding for off- an NSERC national research centre in 1984. It is site research activities. currently funded by NSERC (Natural Sciences This national mandate is complemented by, and and Engineering Research Council), by the indeed supported by, a long-standing vocation Government of Québec through the FQRNT of promoting research in the Montréal area. For (Fonds québécois de la recherche sur la nature et instance, les technologies), by the Université de Montréal, • the CRM supports, through partnership and by private donations. The mission of the agreements, a group of local researchers CRM is to do research in mathematics and chosen mainly from departments of closely related disciplines and to provide mathematics and statistics, but also leadership in the development of the computer science, physics, economics, mathematical sciences in 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 programs, etc.); including the weekly CRM/ISM colloquium, • its general program provides funding for graduate courses offered by distinguished conferences and special events at CRM and visitors and a program of postdoctoral across the country; fellowships; • each year it invites, through the Aisenstadt • it works actively at developing contacts with Chair, one or more distinguished industry. Its joint activities with liaison and mathematicians, to give advanced courses as research centres (CERCA, CIRANO and part of its thematic program; CRIM) and research centres doing applied • it awards four prizes yearly: the CRM-Fields research (CRT, GERAD and INRS- Institute Prize recognizing major Télécommunications) led to the creation of contributions to mathematics, the Aisenstadt the Network for Computing and Prize given for outstanding work done by a Mathematical Modelling (ncm2). NSERC and young Canadian mathematician, the CAP- about twenty partners such as financial CRM Prize for exceptional achievement in institutions, high-tech companies and theoretical and mathematical physics, and government agencies fund this network. 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 ten books per year. Some of its programs, both as participants and as 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 program, with 32 postdoctoral fellows in major institutes in the mathematical sciences. place last year, funded either solely by the The director of the CRM is assisted by two CRM or in partnership with other managerial structures: the Bureau de direction organizations; and the Advisory Committee. The Advisory • it informs the community of its activities Committee is a group of internationally through its web site at renowned mathematicians from Canada and www.CRM.UMontreal.CA; abroad, who approve scientific programs and thematic years, choose recipients of the CRM- • it participates, with the other two Canadian Fields and Aisenstadt prizes, and suggest new centres, in groundbreaking national scientific ventures to explore. initiatives. One example is the MITACS
4 Annual Report 2001 - 2002 CRM Personnel 2001-2002
The Director’s Office Jacques Hurtubise Director Jean LeTourneux Deputy Director, Publications Yoshua Bengio Deputy Director, Industrial Program Anne Bourlioux Deputy Director, Scientific Program John Harnad Deputy Director, Scientific Program (since January 2002) Niky Kamran Deputy Director, Scientific Program (until December 2001) Diane Poulin Secretary
Administration Béatrice Kowaliczko Head of Administration (until April 2002) Vincent Masciotra Head of Administration (since April 2002); 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 Systems Administrator André Montpetit Office systems manager (1/2 time)
Communications Suzette Paradis Communications Officer & Webmaster (1/2 time)
MITACS Nicole Huron Administrative Assistant
CRM Annual Report 2001 - 2002 5 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 program 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 five 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 such as those with Lockheed Martin Canada. Members
Ali, Syed Twareque Bergeron, Nantel Darmon, Henri Granville, Andrew Math. & stat., Math. & stat., Math. & stat., Math. & stat., Concordia Univ. York Univ. McGill Univ. Univ. de Montréal Angers, J.-F. Bourlioux, Anne David, Chantal Grundland, Michel Math. & stat., Math. & stat., Math. & stat., Math., UQTR Univ. de Montréal Univ. de Montréal Concordia Univ. Hall, Richard L. Apostolov, Vestislav Boyer, Steven Delfour, Michel Math. & stat., Math., UQAM Math., UQAM Math. & stat., Concordia Univ. Univ. de Montréal Arminjon, Paul Brassard, Gilles Hallett, Michael Math. & stat., DIRO, Durand, Stéphane Math. & stat., Univ. de Montréal Univ. de Montréal Collège Édouard- McGill Univ. Montpetit Bandrauk, André Broer, Abraham Harnad, John Chimie, Math. & stat., Dssouli, Rachida Math. & stat., Univ. de Sherbrooke Univ. de Montréal Computer Science, Concordia Univ. Concordia Univ. Baribeau, Line Brunet, Robert Hurtubise, Jacques Math. & stat., Math. & stat., El-Mabrouk, Nadia Math. & stat., Univ. Laval Univ. de Montréal DIRO, McGill Univ. Univ. de Montréal Bartello, Peter Bryant, David Hussin, Véronique Math. & stat., Math. & stat., Fournier, Richard Math. & stat., McGill Univ. McGill Univ. Dawson College Univ. de Montréal Beaulieu, Liliane Clarke, Francis Frigon, Marlène Jakobson, Dmitry Cégep du Vieux Montréal Univ. de Lyon Math. & stat., Math. & stat., Univ. de Montréal McGill Univ. Bédard, Robert Collin, Olivier Math., UQAM Math., UQAM Gagnon, Langis Jaksic, Vojkan CRIM Math. & stat., Bélair, Jacques Crépeau, Claude McGill Univ. Math. & stat., School of Computer Science Gander, Martin Univ. de Montréal McGill Univ. Math. & stat., Kamran, Niky McGill Univ. Math. & stat., Benali, Habib Csürös, Miklos McGill. Univ. INSERM, France DIRO, Gauthier, Paul Univ. de Montréal Math. & stat., Kharlampovich, Olga Bengio, Yoshua Univ. de Montréal Math. & stat., DIRO, Cummins, Chris J. McGill Univ. Univ. de Montréal Math. & stat., Goren, Eyal Concordia Univ. Math. & stat., Kisilevsky, Hershy Bergeron, Anne McGill Univ. Math. & stat., Math., UQAM Dafni, Galia Concordia Univ. Math. & stat., Goulard, Bernard Bergeron, François Concordia Univ. Physique, Klemes, Ivo Math., UQAM Univ. de Montréal Math. & stat., McGill Univ.
6 Annual Report 2000 - 2001 CRM Scientific Personnel
Koosis, Paul Major, François Polterovich, Iosif Schmidt, Georg Math. & stat., DIRO, Math. & stat., Math. & stat., McGill Univ. Univ. de Montréal Univ. de Montréal McGill Univ. Korotkin, Dmitri Makkai, Michael Ramakrishna, Ravi Shahbazian, Elisa Math. & stat., Math. & stat., Math. & stat., Lockheed Martin Canada Concordia Univ. McGill Univ. McGill Univ. Stern, Ron Labelle, Gilbert Mashreghi, Javad Ransford, Thomas Math. & stat., Math., UQAM Math. & stat., Math. & stat., Concordia Univ. Univ. Laval Univ. Laval Labelle, Jacques Thaine, Francisco Math., UQAM Maslowe, Sherwin A. Reutenauer, Christophe Math. & stat., Math. & stat., Math., UQAM Concordia Univ. Lalonde, François McGill Univ. Math. & stat., Rosenberg, Ivo Toth, John Univ. de Montréal Mathieu, Pierre Math. & stat., Math. & stat., Physique, Univ. de Montréal McGill Univ. Langlands, Robert P. Univ. Laval Institute for Advanced Rousseau, Christiane Van Vliet, Carolyne Study, Princeton McKay, John Math. & stat., Physics, Math. & stat., Univ. de Montréal Univ. of Miami Léger, Christian Concordia Univ. Math. & stat., Roy, Roch Valin, Pierre Univ. de Montréal Miasnikov, Alexei Math. & stat., Lockheed Martin Canada Math. & stat., Univ. de Montréal Leroux, Pierre McGill Univ. Vinet, Luc Math., UQAM Russell, Peter Math. & Phys., Nekka, Fahima Math. & stat., McGill Univ. Lesage, Frédéric Pharmacie, McGill Univ. CRM, Univ. de Montréal Winternitz, Pavel Univ. de Montréal Sabidussi, Gert Math. & stat., Nigam, Nilima Math. & stat., Univ. de Montréal Lessard, Sabin Math. & stat., Univ. de Montréal Math. & stat., McGill Univ. Wise, Daniel Univ. de Montréal Saint-Aubin, Yvan Math. & stat., Patera, Jiri Math. & stat., McGill Univ. LeTourneux, Jean Math. & stat., Univ. de Montréal Physique, Univ. de Montréal Worsley, Keith Univ. de Montréal Sankoff, David Math. & stat., Perron, François Math. & stat., McGill Univ. Lévesque, Claude Math. & stat., Univ. de Montréal Math. & stat., Univ. de Montréal Zolésio, Jean-Paul Univ. Laval Schlomiuk, Dana INRIA, France Petridis, Yiannis Math. & stat., Lina, Jean-Marc CRM, Univ. de Montréal CRM, Univ. de Montréal Univ. de Montréal
CRM Annual Report 2001 - 2002 7 Scientific Personnel
Postdoctoral Fellows
Each year the CRM plays host to a number of postdoctoral fellows. The sources for their funding include the NSERC postdoctoral program, the NATO international program administered by NSERC, the CRM (alone or with the ISM), and individual research grants from CRM’s members. The list below includes only postdoctoral fellows in residence at CRM or funded or co-funded by CRM, with their funding source given in brackets. Some of the fellows were in residence at CRM for only part of the year – the affiliation is that where the doctoral degree was obtained.
Aguiar, Marcelo Deteix, Jean Mei, Ming Schiffler, Ralf Texas A&M Univ. Univ. de Montréal Kanazawa Univ. UQAM (CRM-ISM) (CRM-GIREF) (CRM-McGill) (FCAR) Allen, Steve Guimond, Louis-Sébastien Pal, Ambrus Sikora, S. Adam Univ. de Sherbrooke Univ. de Montréal Colombia Univ. Univ. de Maryland
(ncm2-Lockheed Martin) (CRSNG) (CRM-ISM) (CRM-ISM) Bertola, Marco Hagedorn, Thomas Penskoi, Alexei Tempesta, Piergiulio S.I.S.S.A. Univ. of Lethbridge Univ. de Montréal Univ. degli studi di (CRM-ISM) (Sloan Fellowship) (CRM) Lecce Brightwell, Mark Langerman, Stefan Polterovich, Iosif (CRM-ISM) Univ. of Glasgow Rutgers Univ. Weizmann Institute of Urquiza, José Manuel (CRM-ISM) (CRM-McGill) Science Univ. Pierre et Marie Buono, Luciano Loutsenko, Igor (CRM) Curie (ncm ) Univ. of Warwick Univ. de Montréal Prasad, Amritanshu 2
(NSERC) (ncm2) Univ. of Chicago Vénéreau, Stéphane Casesnoves, Raquel Maillot, Sylvain (CRM-McGill-CICMA) Institut Fourier Univ. de Montréal Univ. Paul Sabatier Rasmussen, Jorgen (CRM-McGill) (CRM) (CRM) Univ. of Lethbridge Vitse, Pascale Chapoton, Frédéric Masakova, Suzana (CRM-ISM) Univ. de Bordeaux I (CRM-ISM) Paris VI Czech Technical Univ. Saikia, Anupam (LACIM-CRM) (NATO) Trinity College, Univ. of Wang, Sung Ho Corteel, Sylvie Matessi, Diego Cambridge Duke Univ. (CRM-ISM) (CRM-ISM) Université de Paris-Sud Univ. of Warwick (CRM-ISM) (CRM-ISM) Savitt, David Dai, Jack Harvard Univ. (NSERC) Iowa State Univ. (CRM-ISM)
8 Annual Report 2001 - 2002 CRM Scientific Personnel
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 Shinagawa, Kaori Tateno, Katsumi Institut de cardiologie École Polytechnique de Institut de cardiologie McGill Univ. de Montréal Montréal de Montréal Titcombe, Michele Bub, Gil Hong, Gu Slimane, Leila McGill Univ. McGill Univ. Univ. of Waterloo Univ. Laval Villeneuve, Daniel Caporossi, Gilles Kagabo, Issa Stojkovic, Goran École Polytechnique de Univ. de Montréal École Polytechnique de École Polytechnique de Montréal Montréal Montréal Chavez, Francisco Wang, Shaojun Univ. of Toronto Kanamori, Takafumi Stojkovic, Mirela Univ. of Waterloo Univ. de Montréal École Polytechnique de Davidson, Joern Ziarati, Koorush Montréal Univ. of Toronto Mladenovic, Nenad HEC Montréal École Polytechnique de Takeuchi, Ichiro Deerakhchan, Katayoun Zou, Renqiang Montréal Univ. de Montréal Institut de cardiologie Institut de cardiologie de Montréal de Montréal
CRM Annual Report 2001 - 2002 9 Scientific Personnel
Visitors
Each year the CRM hosts a large number of visitors. The majority comes to the centre to participate in scientific activities: in the year 2001-2002,!1667 such participants registered for workshops run solely by the CRM. In addition, the CRM helped fund about twenty other scientific events. The following list includes, only visitors who were in residence for long periods, ranging from a week to several months.
Akhperjanian, Ashot Fleischmann, Klaus Khesin, Boris Mélard, Guy Yerevan Physics Inst. Weiestrass Inst. for Applied Univ. of Toronto Univ. Libre de Bruxelles Aratyn, Henrik Analysis & Stochastics Kirillov, Alexandre Moody, Robert V. Univ. of Illinois Frenkel, Edward Univ. of Pennsylvania Univ. of Alberta Ben-Zvi, David Univ. of California, Berkeley Klaassen, Chris A. Murty, Ram Univ. of Chicago Gazeau, Jean-Pierre Korteweg-de Vries Inst. for Queen’s Univ. Berest, Yuri U. Paris VII Denis Diderot Mathematics, UvA Murty, V. Kumar Cornell Univ. Geck, Meinolf Knop, Friedrich Univ. of Toronto Biswas, Atanu Univ. Claude Bernard Rutgers Univ. Nieto, Luis Miguel Indian Statistical Inst. (Lyon I) Kokotov, A. Univ. de Valladolid Blouza, Adel Geiger, Jochen Concordia Univ. Onn, Uri Univ. Paris VI Johann Wolfgang Goethe- Lafforgue, Laurent Technion Inst. Univ. Bridson, Martin Univ. Paris-Sud Orlov, Aleksander Pembroke College Greven, Andreas Ledrappier, François Oceanology Inst. Univ. Erlangen-Nürnberg Brinzanescu, Vasile École Polytechnique Osborn, Tom Inst. of Mathematics Simon Grodzicky, Roman (Palaiseau, France) Univ. of Manitoba Univ. de Montréal Stoilow Leitner, Frederick Ouansafi, Abdellatif Casselman, William A. Guillemin, Victor Univ. of Arizona Univ. de Montréal MIT Univ. of British Columbia Levi, Decio Patera, Jan Cojocaru, Alina Carmen Havin, Victor Univ. di Roma Tre Czech Technical Univ. McGill Univ. Queen’s Univ. Levy, Jason Pelantova, Edita Cressie, Noel A.C. Helmers, Roelof Univ. of Ottawa Czech Technical Univ. CWI Amsterdam Ohio State Univ. Lévy Véhel, Jacques Pogosyan, George Dawson, Donald Heusener, Michael INRIA, Projet Fractales Bogoliubov Laboratory of Carleton Univ. Univ. Blaise Pascal Liben-Nowell, David Theoretical Physics (Clermont-Ferrand II) Deninger, Christopher MIT Polanco Ruig, Luis B. Univ. of Münster Houzel, Christian Longhi, Ignazio Univ. de Valencia UPS, 2065 CNRS Dorodnitsyn, Vladimir Univ. of Münster Popov, Vladimir Keldysh Inst. of Applied Itskov, Vladimir Lusztig, George Steklov Mathematical Inst. Univ. of Minnesota Mathematics MIT Pouryayevali, Mohamad Du Cloux, Fokko Jiang, Yu Lysionok, Igor Reza Univ. de Lyon I Univ. Autonoma Steklov Mathematical Inst. Univ. of Isfahan Metropolitana-Iztapalapa Dumas, Laurent Ma, Li Racine, Michel Kalnins, Ernest Günther Univ. Paris VI Tsinghua Univ. Univ. of Ottawa Univ. of Waikato Fleischer, Isidore Magri, Franco Raffinot, Mathieu Karrakchou, Jamila Univ. di Milano Univ. de Versailles École Mohammadia d’ingénieurs
10 Annual Report 2001 - 2002 CRM Scientific Personnel
Raoult, Annie Sorger, Christoph Thomova, Zora Vulpe, Nicolae Univ. Joseph-Fourier Univ. de Nantes SUNY Inst. of Technology Academy of Sciences of Rasmussen, Christopher Springer, Tonny A. Touzi, Nizar Moldova Univ. of Arizona Univ. of Utrecht CREST Wakolbinger, Anton Roussarie, Robert Stembridge, John R. Tyurin, Andrei Johann Wolfgang Goethe- Univ. de Bourgogne Univ. of Michigan Steklov Inst. of Mathematics Univ. Sabin, Malcome Strasburger, Aleksander van Diejen, Jan Felipe Walton, Mark Numerical Geometry Ltd. Univ. of Bialystok Universidad de Talca Univ. of Lethbridge Sahakyan, Vardan Strawdermann, William E. Varsaie, Saad Zeron, Eduardo Santillan Yerevan Physics Inst. Rutgers Univ. Inst. for Advanced Studies Cinvestav-IPN (National Polytechnical Inst.) Scott, Keith Sujatha, R. in Basic Sciences Atlantic Nuclear Services Tata Inst. of Fundamental Verger-Gaugry, Jean-Louis Zhang, Yuanli Ltd. Research Univ. J. Fourier, Grenoble Univ. de Montréal Sengupta, Jyotirmoy Svobodova, Milena Violette, Donald Zich, Jan Tata Inst. of Fundamental Czech Technical Univ. Univ. de Moncton Czech Technical Univ. Research Szmigielski, Jacek Vogan, David A. Jr Zuk, Andrzej Sheftel, Mikhail B. Univ. of Saskatchewan MIT Univ. of Chicago Feza Gursey Inst. Thiriet, Marc Sinha, Kaneenika INRIA Rocquencourt Queen’s Univ.
CRM Annual Report 2001 - 2002 11 Management Bureau de direction 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 de Montréal and the dean of its or scientists with close ties to the mathematical Arts and Sciences faculty are represented on sciences. The rector of the Université de the Bureau. The Bureau adopts the policies of Montréal and the director of the CRM attend the Centre, recommends the nomination and the meetings of the Advisory Committee. The the promotion of researchers and the Advisory Committee is informed periodically appointment of regular members, advises the of the activities of the Centre, through the director on the preparation of the budget and director, and transmits any advice that it deems the Université de Montréal on the choice of the relevant to the Bureau de direction. director.
Bergeron, François Hurtubise, Jacques Craig, Walter Luskin, Mitchell UQAM Director CRM, McMaster Univ. Univ. of Minnesota McGill Univ. Brassard, Gilles Glynn, Peter Murty, Ram Univ. de Montréal Hussin, Véronique Stanford Univ. Queen’s Univ. Univ. de Montréal Caillé, Alain Haiman, Mark Odlyzko, Andrew Vice-rector, Research Ransford, Thomas Univ. of California Univ. of Minnesota Univ. de Montréal Univ. Laval Hambleton, Ian Rousseau, Christiane Cléroux, Robert Rémillard, Bruno McMaster Univ. Univ. de Montréal Univ. de Montréal UQTR Hitchin, Nigel Zelditch, Steven Hubert, Joseph Rousseau, Christiane Oxford Univ. Johns Hopkins Univ. Associate Dean, Univ. de Montréal Research, FAS Lawless, Jerry Univ. de Montréal Saint-Aubin, Yvan Univ. of Waterloo Univ. de Montréal
12 Annual Report 2001 - 2002 CRM Management
Computer Facilities
The CRM offers its members and visitors a Unix connections with RISQ (Réseau interordinateurs environment based on a Sun Enterprise-450 scientifique québécois) and CA*net (the equipped with four 400-MHz Ultra-Sparc Canadian Internet transit service). Members and processors and 2 Gb of memory as a main guests can now connect their personal laptops server,* and a secondary server Sun Sparc-1000 (or computers) to the CRM private network with eight 40-MHz processors and 384 Mb of directly, or if they are outside CRM offices, memory for lightweight tasks. A new Linux through phone links to our PPP server and its server (single processor PC at 1.4-MHz and 2 Gb four modems. of memory) was added at the beginning of 2002 to offer a Linux environment to CRM The support staff works on Sun stations or on researchers. This computing power is Macintoshes tied to the Sun server for all distributed through the offices and common services, such as mail and backups. A three-year rooms via 30 Sun workstations (from Sparc-4 to plan for the replacement of all support staff Ultra-10), several X-terminals, and four Linux computers started in 1999 and was completed workstations. this year. Phase 1 of a new database was completed at the end of 2001. This database The software libraries include compilers (FORTE helps support staff to better manage the contacts, environment for C, C++ and Fortran, GNU activities, registrations to activities, and offices of compilers, Java, etc.), programs for symbolic CRM. Phase 2, which should be completed at the manipulations and numerical computations end of 2002, aims at enabling online printing of (Mathematica, Maple, Macaulay, Matlab), administrative forms and at standardizing the several text editors, web browsers, mail tools, information needed at various stages of the and most utilities common to the mathematical preparation of scientific activities (registrations, world (fftw-Discrete Fourier Transform, dstool- announcements, reports, etc.) A dynamic tool for dynamical systems, etc.). Upgrades to directory on the Web will also replace the CRM TeX and its dialects are uploaded whenever they static directory with secure access to the are released. Unix applications to communicate database. with the PC and Mac world are also installed, such as SAMBA (PC file and printer server), Printing needs are served by two HP-8000DN OpenOffice (Office suite), and AUFS (file server workgroup printers (1200-dpi double-sided), as for Macintosh). A Web server (Apache under well as an ink-jet network printer Epson-900N Unix) with a secure SSL version and a for colour printing, and some small printers for recognized 128-bit Thawte certificate that support staff. The CRM established a printing enables secure registration for participants to quota system in 2001 in order to save paper. CRM activities hosts the CRM web pages. In The CRM’s servers are installed in a room 2001, a new look was given to our web pages, specifically designed for computers, with including some Flash programming, and more independent controlled environment and UPS information. (Uninterruptible Power Supply). For security, many programs for surveillance In 2002, a new room with five X-terminals and and access control are in place, including three Mac computers was installed for frequent updates of the operating system. Most conference participants at CRM to give them of our computers are connected to an alarm access to Telnet, FTP and SSH. system. *The main server (Enterprise-450), 22 Sun Since 1999, the CRM operates its own private workstations Ultra-5 and Ultra-10 and the complete local area network (LAN): five BayNetworks Local Area Network installed in 1999 were all paid by Baystack-450 switches, providing 120 ports on a grant from the Canadian Foundation for Innovation twisted-pair at 10/100 Mb/s and four optic fiber together with the Government of the Province of links supporting Gigabit Ethernet. This private Québec and a donation (20% of total value) from Sun local network is linked to the network of the Microsystems (for computers) and Anixter (for the Université de Montréal that maintains the network).
CRM Annual Report 2001 - 2002 13 Homage to André Aisenstadt
Arrival in Canada Having obtained his PhD, André Aisenstadt faced a dilemma: Herman Weyl began making approaches in England so that he could continue his research at Oxford or Cambridge, but his father, a prosperous businessman, worrying that his son would begin an academic career, invited him to join the family entreprise. The father won, but the son would always regret, it seems, having abandoned mathematics. In 1939, André Aisenstadt immigrated to Canada and settled in Montréal for cultural reasons. Soon after his arrival, Mackenzie King as hed him to participate in the creation of the Central Mortgage and Housing Agency and in the establishment of a housing building program for veterans. While working on these projects in Ottawa, he launched an enterprise in Montréal, the Parkdale Homes Development Corporation, which built large sectors of the city.
Charitable endeavours On 4 October 2001, André Aisenstadt, the Around 1967, his wealth established, André CRM’s great benefactor, passed away. He Aisenstadt abandoned the construction industry declared once, in a conversation: “Age is in order to focus on charitable activities. His without importance. It’s what you do that wife, Niussia Rosenstein, an accomplished counts.” An exceptionally long life permitted pianist, convinced him to actively participate in him to demonstrate this assertion in striking the establishment of the Marlboro Festival and ways. Music School. All those who had the pleasure of meeting him know with what verve he would The sciences reminisce about Marlboro and more particularly After leaving his native Russia, he began about two of his friends, Rudolf Serkin and engineering studies in Darmstadt, during which Pablo Casals. In these same years began his he discovered a deeper interest for mathematics financial support of the CRM. A first donation than engineering. He thus decided to change his led to the creation of the Aisenstadt Chair that studies to mathematics, which he pursued at the enabled the Centre to invite during those years universities of Würzburg and Jena, afterwards the most remarkable mathematicians of the time. completing doctoral studies in mathematical Thanks to another financial gift, the André physics in Zurich under the direction of Erwin Aisenstadt Prize, that recognizes the excellence Schrödinger. He counted among his teachers of young Canadian mathematicians, was Hermann Weyl and Andreas Speiser, and among established in 1991. And the building that his fellow students John von Neumann and houses the mathematical sciences at the Enrico Fermi. Even though Einstein had already Université de Montréal bears his name in left Zurich by then, he would return often and it recognition of a major financial contribution for is during one of these visits that André its construction. Aisenstadt established a friendship that lasted until the end of the great physicist’s life.
14 Annual Report 2001 - 2002 CRM Homage to André Aisenstadt
Mathematics first A love of art It would be difficult to give an exhaustive list of The Aisenstadt university building, the Chair all the organizations that benefited from André and the Prize will help future generations Aisenstadt’s generosity, but a short list would remember the debt they have towards the include the Montréal Jewish Hospital, the person who gave them their name. It is Institut de recherches cliniques de Montréal and nonetheless important not to forget the values the Montréal Symphony Orchestra. It would that underlay the charitable activities of this seem though that he drew particular satisfaction remarkable man. Didn’t he say in that same from having contributed to the development of conversation — For me, art — and by art I mean mathematics: “Thanks to my relationship with mathematics as much as music, literature and the CRM,” he said in the same conversation painting — is neither an hors d’oeuvre nor a dessert, quoted above, “I had a renaissance as a it is the main course of life. mathematician.” It is therefore with always renewed pleasure that he would meet the Jean LeTourneux holders of the Aisenstadt Chair and the winners Deputy Director of the Prize.
An afternoon in memory of André Aisenstadt
On January 18th, 2002 the CRM hosted a small celebration of André Aisenstadt’s role in the Montréal mathematical community, with three special speakers. The first, Niky Kamran, was the first recipient of the André-Aisenstadt prize (1991). The title of his talk was L’opérateur de Dirac en géométrie de Kerr. Francis Clarke, of the Institut Universitaire de France and the Université de Lyon, director of the CRM from 1984 to 1993, spoke on La théorie du retour d’état (feedback) en théorie du contrôle: une introduction, The last speaker, Jingyi Chen, the 2001 winner of the André-Aisenstadt prize, gave his prize lecture on Quaternionic mappings between hyperkähler manifolds. Reminiscences followed the scientific part of the afternoon: Anatole Joffe and Francis Clarke, who were successive directors of the CRM, spoke with some emotion of their association with André Aisenstadt, and Robert Lacroix, the Rector of the Université de Montréal, spoke of André Aisenstadt’s role within the University. The afternoon’s events were closed off with a reception, which recalled the memory of a man who not only loved science but who also had an unfailing sense of hospitality.
CRM Annual Report 2001-2002 15 Scientific Activities
The core of each year’s scientific program at the CRM is its thematic program. The Advisory Committee chooses the topic 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), Mathematical Methods in Biology and Medicine (2000-01). A year’s activities can combine a good number of workshops and conferences, one or two Aisenstadt Chairs, a number of visiting scientists in residence, and some postdoctoral 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 2001-2002: Groups and Geometry
The role of group actions and groups in general GROUPS, TOPOLOGY AND is ubiquitous in geometry, and the year’s DIFFERENTIAL GEOMETRY program concentrated on some areas in which June-December 2001 there has been important recent progress. The Groups and Low-Dimensional year consisted of two segments, the first more Topology differential-geometric in flavour, and the other June-July 2001 one concentrating specifically on the links Org.: Steven Boyer (UQAM), Dani Wise (Brandeis & between algebraic McGill) geometry, group theory The two workshops and and representation five mini-courses were a theory. There was a tremendous success by special focus on training, any measure. Each with intensive mini- week had more than courses, introductory 100 participants, many series, and CRM-ISM of whom were involved graduate classes in all three weeks. One specially organized in of the most satisfying conjunction with the aspects was the thematic year. There attendance of a great were ten postdoctoral number of graduate fellows with research students who were interest connected to the drawn from six theme year. For the first different continents. time, a grant of The format of US$50,000 was received sandwiching the mini- from the National courses between the Science Foundation with workshops meant that a the specific purpose of great many students funding US students and took part in weeks 1 postdoctoral researchers and 3 as well, much to interested in participating in CRM’s theme year the delight of the more senior participants. activities. There were a total of 1305 registered Throughout the scientific level of the talks as participants for the activities. well as their exposition qualities were of a very high order. The general feeling was that the
16 Annual Report 2001 - 2002 CRM Scientific Activities research areas covered were in a healthy state Martin Bridson (Univ. of Oxford) with a promising future. Non-positively curved spaces and hyperbolic groups The topics covered during the workshop on Ruth Charney (Ohio State Univ.) groups and 3-manifolds included geo- The geometry of Coxeter and Artin groups metrization of 3-dimensional orbifolds, non- Benson Farb (Univ. of Chicago) hyperbolic Dehn fillings of hyperbolic 3- A crash course on the geometry of groups manifolds, the weak Lopez conjecture, the word- Peter Shalen (Univ. of Illinois at Chicago) hyperbolicity of the fundamental groups of Representations of 3-manifold groups laminar 3-manifolds, the virtual Haken conjecture, the generalized Smale conjecture, WORKSHOP ON GEOMETRIC GROUP THEORY Heegard splittings, representations of the braid July 9-13, 2001 group, and geometric cobordisms of manifolds. Org.: Steven Boyer (UQAM), Dani Wise (Brandeis & The mini-course lecturers put a tremendous McGill) effort into the preparation and presentation of The theory of infinite groups was revolutionized their subjects with the result that each did a truly by an infusion of ideas from geometry and exceptional job of presenting what was at times topology. This has led to the resolution of many quite technical and demanding material. It is old problems and the formulation of new hard to imagine better or more accessible problems and methods that have broadened the introductions to these areas. scope of the field. This workshop focused on The topics covered during the workshop on these new developments in geometric group geometric group theory included: Word- theory. hyperbolic groups, decision problems, the Invited speakers: Iain Aitcheson (Univ. of Melbourne), M. Bestvina (Univ. of Utah), B. Bowditch (Univ. of boundary of a group, CAT(0) geometry, Southampton), Noel Brady (Univ. of Oklahoma), M. Bridson representation varieties, mapping class group, (Univ. of Oxford), S. Gersten (Univ. of Utah), I. Kapovich proof of the Tarski conjecture on the elementary (Univ. of Illinois at Urbana-Champaign), M. Kapovich (Univ. of Utah), O. Kharlampovich (McGill Univ.), Bruce Kleiner theory of free groups, splittings of groups, (Univ. of Michigan at Ann Arbor), Igor Lysionok (Steklov isoperimetric functions, torsion groups, Institute), J. McCammond (Texas A & M Univ.), John Meier (Lafayette), Lee Mosher (Rutgers), A. Miasnikov (CCNY), quasiconvex subgroups, group theoretical Graham Niblo (Southampton), P. Papazoglou (Univ. Paris- approaches to the geometrization conjecture. Sud), Michah Sageev (Technion), John Stallings (Berkeley), Paul Schupp (UIC), Zlil Sela (Hebrew Univ.). There was also an additional panel of nine contributed talks featuring: WORKSHOP ON GROUPS AND 3-MANIFOLDS Patrick Dehornoy (U. Caen), Murray Elder (Texas A&M), June 25-29, 2001 Max Forester (Warwick), Daniel Groves (Oxford), Dan Org.: Steven Boyer (UQAM), Dani Wise (Brandeis & Guralnick (Technion), Chris Hruska (Cornell), Jan-Mark McGill) Iniotakis (Warwick), Tim Riley (Oxford), Eric Swenson (BYU). This workshop focused on recent progress on various open topological and geometric Topology of Manifolds and Group classification problems as well as some of the Actions newer research directions. August 20-24, 2001 Invited speakers: S. Bigelow (Univ. of Melbourne), M. Org.!: Ian Hambleton (McMaster), Ronnie Lee (Yale) Boileau, (Univ. Paul Sabatier), D. Calegari (Harvard Univ.), D. Cooper (Univ. of California, Santa Barbara), M. Culler Recently there have been important (Univ. of Illinois at Chicago), N. Dunfield (Harvard Univ.), breakthroughs in the study of the topology of C. Gordon (Univ. of Texas at Austin), S. Kerckhoff (Stanford Univ.), M. Lackenby (Univ. of Oxford), D. Long (Univ. of manifolds and related topics on group actions, California, Santa Barbara), J. Luecke (Univ. of Texas at especially in the area of 3-and 4-dimensional Austin), Y. Moriah (Technion – Israel Institute of manifolds with new input from the Seiberg- Technology), J. Porti (Univ. Autonoma de Barcelona), A. Reid (Univ. of Texas at Austin), Y. Rieck (Nara Women’s Witten theory and symplectic topology. This Univ.), H. Rubinstein (Univ. of Melbourne), P. Shalen (Univ. workshop provided an ideal setting to present of Illinois at Chicago), Y.-Q. Wu (Univ. of Iowa), X. Zhang these new advances and related developments in (SUNY Buffalo). other areas of topology. MINI-COURSES The workshop had 38 participants, including a July 2-6, 2001 nice mixture of mathematicians from different Michel Boileau (Univ. Paul Sabatier) areas of geometric and algebraic topology. The Geometrization of 3-dimensional orbifolds aim of the conference to bring about formal and
CRM Annual Report 2001 - 2002 17 Scientific Activities informal discussion between different Introductory Lectures perspectives, was certainly realized in the October 29-November 1, 2001 relaxed and convivial setting of the CRM. The V. Guillemin (MIT) The convexity theorem and moment polytopes organizational support from the CRM was A.A. Kirillov (Pennsylvania) outstanding, as usual. The Virasoro group and related complex geometry The program was interesting and varied, with a Workshop on the Geometry of Infinite- large number of talks by recent Ph.D.’s and Dimensional Lie Groups postdoctoral fellows. November 2-6, 2001 Invited speakers: J. Morgan (Columbia Univ.), R. Gompf Invited speakers: O. Bogoyavlenskij (Queen’s), V. Guillemin (Univ. of Texas at Austin), T.-J. Li (Princeton Univ.), D. (MIT), J. Harnad (CRM & Concordia), L. Jeffrey (Toronto), Ruberman (Brandeis Univ.), S. Vidussi (Univ. of California), M. Kapranov (Toronto), A. Kirillov (Pennsylvania), F. F. Quinn (St. Francis Xavier Univ.), S. Krushkal (Yale Univ.), Lalonde (UdeM), J. Leslie (Howard), E. Meinrenken B. Williams (Univ. of Notre Dame), A. Edmonds (Indiana (Toronto), G. Misiolek (Notre Dame), P. Olver (Minnesota), Univ.), M. McCooey (McMaster Univ.), M. Marcolli (Max- H. Omori (Tokyo), V. Ovsienko (CNRS-Luminy), A. Pianzola Planck-Institute für Mathematik), H. Boden (McMaster (Alberta), M. Pinsonnault (UQAM), T. Ratiu (EPFL, Univ.), R. Fintushel (Michigan State Univ.), P. Feehan Lausanne), T. Robart (Howard), C. Roger (Lyon I), P. (Rutgers Univ.), S. Strle (McMaster Univ.), S. Cappell Slodowy (Hamburg), R. Wendt (Fields Institute), P. (Courant Institute), P. Ozsvath (Princeton Univ.), J. Davis Winternitz (CRM), C. Woodward (Rutgers Univ.), I. (Univ. of Toronto), H. Johnston (Vassar College), R. Schultz Zakharevich (Ohio State). (Univ. of California), E. Miller (Polytechnic Univ.), G. Friedman (Yale Univ.), B. Owens (Trinity College), E. GROUPS AND ALGEBRAIC GEOMETRY Pedersen (State Univ. of New York at Binghamton). January-June 2002 The importance of algebraic geometry in Infinite-Dimensional Lie Groups representation theory has grown enormously October 29 to November 6, 2001 during the past decades with the arrival of such Org.: Niky Kamran (McGill), Boris Khesin (Toronto) techniques as D-modules and perverse sheaves. From a differential-geometric point-of-view, Geometry intervenes in a crucial fashion in the infinite-dimensional Lie groups arise as proof of such results as the Kazhdan-Lusztig automorphism groups of various geometric conjecture, the construction of canonical bases structures on the manifolds, such as a volume for representations, and the work of Beilinson- form, a foliation, a contact structure or a Drinfeld on the Geometric Langlands program. symplectic structure. The study of these infinite- A number of deep connections have arisen dimensional Lie groups becomes a fundamental between the algebraic geometry and algebraic problem in areas of mathematics as diverse as combinatorics, whose ramifications extend all hydrodynamics and symplectic topology. the way to mathematical physics and topology. Another wide class of infinite-dimensional Lie A special emphasis of the program will be in groups is formed by loop groups, Kac-Moody graduate training, and a variety of short courses groups, and more generally, by gauge groups on will be organized, as well as graduate courses of manifolds of arbitrary dimension. The successes a more introductory nature. Funding is available in the study of these groups have been for graduate students wishing to attend. immensely fruitful both in low-dimensional geometry and topology and in quantum field theory. Graduate courses January-April 2002 Infinite-dimensional Lie groups are also The semester included several graduate courses fundamental in the theory of integrable systems run by ISM to prepare local students to the and their hierarchies. In this context, their action thematic year activities. becomes quite explicit on spaces of pseudo- Abrahamm Broer (Montréal) differential and Fourier integral operators. This Hilbert schemes of points and their applications two-week session started out two very beautiful Henri Darmon (McGill) series of four conferences given by Victor Automorphic forms Guillemin (MIT) and A. Kirillov (Penn.). The Eyal Goren (McGill) following week was occupied by a workshop Curves, vector bundles on curves and their moduli that reviewed a good sample of the topics Frédéric Lesage (Montréal) mentioned above. Altogether, there were many Algèbres de Kac-Moody very interesting discussions between people working on various aspects of the problem and the interactions were very fruitful.
18 Annual Report 2001 - 2002 CRM Scientific Activities
WORKSHOP ON HILBERT MODULAR VARIETIES Invited speakers: J. Achter (Columbia), F. Andreatta (Padua), AND FORMS N. Archinard (CICMA), S. Baba (CICMA), A. Brown (Tata), H. Darmon (McGill), L. Dembele (McGill), F. Diamond January 3-6, 2002, Far Hills Inn, Québec (Brandeis), J. Ellenberg (Princeton), A. Ghitza (MIT), E. Org.: E. Z. Goren and H. Darmon (McGill) Goren (McGill), P. Green (Harvard), F. Jarvis (Sheffield), E. The Workshop was dedicated to surveying Kani (Queen’s), A. Logan (Berkeley), E. Nevens (Imperial College), M.-H. Nicole (McGill), U. Onn (Technion), A. Pal recent developments in the study of Hilbert (CRM), A. Prasad (CRM), R. Pries (Columbia), R. modular varieties and forms, such as: (i) Ramakrishna (Cornell), A. Saikia (CICMA), D. Savitt (CICMA), R. Sreekantan (Tata), M. Thillainatesan stratification and classification of Hilbert (Columbia), A. Tupan (CICMA), Chia-Fu Yu (Columbia). modular varieties, special loci and cycles; (ii) Hilbert modular forms: congruences, and Winter School on Computations in associated Galois representations; (iii) rational Coxeter Groups points on Hilbert modular varieties. Application January 21-28, 2002 to the Langlands program and the Fontaine- Org. : W. Casselman (UBC), R. Bédard (UQAM), F. du Mazur conjecture; (iv) periods of Hilbert Cloux (Lyon I), M. Geck (Lyon I) modular forms. Application to the construction Each lecturer gave five lectures. Bill Casselman of rational points on elliptic curves and modular gave the introductory lectures on Coxeter abelian varieties. groups, Fokko du Cloux lectured on details of The workshop has been a tremendous success. It machine computations in Coxeter groups, brought together experts and junior researchers Meinholf Geck lectured on character tables and in the area of Hilbert modular varieties and Hecke algebras of finite Coxeter groups, and forms. We had an intensive program, consisting Robert Bédard summarized the state of current of 15 lectures in three days, given by some of the knowledge about Kazhdan-Lusztig cells in affine 28 participants. The ambient atmosphere, in a Coxeter groups. Evenings were spent in work secluded cozy Laurentian resort, with the sessions at computers, involving both lecturers opportunity of walks in the woods, cross- and students. These were something of an country skiing and other activities, was a major experiment, and only partially successful, but factor in the success of the workshop in the sense the idea was basically a fruitful one. If this is to of interaction between researchers in the field, be repeated in the future, they should probably and helped to establish the informal and be made more formal. dynamic atmosphere we were aspiring to It is intended that the entire series will be achieve. eventually available on the Internet. Still The scientific level of the workshop was very photographs were made of every blackboard high. Much of the results reported were very written, and very soon the overhead new, not yet published, and helped bring the transparencies will be scanned, also. These are participants up to date with current research. currently available at The mathematical discussion was continued, http://www.math.ubc.ca/people/faculty/cass/ during the joint meals, and well into the night in coxeter/farhills/lectures.html along with a the lounge. Particular topics, such as the Serre rewritten version of about half of the lectures by conjecture for Hilbert modular forms, were in the Casselman, currently being expanded. air. It is clear that several participants of the The material covered in the courses is not at all workshop, who work on aspects of that currently available publicly in a digestible form, conjecture, will use some of the results reported and the long-term benefit of the workshop will by the other participants. likely be the Internet notes.
Group Actions on Rational Varieties February 27 to March 3, 2002 Org.: P. Russell (McGill) The workshop had an international composition, with participants from Canada, Japan, Singapore, Taiwan, the USA, the Netherlands, France, Germany, Chile, Russia, Sweden, Switzerland and Poland. A special effort to bring graduate students and posdoctoral fellows to the
CRM Annual Report 2001 - 2002 19 Scientific Activities workshop paid off, ten attended and of these six Week Two gave talks. The second week was devoted to a workshop on Recent developments in group actions on affine Invariant Theory, for which many of the spaces and related varieties with simple younger mathematicians stayed to listen. The topology made up, as planned, the main theme experts listed below gave talks of 50 minutes of the workshop. Algebraic, complex analytic duration, bearing in mind the audience. In this and topological aspects were covered. second week, the focus was on current problems Interestingly, the workshop brought into sharp in keeping with the workshop nature. The focus the important role played by Danielewski speakers included Loek Helminck, Julia surfaces both in the study of surfaces with trivial Hartmann, Marcus Hunziker, Nondas Makar-Limanov invariant and the study of Kechagias, Gregor Kemper, Frederich Knop, additive actions on affine 3-space. This Alexander Kuehn, Lucy Moser-Jauslin, Vladimir surprising connection had only very recently Popov, Yasmine Sanderson, Mufit Sezer, Joel become apparent. Segal, R. James Shank, Nicolas Thiery, and An excursion to Mt. St. Hilaire was highly Wilberd van der Kallen. appreciated by all participants in the workshop. Proceedings The excursion ended with a lively session on A volume of proceedings of the Workshop is open problems at the Gault Estate. These are planned in the CRM Proceedings and Lecture now in the process of being collected and will be Notes Series, published by the American made publicly available as part of the CICMA Mathematical Society. The four main lecturers preprint series. have submitted expository articles summarizing Invited speakers: A. Broer (Université de Montréal), P. their lectures, and we expect to have 14 Cassou-Noguès (Université Bordeaux I), D. Daigle (Université d’Ottawa), K. Fieseler (Uppsala University), G. additional papers, all of which are being Freudenburg (University of Southern Indiana), R. Ganong refereed at the time of this report. As well, there (York University), M. Gizatullin (Universidad Tecnica will be an article describing current problems Federico Santa Maria), A. Hundemer (McGill University), Z. Jelonek (Polish Academy of Sciences), S. Kaliman (University with contributions from many of the of Miami), M. Kang (Taiwan National University), H. Kraft participants. (Universität Basel), F. Kutzschebauch (Uppsala University), S. Marcello (Universität Regensburg), K. Masuda (Himeji Invited speakers: Jaydeep Chipalkatti, Jianjun Chuai, Harm Derksen, Peter Fleischmann, Julia Hartmann, Loek Inst. of Tech.), M. Miyanishi (Osaka University), L. Moser- Jauslin (Université de Bourgogne), V. Popov (Steklov Helminck, Markus Hunziker, Wilberd van der Kallen, Mathematical Institute), M. Roczen (Humboldt-Universität Dikran Karagueuzian, Kiumars Kaveh, Nondas Kechagias, Gregor Kemper, Friedrich Knop, Hanspeter Kraft, Alexander zu Berlin), A. Sathaye (University of Kentucky), V. Shpilrain (The City College of New York), S. Vénéreau (CRM), D. Kuehn, Lucy Moser-Jauslin, Mara Neusel, Vladimir Popov, Wright (Washington University), D. Zhang (National Leonid Rybnikov, Yasmine Sanderson, Gerald Schwarz, Joel Segal, Mufit Sezer, R. James Shank, Alexander Smirnov, University of Singapore). Nicolas Thiery, Oxana Yakimova. Classical Invariant Theory Workshop Concentration Period on the Langlands April 8-19, 2002, Queen’s University, Kingston Program for Function Fields Org.: H.E.A. Eddy Campbell (Queen’s), & David Wehlau (Royal Military College, Kingston) April 29 to May 17, 2002 Org.: H. Darmon (McGill), J. Hurtubise (CRM) Week One On a vu ces dernières années des percées The first week of the workshop was devoted to spectaculaires dans le programme de Langlands introductory lectures aimed at graduate sur des corps de fonctions tant en caractéristique students, younger mathematicians and for those zéro qu’en caractéristique p. Le but de cette who wished to acquire a breadth of knowledge période de concentration était de fournir aux across invariant theory. The workshop was part participants un survol de quelques-unes des of the theme year on Groups and Geometry being techniques essentielles du domaine ainsi que des held under the auspices of the Centre de nouveaux résultats. Le résultat fut une des séries recherches mathématiques. de conférences les plus spectaculaires qu’a vues During the first week, four distinguished le CRM depuis plusieurs années. mathematicians gave a series of lectures. They April 8-26, 2002! were Professors P. Fleischmann (Kent), La première partie du programme fut occupée Hanspeter Kraft (Basel), G. W. Schwarz par des cycles de conférences de trois ou quatre (Brandeis), and Harm Derksen (Michigan). heures donnés par des gens de la région de Montréal, pour étudiants de 2e et 3e cycles et
20 Annual Report 2001 - 2002 CRM Scientific Activities post-doctorants sur la matière nécessaire à une for the L-series of such objects. Also discussed compréhension du programme de Langlands. La were advances in the associated theory of liste des conférenciers et de leurs sujets modular forms associated to Drinfeld modules. comprend!: In particular, we will discuss Boeckle’s Abraham Broer (Montréal) association of Galois representations to cusp D-modules forms. Jacques Hurtubise (CRM & McGill) Edward Frenkel (UC Berkeley) The Hitchin systems Aisenstadt Chair 2001-2002 Jason Levy (Ottawa) Recent developments in the geometric Langlands Trace formulae Program Ram Murty (Queen’s) In recent years it was realized that the Langlands A Survey of the Langlands Program in number fields conjectures (in the function field case) might be Ambrus Pal (CRM) formulated geometrically and hence over an Introduction to shtukas arbitrary ground field, for instance, the field of Amritanshu Prasad (CRM) complex numbers. In that case the role of the Automorphic representations representation theory of groups over local non- Archimedean fields is played by the David Savitt (McGill) representation theory of affine Kac-Moody Étale cohomology algebras, as can be seen from the recent work of 30 April to 16 May 2002 A. Beilinson and V. Drinfeld. These lectures Cette période comprenait deux phases. La reviewed the geometric Langlands conjectures première a porté sur les multiples ingrédients and various approaches to proving them. Also des preuves des conjectures de Langlands; les discussed were the intriguing parallels between conférences de la Chaire Aisenstadt de E. the finite field and the complex field settings. Frenkel et de L. Lafforgue ont constitué la deuxième. À travers ces deux parties, les Laurent Lafforgue (IHES) personnes assistant à l’atelier eurent aussi la Aisenstadt Chair 2001-2002 chance d’entendre sept conférences de R. Chtoucas de Drinfeld et correspondance de Langlands Langlands les entretenant de ses idées récentes La présentation a porté sur les grandes lignes de sur l’endoscopie. la démonstration de la correspondance de The speakers were (with abstracts): Langlands pour GL(r) sur les corps de fonctions, généralisant la preuve de Drinfeld dans le cas du David Ben-Zvi (Chicago) rang r = 2. Plus particulièrement on s’est attaché Opers à montrer le rôle des principaux ingrédients de Opers are a remarkable class of connections on la démonstration!: la géométrie des chtoucas de algebraic curves, arising in integrable systems, Drinfeld et de leurs compactifications!; la conformal field theory and representation formule des traces d’Arthur-Selberg!; la formule theory, which play a central role in the work of des points fixes de Grothendieck-Lefschetz!; les Beilinson-Drinfeld on the geometric Langlands propriétés connues des fonctions L de paires tant correspondence. A tour of some of the different du côté automorphe que galoisien. places opers appear was offered, visiting the Hitchin system, Hamiltonian reduction of Kac- Robert Langlands (IAS) Moody algebras, differential operators and the Au-delà de l‘endoscopie KdV equations, projective structures and the Grâce aux travaux récents d’Arthur sur Virasoro algebra, and vertex algebras. l’endoscopie et la formule des traces et à d’autres travaux pas moins importants de grand nombre David Goss (Ohio State) de mathématiciens sur le lemme fondamental, Recent advances in characteristic p arithmetic nous commençons à mieux comprendre non pas We will discuss recent advances in the theory of seulement comment utiliser la formule des traces the finite characteristic arithmetic associated to pour établir le transfert des formes automorphes Drinfeld modules. Included will be some recent d’un groupe à un autre, mais aussi quelle est la ideas related to a possible Riemann hypothesis vraie portée, en particulier le contenu
CRM Annual Report 2001 - 2002 21 Scientific Activities géométrique ou topologique, des problèmes à mécanique statistique, ainsi que deux de ses première vue techniques qu’il faut surmonter. étudiants. L’atelier visait tout particulièrement à Il n’en reste pas moins que les méthodes utilisées souligner ses contributions au développement sont toujours d’un pouvoir limité et ne suffisent des mathématiques à Montréal. pas à la résolution générale des problèmes posés Invited speakers: par la fonctorialité, en particulier ceux qui James Arthur (Toronto) interviennent dans les conjectures d’Artin ou Développements en germes pour les groupes réels de Ramanujan-Selberg. Elles nous inspirent Laurent Clozel (Paris-Sud & Caltech) toutefois une grande confiance dans la formule Rigidité et équipartition!: résultats et conjectures des traces telles que développée dans les Dennis Gaitsgory (Chicago) dernières années et, emporté par cette confiance, On the geometric Langlands conjecture for GLn l’objectif dans ce cours fut de chercher une voie qui puisse nous permettre de dépasser ce qu’on Philippe Pouliot (Texas) a fait jusqu’à présent. Finite number of states, de Sitter space, and quantum groups at roots Le cours s’adressait aux jeunes Yvan Saint-Aubin (Montréal) mathématicien(ne)s spécialist(e)s de la théorie Deux exemples simples de transition de phase!: la analytique ou de la théorie algébrique des percolation et le modèle d’Ising nombres ou des formes automorphes voulant travailler dans la théorie moderne des formes automorphes, un sujet ou toutes ces théories se Computational Lie Theory brassent. Quelques connaissances préalables des May 27 to June 7, 2002 formes automorphes sur GL(2) étaient exigée Org.: W. Casselman (UBC), F. Knop (Rutgers) aussi bien qu’une absence d’idées fixes. Le cours There were two series of lectures by Meinholf fut en grande partie axé sur un examen d’un Geck on applications of GAP in doing research point de vue inhabituelle de la formule des involving Coxeter and algebraic groups, and by traces telles que décritent dans le livre de John Stembridge mostly on tensor product Jacquet-Langlands. decomposition, with examples using Maple. The workshop complemented the Aisenstadt lectures Alexander Polishchuk (Boston) given concurrently by George Lusztig. Introduction to perverse sheaves The most surprising lecture was by Greg These lectures focussed on the definition and Warrington, who exhibited several counter- presentation of some examples of perverse examples to what many people had earlier sheaves in two contexts: (1) complex geometry, thought – that the m coefficients for the (2) algebraic geometry in positive characteristic. symmetric groups were always 1. Really Also discussed were the Riemann-Hilbert surprising was that this had been known for correspondence in case (1) and faisceaux-fonctions several years by Tim McLarnahan, but that his dictionary in case (2). discoveries had not been published. Warrington had written his own programs to explore the Christophe Sorger (Nantes) phenomenon further. Moduli stacks of G-bundles Invited speakers: R. Bédard (UQAM), R. Bezrukavnikov (Chicago), M. Brion (Joseph Fourier), F. du Cloux (Lyon I), After collecting preliminary material on M. J. Dyer (Notre Dame), W. Fulton (Michigan), M. Geck algebraic stacks useful for moduli problems, (Lyon), G. J. Heckman (Nijmegen), A. G. Helminck (North moduli of G-bundles were introduced and some Carolina State), F. Knop (Rutgers), J. McKay (Concordia), M. Noumi (Kobe), E. M. Opdam (Amsterdam), A. Ram of the (by now) basic theorems as the (Wisconsin), Y. B. Sanderson (William Paterson) T. A. uniformization theorem were proved. Springer (Utrecht), J. R. Stembridge (Michigan), B. Sturmfels (Berkeley), P. Trapa (Harvard), J. F. van Diejen (Chile), M. van Leeuwen (Poitiers), D. A. Vogan Jr (MIT), N. R. Wallach Workshop in honour of Robert Langlands (California, San Diego), G. Saunders Warrington (Harvard), May 17, 2002 A. Zelevinski (Northeastern). Un atelier en l’honneur de R. Langlands fut tenu le 17 mai pour souligner son 65e anniversaire. Les conférenciers comprenaient quelques-uns de ses collaborateurs en théorie des nombres et en
22 Annual Report 2001 - 2002 CRM Scientific Activities
Algebraic Transformation Groups of cohomology and Chow groups related to flag June 10-14, 2002 manifolds and Schubert varieties; quantum Org.: A. Broer (Montréal), J. Carrell (UBC) cohomology and Schubert calculus. The purpose of the workshop was to bring Invited speakers: K. Behrend (UBC), A. Bertram (Utah), T. together experts in algebraic groups, algebraic Braden (Massachusetts), M. Brion (Grenoble), W. A. geometry, representation theory and related Casselman (British Columbia), V. Ginzburg (Chicago), M. Haiman (UCSD), G. Heckman (Nijmegen), R. B. Howlett areas, especially those touching on: geometric (Sydney), F. Knop (Rutgers), A. Knutson (Berkeley), B. methods in representation theory using tools Kostant (MIT), S. Kumar (North Carolina), L. Manivel like equivariant cohomology and perverse (Grenoble), E. Meinrenken (Toronto), I. Mirkovic (Massachusetts), H. Nakajima (Kyoto), D. Peterson (UBC), Y. sheaves; the Hilbert scheme of points on a B. Sanderson (William Paterson), T. A. Springer (Utrecht), D. surface and its connection with the n!-conjecture E. Taylor (Sydney), E. Vasserot (Cergy-Pontoise), C. in algebraic combinatorics; equivariant versions Woodward (Rutgers).
CRM Annual Report 2001 - 2002 23 Scientific Activities
Aisenstadt Chair
The Aisenstadt Chair was endowed by Montréal philanthropist Dr. André Aisenstadt. Under its auspices, one or more 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, Duong H. Phong, Michael S. Waterman and Arthur T. Winfree. The CRM was honoured to have as Aisenstadt chairholders, during the 2001-2002 theme year in Groups and Geometry, Professors Edward Frenkel of the University of California at Berkeley, Professor Laurent Lafforgue of the Institut des Hautes Études Scientifiques and Professor George Lusztig of MIT.
Professor Edward Frenkel Professor Frenkel obtained his undergraduate University of California at Berkeley degree from Moscow in 1989 and his Ph.D. from On the week of May Harvard in 1991 under the supervision of 6-14, 2002, Professor B.!Feigin. He was then appointed at the Harvard Edward Frenkel gave Society of Fellows and became in 1997 full a series of eight professor at Berkeley. His mathematical interests conferences titled cover a remarkably wide range of topics, “Recent developments including fields, quantum theory, integrable in the geometric systems, representation theory and algebraic Langlands Program” geometry. as part of the series of lectures on the Professor Laurent Lafforgue Langlands program for function fields. Frenkel’s Institut des Hautes Études Scientifiques lectures were greatly enjoyed by everyone in As part of the attendance for their remarkable clarity, they concentration period on were one of the high points, along with those of the Langlands program for Laurent Lafforgue, of the theme year. Here is the function fields, Professor summary of the talks: Laurent Lafforgue gave a In recent years it was realized that the series of five conferences Langlands conjectures (in the function May 6-14, 2002, with the field case) might be formulated title Chtoucas de Drinfeld et geometrically and hence over an arbitrary correspondance de Langlands. ground field, for instance, the field of Here is the summary of the complex numbers. In that case the role of talks: the representation theory of groups over On se propose de présenter les grandes lignes local non-Archimedean fields is played by de la démonstration de la correspondance de the representation theory of affine Kac- Langlands pour GL(r) sur les corps de Moody algebras, as can be seen from the fonctions, généralisant la preuve de Drinfeld recent work of A. Beilinson and V. dans le cas du rang r=2. On s’attachera en Drinfeld. In these lectures we will review particulier à montrer le rôle des principaux the geometric Langlands conjectures and ingrédients de la démonstration: various approaches to proving them. We • la géométrie des chtoucas de Drinfeld will also discuss the intriguing parallels et de leurs compactifications; between the finite field and the complex • la formule des traces d'Arthur-Selberg; field settings. • la formule des points fixes de Grothendieck-Lefschetz;
24 Annual Report 2000-2001 CRM Scientific Activities
• les propriétés connues des fonctions L Professor George Lusztig de paires tant du côté automorphe que MIT galoisien. On May 27, 2002, Professor The following week, he gave us an additional George Lusztig gave a public series of three talks on several variations of conference entitled “Homo- Grassmannians and their compactification; some morphisms of the icosahedral specific cases constitute a key ingredient of his group into reductive groups,” proof for the Langlands conjecture for GL(r) over in which he explored function fields; he has since greatly generalized homomorphisms of finite the theory. The material of those three talks as groups, in particular the well as those from the previous series will be icosahedral group, into published as a CRM monograph. reductive groups. Those homomorphisms are After graduating from the École Normale strongly constrained and Professor Lusztig Supérieure, Laurent Lafforgue entered the CNRS presented one classification. This conference was as a research fellow in 1990. In 1994, he followed by a more specialized series, titled presented his thesis D-Chtoukas de Drinfeld, “Hecke algebras with unequal parameters,” under the guidance of Gérard Laumon. First given as part of the workshop on computational appointed as a professor at Orsay, he accepted Lie theory. Those talks were very well received an appointment as permanent professor at IHÉS and will be the object of an AMS-CRM in 2000. He was awarded the Cours Peccot at the monograph. Collège de France in 1996 and was an invited Holder of the Norbert Wiener Chair at MIT, speaker at the International Congress of Professor Lusztig is one of the greatest Mathematicians in Berlin in 1998. In 2002, he contemporary mathematicians and has had an received the Fields Medal for this proof of the impact during his very successful career on a Langlands conjecture on the correspondence wide range of mathematical problems. Among connecting arithmetic properties to analytic others, he has produced fundamental results on properties of automorphic representations. the representations of finite groups of the Lie type; a construction for canonical bases of representations based on quantum algebras; as well as results at the core of the cohomology methods in representation theory.
CRM Annual Report 2001 - 2002 25 Scientific Activities
General Program 2001-2002 The CRM’s general program funds a wide variety of scientific events, both on-site, elsewhere in Canada 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 program promotes research in mathematical sciences at all levels. The program is quite flexible, to allow for opportunities as they arise.
Second public lecture of the Canadian Eighth Canadian conference of Journal of Statistics mathematics students June 14, 2001, Simon Fraser University June 12-17, 2001, Université Laval Org.: Christian Genest (Laval), Richard Lockhart (Simon Org.: Pier-André Bouchard St-Amant (Laval), Jean-Philippe Fraser) Boulet (Laval), Sylvain Hallé (Laval), Jean-François Plante (Laval) Dans le cadre du 29e congrès annuel de la Société statistique du Canada, tenu à l’Université Simon Cette conférence annuelle s’adresse aux Fraser (Burnaby, Colombie-Britannique) du 10 étudiants canadiens de premier cycle dont le au 14 juin 2001, le professeur Peter M. Hooper de programme d’études contient des l’Université de l’Alberta a présenté ses travaux mathématiques avancées. Les étudiants inscrits de recherche concernant un modèle de sont invités à présenter un exposé de 20 ou 50 régression flexible défini à partir d’une base de minutes sur un sujet mathématique de leur fonctions logistiques adaptatives. choix. Aux exposés d’étudiants s’ajoutent cinq conférences données par des professeurs L’article du professeur Hooper a ensuite fait d’universités canadiennes. Ainsi, Nelly Simoes l’objet d’un débat public, animé par le rédacteur nous a fait un exposé très intéressant sur la en chef de La revue canadienne de statistique (RCS), théorie des files d’attente. le professeur Richard A. Lockhart. Plusieurs spécialistes du domaine ont commenté Évidemment, les étudiants ont également profité publiquement les travaux du professeur Hooper, de l’occasion pour découvrir la ville de Québec. soit Mary J. Lindstrom (University of Wisconsin Ils avaient la possibilité d’aller visiter la citadelle at Madison), James O. Ramsay (McGill de Québec ou simplement d’aller se promener University), Nancy E. Heckman (University of dans le Vieux Québec, ce qui fût grandement British Columbia), ainsi que Hugh A. Chipman apprécié. et Hong Gu (University of Waterloo). Les congressistes, présents en grand nombre à ce Séminaire de mathématiques débat, ont également été invités à poser des supérieures: Modern Methods in questions ou à formuler des suggestions. Scientific Computation & Applications July 9-20, 2001, Université de Montréal Les commentaires retenus, ainsi que les réponses Org.: G. Sabidussi (Montréal), K. Mikula (Slovak Technical du professeur Hooper, ont été publiés avec University), A. Bourlioux (Montréal), M. Gander (McGill), l’article dans le numéro de septembre 2001 de La S. Lessard (Montréal), G. C. Papanicolaou (Stanford), A. Stuart (Warwick) revue canadienne de statistique (Vol. 29, No 3, 2001, th pp. 343-378). Une version pdf de l’article est The 40 session of the Séminaire de accessible en permanence sur la vitrine Internet mathématiques supérieures (9-20 July 2001) was de la RCS, à l’adresse http://www.mat.ulaval.ca/rcs devoted to Modern Methods in Scientific Computation and Applications. No session of the Étant donné le franc succès remporté par cette SMS during the last 25 years having dealt with activité, la RCS et le CRM ont décidé de numerical mathematics, the program for 2001 poursuivre leur collaboration en organisant, à e was specifically designed to show how wide the Montréal cette fois, un 3 débat public. Celui-ci a influence of scientific computing had become eu lieu le 22 mars 2002. during that period. The main themes were image processing, mathematical finance, electrical engineering, thin films, moving interfaces, and turbulent combustion, the common thread running through these subjects being the numerical solution and analysis of the asymptotic behavior of the partial differential equations involved in these problems. The
26 Annual Report 2001 - 2002 CRM Scientific Activities following 8 mini-courses were given: Domain FUSION 2001: 4th International decomposition methods (L. Halpern, Paris XIII, Conference on Information Fusion and F. Nataf, École Polytechnique); Multigrid August 7-10, 2001, Montréal methods (G. Haase and U. Langer, Linz); 261 participants Org.: E. Shahbazian (Lockheed Martin Canada & CRM), D. Numerical aspects of deterministic and random Blair (Georgia Tech.), P. Willett (U. Conn.), P. Valin dynamical systems (T. Humphries, Sussex, and (Lockheed Martin Canada & CRM). A. Stuart, Warwick); Matrix analysis of Fusion 2001 provided a forum for fusion extremely large systems (Z. Bai, UC Davis, and research, applications, and technological G. Golub, Stanford); Stochastic differential advances by scientists and engineers working in equations and volatility analysis (G. all aspects of information and data fusion Papanicolaou, Stanford, and R. Sircar, techniques and systems. This fourth incarnation Princeton); Applications of PDEs in image of the International Conferences on Information Fusion was held on behalf of the International processing (K. Mikula, STU Bratislava, and J. Society on Information Fusion (ISIF) in Montréal Sethian, Berkeley); Asymptotic analysis of from August 7-10, 2001, during a record- rupturing and fingering in thin films (A. breaking heat wave (35 days without rain!). The Bertozzi and T. Witelski, Duke); Numerical organization and sponsorship were shared combustion (P. Souganidis, Texas at Austin, and between Lockheed Martin Canada, the Network A. Bourlioux, Montréal). for Computing and Mathematical Modeling In addition to the 16 speakers, 59 participants (ncm2), the Centre de Recherches Mathématiques coming from 20 different countries attended the (CRM) of the Université de Montréal, Defense Research Establishment Valcartier (DREV), the session. Besides the support by the CRM, the Canadian Space Agency (CSA), Mathematics of SMS benefited from support by NATO (through Information Technology and Complex Systems its Advanced Study Institutes Program), the (MITACS), and was under the technical co- Université de Montréal, and McGill University. sponsorship of the IEEE AES Society. Martin Gander (McGill) and Anne Bourlioux Conference topics covered theoretical and (Montréal) were the scientific organizers of the technical advances for fusion algorithms and session. systems, and provided real-world applications. The proceedings have been published by Kluwer There were 146 technical contributions from 304 Academic Publishers in the NATO Science Series authors representing 19 countries. There were II, Vol. 75. also seven organized sessions on Computationally Intensive Distributed Sensor Statistics 2001 Canada: The Fourth Networks, Formal Methods, Image Fusion & Canadian Conference in Applied Exploitation, Distributed Tracking, Situation Statistics Analysis and Situational Awareness, Knowledge Base Role in Information Fusion, Non-linear July 6-8, 2001, Université Concordia Org.: Y. Chaubey (Concordia), F. Nebebe (Concordia) Filtering and Probabilistic Multi-Hypothesis Tracking. For a more detailed report, see The conference was a success. It attracted www.crm.umontreal.ca/fusion. approximately 250 participants representing government, education and industry from all Seconde conférence à la mémoire de over the globe. Important problems associated Gilles Fournier with current issues in genomics, environment, August 13-15, 2001, Université de Sherbrooke health, networking and data management, along Org.: Marlène Frigon (Montréal), Andrzej Granas with theoretical developments in statistics were (Montréal), Tomasz Kaczynski (Sherbrooke) discussed. The conference featured 144 speakers Les thèmes principaux de cette seconde in seven plenary sessions and 42 invited and conférence dédiée à la mémoire de Gilles contributed papers sessions. On overwhelming Fournier ont été la théorie des points fixes et la demand from the contributors, the organizers théorie de points critiques ainsi que leurs decided to publish refereed proceedings of the applications aux équations différentielles et aux conference in a volume entitled Recent Advances systèmes dynamiques. À cette occasion, des in Statistical Methods, edited by Yogendra P. développements récents de ces domaines ont été Chaubey and published by World Scientific présentés par des experts conduisant à des Publishing (UK) Ltd. échanges stimulants entre eux et les participants. Des conférences de nature historique ont aussi
CRM Annual Report 2001 - 2002 27 Scientific Activities
été présentées notamment sur la contribution de conference theme during the year in Analysis at Gilles Fournier. CRM and Fields Institute in 2003/2004. La participation à cette conférence a été Invited speakers: A. Gamburd (Stanford), I. Vardi (IHES), P. Bleher (Indiana, Purdue), Z. Rudnick (Tel Aviv), R. Speicher excellente. Cette conférence était suivie par un (Queen’s), I. Dumitriu (MIT), E. Duenez (Johns Hopkins), A. atelier sur l’indice de Conley. Ainsi, plusieurs Bourget (McGill), H. Widom (Santa Cruz), K. Soundararajan personnes ont prolongé ou devancé leur séjour à (IAS), H. Donnelly (Purdue), P. Sarnak (Princeton), U. Smilansky (Weizmann), B. Eynard (CRM), T. Tate (Keio), A. Sherbrooke (selon le cas) pour participer aux Uribe (Michigan), M. Min-Oo (McMaster), V. Jaksic (Johns deux conférences. Aussi, il y a eu une bonne Hopkins), J. Harnad (CRM), W. Craig (McMaster), I. Rivin participation d’étudiants de cycles supérieurs (Temple), M. Bertola (CRM). d’ici et de l’étranger. Histoires de catégories Septembre 13-14, 2001, CRM Invited speakers: M. Allili (Lennoxville), F. Collin Org.: Luc Bélair (UQAM), Liliane Beaulieu (CRM) (Sherbrooke), P. Deguire (Moncton), Z. Dzedzej (Gdansk), N. El Khattabi (Maroc), A. Felshtyn (Greifwald), K. Geba Cet atelier des 13 et 14 septembre, auquel ont (Gdansk), A. Granas (Montréal), A. Marino (Pise), M. participé des mathématiciens, des historiens et Martelli (Cal St. Fullerton), J. Mawhin (Université Catholique de Louvain), K. Saadi Drissi (Maroc), N. Schlomiuk des philosophes des mathématiques, avait pour (Montréal), H. Steinlein (Munich), A. Szulkin (Stockholm). objectif principal de faire le point sur l’histoire de la théorie des catégories. La parole était Spectral Statistics and High Energy largement donnée aux protagonistes de cette Eigenstates histoire. Les événements du 11 septembre 2001 August 25 to September 2, 2001, CRM ont chambardé l’horaire prévu, en empêchant C. Org.: Dmitry Jakobson, John Toth, Yiannis Petridis Houzel et C. McLarty de faire le voyage. C. (McGill). McLarty a pu reporter sa participation au 21 The workshop brought together mathematicians septembre. Les organisateurs tiennent à and physicists working in the areas of Random remercier les participants, et en particulier les Matrix Theory, Riemann-Hilbert Problems, conférenciers, pour avoir rendu ces journées fructueuses, dans un contexte international peu Toeplitz Quantization, Analytic Number Theory propice aux souvenirs du temps passé. Les (Automorphic Forms and L-functions), comptes-rendus de ces journées seront publiés Semiclassical Theory and Partial Differential sous la direction de Liliane Beaulieu. Equations, focusing on spectral statistics and Invited speakers: L. Beaulieu (CRM), C. Houzel (Paris), J. asymptotic properties of high energy Lambek (McGill), W. Lawvere (Buffalo), M. Makkai (McGill), Eigenstates, and resulting in lively interaction C. McLarty (Case Western), G. Reyes (Montréal). among the participants. For many conference e participants, this was their first visit to Montréal, Journée statistique du CRM et 3 and several of them mentioned to organizers conférence publique de la Revue their very positive impressions of the conference, statistique du Canada the CRM and the city, and indicated their desire March 22, 2002, CRM Org.: Christian Genest (Laval), Christian Léger (CRM, to come again. Montréal). Four very successful introductory courses were Le Centre de recherches mathématiques (CRM) presented by: P. Bleher, Semiclassical Asymptotics et la Revue canadienne de statistique (RCS) se in Random Matrix Models 1,2,3; Z. Rudnick, sont à nouveau associés afin de présenter la 3e Quantum Maps: Semiclassics and Number Theory Conférence publique de la RCS dans le cadre de 1,2,3; A.!Uribe, Berezin-Toeplitz Operators 1,2,3; la Journée statistique du CRM. Suite au succès and S. Zelditch, 1. Highly Excited Quantum obtenu lors de la présentation des deux Eigenstates, 2. Riemannian Manifolds with Extreme premières conférences publiques tenues lors des Eigenfunction Growth, and 3. Random Spherical deux derniers congrès annuels de la SSC, la RCS Harmonics. a innové en présentant sa troisième Conférence Building on the success of the conference, and on publique au CRM le 22 mars 2002. the success of two sectional meetings of the AMS La Conférence publique portait sur l’article at CRM in May 2002 (on Random Matrices, and intitulé Box-Cox transformations in linear models: on Spectral Geometry and Analytic Aspects of Large sample theory and tests of normality, des Automorphic Forms), the organizers are auteurs Gemai Chen de l’Université de Calgary, planning three workshops related to the ainsi que Richard A. Lockhart et Michael A. Stephens de l’Université Simon Fraser. En
28 Annual Report 2001 - 2002 CRM Scientific Activities
étudiant la théorie asymptotique des estimateurs Theory, particularly in Canada. To advance dans le modèle de transformation de Box et Cox, these goals the CNTA organizes major les auteurs ont constaté que la distribution de international conferences, with the aim of l’estimateur de régression dépend fortement du exposing Canadian students and researchers to the latest developments in number theory world paramètre de transformation alors que si on wide. This year, the CNTA VII conference was normalise par le paramètre de dispersion des immediately preceded by a three-week erreurs, la dépendance par rapport au paramètre workshop on the Langlands Program for de transformation est grandement diminuée. De function fields at the CRM. Sessions covered plus, l’hypothèse de la normalité des erreurs est topics in algebraic number theory, très importante et ils démontrent comment on computational number theory, analytic number peut tester cette hypothèse dans ce contexte de theory, diophantine analysis and approximation, transformation. L’article a été commenté par and arithmetic algebraic geometry. There were Kjell Doksum de l’Université de la Californie à 187 participants. Berkeley et Richard A. Johnson de l’Université Invited Speakers: M.!Bennett (Urbana-Champaign), A.!Besser (Ben-Gurion), M.!Bhargava (Princeton), J.!Borwein (Simon de Wisconsin-Madison, par Peter M. Hooper de Fraser), D.!Boyd (UBC), D.!Brownawell (Penn. State), l’Université de l’Alberta et par Peter J. Y.!Bugeaud (Strasbourg!I), D.!Burns (King’s College), I.!Chen McCullagh de l’Université de Chicago. Une (Simon Fraser), H.!Cohen (Bordeaux), B.!Conrad (Michigan), C.!Consani (Toronto), J.!Cremona (Nottingham), H.!Darmon réplique de la part des auteurs a conclu la (McGill), C.!Deninger (Munster), W.!Duke (UCLA), session. La contribution des divers intervenants R.!Dvornicich (Pisa), S.!Edixhoven (Rennes), J.!Friedlander a permis de mieux comprendre ce problème (Toronto), D.!Goss (Ohio State), A.!Granville (Georgia), A.!Iovita (Washington), C.!Khare (Utah), H.!Kim (Toronto), important de la théorie de la régression. J.!Lagarias (AT&T Labs), M.!Laurent (Luminy, CNRS), G.!Martin (UBC), W.!McCallum (Arizona), D.!McKinnon La Journée statistique du CRM a débuté le matin (Waterloo), K.!Murty (Toronto), R.!Murty (Queen's), K.!Ono avec des conférences sur les travaux récents de (Wisconsin), G.!Pappas (Michigan State), C.!Pomerance (Bell quatre des conférenciers commentant l’article de Labs), B.!Poonen (Berkeley), C.!Popescu (Johns Hopkins), R.!Ramakrishna (Cornell), M.!Rapoport (Köln), Z.!Rudnick la Conférence publique. Deux des présentations (Tel-Aviv), K.!Soundararajan (Michigan), W.!Stein (Harvard), portaient sur le thème des transformations en C.!Stewart (Waterloo), V.!Vatsal (UBC), D.!Wan (UC Irvine), régression. Richard A. Johnson a introduit A new A.!Weiss (Alberta), T.!Wooley (Michigan). family of power transformations to improve normality alors que Kjell Doksum a parlé de Robustness and Conférence Constance van Eeden!: stability of parameters and estimates. Peter Hooper Statistique mathématique 2002 a présenté Relating patterns of fetal growth to health May 24-25, 2002, CRM outcomes at birth. Org.!: Marc Moore (École Polytechnique), Sorana Froda (UQAM), Christian Léger (CRM) Finalement, Peter McCullagh a discuté de Les 24 et 25 mai dernier, le CRM a été l’hôte Statistical models for Monte-Carlo integration. La d’une conférence soulignant le 75e anniversaire participation des étudiants et des boursiers de naissance de Mme Constance van Eeden ainsi postdoctoraux a été particulièrement importante. que sa longue et remarquable carrière en L’expérience consistant à présenter une recherche et en direction d’étudiants. Mme van conférence publique de la RCS en dehors du Eeden est Professeur émérite à l’Université de congrès annuel de la Société statistique du Montréal ainsi que Professeur honoraire de Canada a donc été couronnée de succès. l’Université de la Colombie Britannique. Invited speakers: G. Chen (Calgary), K. Doksum (Berkeley), P. Hooper (Alberta), R. Johnson (Wisconsin at Madison), Ancien étudiant à la maîtrise de Mme van R.!Lockhart (Simon Fraser), P. McCullagh (Chicago), Eeden, Louis-Paul Rivest de l’Université Laval a M.!Stephens (Simon Fraser). débuté la Conférence en présentant Un modèle de CNTA VII Meeting of the Canadian statistique directionnelle pour la détection et la Number Theory Association correction du «!crosstalk!» en cinématique humaine. Puis Roelof Helmers, compatriote du CWI May 19-25, 2002, CRM, Université de Montréal. Org.: H. Kisilevsky (Concordia) & E. Goren (McGill) Amsterdam, a présenté ses travaux sur Statistical The Canadian Number Theory Association estimation of Poisson intensity functions. Denis (CNTA) was founded in 1987 at the International Larocque des HEC, son dernier étudiant au Number Theory Conference at Laval University. doctorat à l’Université de Montréal, a fait un The purpose of the CNTA is to enhance and survol des plus récentes méthodes en statistique promote learning and research in Number non paramétrique dans A review of modern
CRM Annual Report 2001 - 2002 29 Scientific Activities methods based on signs and ranks for Perron de l’Université de Montréal a présenté un multidimensional data. Bill Strawderman, de survol de ses plus importantes contributions, l’Université Rutgers et statisticien en résidence dont plusieurs sont récentes, à l’estimation dans du Fonds Constance van Eeden à UBC en 1999, des espaces paramétriques contraints. nous a entretenus de Bayes minimax estimation of Plus d’une cinquantaine de chercheurs, a normal mean vector for general quadratic loss. Un étudiants, ex-étudiants ou ex-collègues de Mme autre compatriote de l’Université d’Amsterdam, van Eeden ont pu bénéficier de cet excellent Chris Klaassen, a présenté ses travaux sur programme scientifique. Finalement un livre Asymptotic most accurate confidence intervals in the intitulé Mathematical Statistics and Applications: semiparametric symmetric location model. Jim Festschrift for Constance van Eeden est Zidek, un de ses plus fidèles collaborateurs de présentement en préparation. Édité par Marc UBC, a présenté une très bonne conférence au Moore de l’École Polytechnique et Sorana Froda titre fort intriguant de Uncertainty. de l’Université du Québec à Montréal, deux De plus, Yves Lepage de l’Université de anciens étudiants au doctorat de Mme van Montréal et second étudiant au doctorat de Mme Eeden, ainsi que par Christian Léger du CRM et van Eeden a fait un survol de sa contribution de l’Université de Montréal, ce livre sera publié exceptionnelle à la statistique non paramétrique en 2003 conjointement par le CRM et l’IMS ainsi qu’à la direction d’étudiants (plus de 13 au (Institute of Mathematical Statistics). doctorat et 18 à la maîtrise). Finalement, François
30 Annual Report 2001 - 2002 CRM Scientific Activities
CRM Prizes CRM-Fields Institute Prize André-Aisenstadt Prize In 1994, the Centre de recherches Created in 1991, the André-Aisenstadt mathématiques (CRM) and the Fields Institute Mathematics Prize is intended to recognize and announced the creation of a new prize to be reward talented young Canadian awarded for exceptional contributions to the mathematicians. The Prize, which is given for mathematical sciences. The recipient of the research achievement in pure and applied prize is chosen by the Advisory Committee of the CRM and the Scientific Advisory mathematics, consists of a $3000 award. The Committee of the Fields Institute according to recipient is chosen by the CRM Advisory the criterion of excellence in research. The Committee. At the time of nomination, prize consists of both a $5,000 award and a candidates must be Canadian citizens or medal, and the winner is required to give a permanent residents of Canada, and no more lecture at the CRM and the Fields Institute. The than seven years from their Ph.D. The previous past recipients are: H.S.M. Coxeter (1995), G.A. winners of the André-Aisenstadt Prize were: Elliot (1996), J. Arthur (1997), R.V. Moody Niky Kamran (1991), Ian Putnam (1992), (1998), Stephen A. Cook (1999), Israel Michael Michael Ward and Nigel Higson (1994), Adrian Sigal (2000), and William T. Tutte (2001). The S. Lewis (1995), Henri Darmon and Lisa Jeffrey CRM-Fields Institute 2002 Prize is awarded to (1996), Boris Khesin (1997), John Toth (1998), Professor John B. Friedlander. Changgeng Gui (1999), and Dr. Eckhard Professor Friedlander Meinrenken (2000). CRM was delighted to is one of the world’s award the 2001 André-Aisenstadt Prize to foremost analytic Professor Jingyi Chen of the University of number theorists, British Columbia and is a recognized Mr. Chen obtained a leader in the theory Ph.D. from Stanford of prime numbers University in 1992. He has and L-functions. He since been a professor at received his B.Sc. the Massachussetts from the University Institute of Technology, at of Toronto in 1965, a Northwestern University M.A. from the University of Waterloo in 1966, and the University of and a Ph.D. from Penn State in 1972. He was a California. His works in lecturer at M.I.T. in 1974-76, and has been on the geometric analysis have been recognized. He was faculty of the University of Toronto since 1977, awarded the Alfred P. where he served as Chair during 1987-91. He has Sloan Research Fellowship from the National also spent several years at the Institute for Science Foundation (USA) Postdoctoral Advanced Study where he has collaborated with Fellowship. He has published over twenty E. Bombieri and many others. John Friedlander articles and is an invited speaker all over the is a Fellow of the Royal Society of Canada (1988), world. Professor Chen delivered a lecture on was an invited lecturer at the 1994 ICM in Zurich January 18, 2002. Here is the summary: and delivered the CMS Jeffery-Williams Lecture Quaternionic mappings between hyperkahler in 1999. He has contributed significantly to manifolds mathematics in other ways, especially in Quaternionic maps (Q-maps) between Canada, through his role at NSERC hyperkahler manifolds are quaternionic (Mathematics GSC, 1991-94), as Mathematics analogues of Cauchy-Riemann equations of Convenor of the Royal Society of Canada (1990- maps between Kahler manifolds and they arise 93), and as a Council member (1989-95) and naturally in higher dimensional gauge theory. Scientific Advisory Panel member (1996-2000) of Q-maps between quaternion numbers are just the Fields Institute. He has also served on the solutions to Cauchy-Riemann-Fueter equations. Editorial Board of the Canadian Journal of The Q-maps are energy minimizers in their Mathematics and the Canadian Mathematics homotopy classes, hence harmonic. We will Bulletin for the past four years. discuss a necessary and sufficient condition on
CRM Annual Report 2001 - 2002 31 Scientific Activities when a Q-map becomes holomorphic with as that of his colleague and compatriot Jiri respect to some complex structures, and give Patera. examples of Q-maps that cannot be holomorphic. When the domain of Q-maps is CRM-SSC Prize real 4-dimensional, we will analyze the structure In 1999, the Centre de recherches of the blow-up set of a sequence of Q-maps, and mathématiques (CRM) and the Statistical show that the singular set of a stationary Q-map Society of Canada created the CRM-SSC Prize is at most a 1-dimensional Hausdorff rectifiable in statistics in recognition of outstanding set. We will also indicate possible applications of contributions to the Statistical Sciences during this compactness result. the recipient’s first 15 years after earning a doctorate. The CRM-SSC Prize in Statistics CAP-CRM Prize consists of a $3000 award and a medal. The Awarded for the first time in 1995, the recipient is chosen by a joint CRM/SSC CAP-CRM Prize is given for outstanding advisory committee, consisting of three contributions to theoretical and mathematical members named by the SSC and two, physics. It consists of a $2000 award and a including a president, by the CRM. Previous medal. Previous winners were Werner Israel winners were Christian Genest (1999), Robert (1995), William G. Unruh (1996), Ian Affleck Tibshirani (2000) and Colleen Cutler (2001). (1997), J. Richard Bond (1998), David J. Rowe This year, the Centre de recherches (1999), Gordon W. Semenoff (2000), and André- mathématiques and the Statistical Society of Marie Tremblay (2001). The 2002 CAP-CRM Canada have awarded the CRM-SSC 2002 Prize prize has been awarded to Professor Pavel in Statistics to Professor Larry A. Wasserman of Winternitz of the Université de Montréal. Carnegie Mellon University, in Pittsburgh. The Canadian Association The 2002 CRM-SSC Prize of Phycisists (CAP) and in Statistics has been the Centre de recherches awarded to Dr Larry A. mathématiques (CRM) Wasserman of Carnegie Mellon University, are happy to announce Pittsburgh, for the that the 2002 CAP-CRM breadth and originality of Prize in Theoretical and his contributions to Mathematical Physics has statistical theory and his been given to Pavel influence in the Winternitz, professor at development and the Département de application of Bayesian mathématiques et de statistiques of the methodology. The announcement was made at Université de Montréal for his work on the Annual Meeting of the Statistical Society of symmetry methods in physics. In approximately Canada (SSC), held in Hamilton, Ontario, May 250 articles, he has made fundamental 26-29, 2002. contributions to, amongst others, the following Larry Wasserman was born in Windsor, Ontario, subjects: classification of Lie groups and where he grew up. He studied mathematics and algebras, their applications to the study of statistics at the University of Toronto (B.Sc., differential equations and difference equations, 1983; M.Sc., 1985; Ph.D., 1988). He has since been separation of variables in Hamilton-Jacobi and affiliated with Carnegie Mellon University, Schrödinger type equations, quantum groups where he is now Professor of Statistics. The and their applications. Born in Prague in 1936, author or co-author of more than 60 scientific Pavel Winternitz studied in the Soviet Union. articles, he is widely recognized as one of the After his bachelor and master’s degree at the current leaders in Bayesian inference. He has University of Leningrad, he obtained a Ph.D. in brought his expertise to bear on the foundations Theoretical Physics from Dubna’s JINR (1966). In of statistics and on numerous aspects of modern 1972, he joined the Université de Montréal. An statistical theory, including sampling, mixture international symposium was held at the CRM models, multiple testing, goodness-of-fit and in 1997 to celebrate his sixtieth birthday as well robustness issues, and both nonparametric and causal inference. In addition, he maintains active
32 Annual Report 2001 - 2002 CRM Scientific Activities collaborations with astrophysicists and statistical He is also the 1999 winner of the Presidents’ geneticists. Award, given each year by the Committee of Larry Wasserman’s pathbreaking work has Presidents of Statistical Societies to an already earned him several distinctions. Winner outstanding researcher under the age of 40. He of the SSC’s Pierre Robillard Award for the best has been an Associate Editor for The Canadian thesis in probability or statistics defended at a Journal of Statistics and the Journal of Statistical Canadian university in 1988, he was made a Planning and Inference. He continues to serve in Fellow of the American Statistical Association that capacity for The Annals of Statistics and the and of the Institute of Mathematical Statistics in Journal of the American Statistical Association. 1996. Larry is married to an Italian statistician, Isabella Verdinelli. In his spare time, he enjoys reading novels, drinking fine wine, and hanging out in Rome.
CRM Annual Report 2001 - 2002 33 Scientific Activities
National Program Committee
The three Canadian institutes in the 13th Canadian Conference on mathematical sciences, CRM, Fields and PIMS, Computational Geometry have initiated a program for the support of joint August 13-15, 2001 activities of a national stature in the University of Waterloo, Ontario Org.: T. Biedl, E. Demaine, M. Demaine, A. Lubiw (Univ. of mathematical sciences. A National Program Waterloo) Committee of members from the three institutes Supported by the NPC (CRM, Fields, PIMS), Univ. of administers this program, funded to the tune of Waterloo $100,000 per year. This committee makes The Canadian Conference on Computational recommendations to the three directors. The Geometry (CCCG) focuses on the mathematics program has many mandates, the first being to of discrete geometry from a computational point fund conferences and workshops in the of view. Abstracting and studying the geometry mathematical sciences across Canada. These problems that underlie important applications of funds are essentially allocated to activities that computing (such as geographic information fall outside the main purview of the three systems, computer-aided design, simulation, institutes, or that would benefit from joint robotics, solid modeling, databases, and institute funding. The program also aims to graphics) leads not only to new mathematical support activities that are held at the meetings of results, but also to improvements in these the three mathematical sciences societies: CMS, applications. Despite its international following, CAIMS, and SSC, as well as to support the CCCG maintains the informality of a smaller participation of graduate students at these workshop (70-85 attendees) and attracts a large scientific meetings. Finally, it coordinates number of students. international programs and other ventures where it is advantageous for the three institutes Second Workshop on the Conley Index to act as a whole. and Related Topics August 15-18, 2001, Univ. de Sherbrooke, Québec Org.: Tomasz Kaczynski (Sherbrooke), Octav Cornea The International Workshop on (Lille), Michael Dellnitz (Paderborn), Kontantin Dynamical Systems and their Michaikow (Georgia Tech), Marian Mrozek (Kraków), and Application to Biology Hiroe Oka (Ryukoku) August 2-6, 2001, Cape Breton, Nova Scotia Supported by the NPC (CRM, Fields, PIMS) and the Org.: Shigui Ruan (Dalhousie), Gail Wolkowicz Faculté des sciences de l’Université de Sherbrooke (McMaster), Jianhong Wu (York) The workshop is a continuation of the first The 45 participants came from Austria, Canada, Conley Index Workshop held in the Banach China, Japan, Singapore, Spain, Taiwan, the UK, Center (Warsaw, Poland) in June 1997. The and the USA. Among them there were 14 PDFs objective of the workshop is to stimulate an and graduate students. On top of the 38 half- exchange and collaboration on various problems hour talks, there were two panel discussions on related to extensions and applications of the epidemiological models (chaired by Fred Brauer Conley index theory as well as to the and Pauline van der Driessche) and population computation of the index. A particular place was dynamics (chaired by Jim Cushing, Herb given to infinite dimensional Conley index, Freedman and Hal Smith). The workshop computational topology and computational focused on (1) communication of current dynamics, and applications. research results, ideas, and problems in There were 63 participants from 14 countries. dynamical systems and their applications in The principal speakers were Norman Dancer biology, (2) future research directions in (Sydney), Marek Izydorek (Gdansk), William dynamical systems and mathematical biology, Kalies (Florida Atlantic U), Christopher McCord and (3) initiating possible collaborations. It also (Cincinnati), James Reineck (Buffalo), Roman provided a wonderful opportunity for young Srzednicki (Kraków), James Yorke (Maryland), Canadian researchers and graduate students to and Piotr Zgliczynski (Kraków). O. Cornea, K. communicate with the leading researchers and Mischaikow, and M. Dellnitz also gave tutorial to present their research work. The proceedings lectures. of the workshop will be published as a volume in the Fields Institute Communications.
34 Annual Report 2001 - 2002 CRM Scientific Activities
UNB Workshop on Modelling & Western Canada Linear Algebra Scientific Computation Meeting September 29-30, 2001, University of New Brunswick May 10-11, 2002, University of Regina Org.: V. Husain, J. Stockie and J. Watmough Org.: Steve Kirkland Invited speakers!: Claudio Albanese (Toronto), Matt Supported by the NPC (CRM, Fields, PIMS), University of Choptuik (UBC), Leah Keshet (UBC), Brian Wetton (UBC) Regina Conference Fund, and the Faculty of Science of the The workshop was considered to be highly University of Regina. successful by the participants and organizers. Held over two days, WCLAM 2002 featured 18 Forty-two researchers from diverse talks by speakers from Canada, the United States mathematical disciplines participated. The four and Germany. The lectures covered a range of plenary speakers (Claudio Albanese, Matt research areas associated with linear algebra, Choptuik, Leah Keshet, and Brian Wetton) gave including matrix theory, operating theory, graph overviews of the problems and computational theory, applied mathematics, numerical analysis methods in their respective fields, mathematical and combinatorics. The list of speakers included finance, numerical relativity, computational two winners of the Hans Schneider prize, which biology, and fluid mechanics. Several is given out every three years by the contributed talks covered a broad range of topics International Linear Algebra Society for in these fields, as well as in numerical analysis outstanding contributions to research in linear and physics. algebra. As with previous WCLAM’s, student The success of the workshop inspired discussion and postdoctoral participation is encouraged, of establishing an annual or bi-annual series of and WCLAM 2002 had ten such participants. such meetings in the Atlantic region. Indeed two students were given financial support towards their travel expenses in order CMS Winter Meeting that they could speak at the meeting. December 8-10, 2001 The meeting’s atmosphere is informal, with no Toronto Colony Hotel, Toronto, Ontario parallel sessions, and with plenty of time for Org.: Tom Salisbury (president), Juris Steprans (local committee predident), Stan Kochman, Nantel Bergeron, one-on-one discussion. As a result, WCLAM Monique Bouchard (CMS) 2002 is not only a forum for disseminating Supported by the NPC Canadian Mathematical Society research results, but also a venue for establishing NPC (Fields/CRM/PIMS), Dean of Arts, York University new research contacts and for making Department of Mathematics and Statistics, York University Number of participants: 269 connections across a broad array of research In 2001, the CMS’s annual winter meeting interests. Invited speakers: Jane Day (San Jose State Univ.), Ludwig included eight special sessions and nine plenary Elsner (Univ. Bielefeld), Chris Godsil (Univ. of Waterloo) lectures (including one public lecture and two prize lectures). Four satellite conferences were The 30th Canadian Annual Symposium planned in conjunction with the meeting. A on Operator Algebras and Operator grant from the National Program Committee Theory provided the funding for two of the special May 13-17, 2002, Lakehead University sessions Industrial Mathematics, organized by Org.: Andrew J. Dean Huaxiong Huang; Moonshine, organized by Chris The 30th Canadian Annual Symposium on Cummins). NPC funds were also used for the Operator Algebras and Operator Theory took support of graduate students attending the place at Lakehead University in Thunder Bay, meeting. Ontario. Our main speaker was Professor Adrian Invited speakers: Kai Behrend (UBC), Martin Golubitsky Ocneanu of Pennsylvania State University, who (University of Houston), Katherine Heinrich (University of Regina), Nathan Ng (University of Georgia), John Ockendon gave a series of three lectures on the (Oxford University), Arturo Pianzola (University of Alberta), geometrization of quantum subgroups and David Pimm (University of Alberta), Richard Schoen (Stanford University), Dan Voiculescu (Berkeley). subfactors. The conference was opened by Professor K. Davidson of the University of Waterloo and the Fields Institute, who spoke about his joint work with Laurent Marcoux on spans of unitary and similarity orbits. This bit of scheduling may have been a mistake on the part of the organizer, as
CRM Annual Report 2001 - 2002 35 Scientific Activities they continued to improve their result as the Mechanics of Lattice Models, and Scattering conference went on! Theory and Integrable Systems. Also on the list of invited speakers were such regulars of Canadian Operator Symposia past as CAIMS George Elliott, Man-Duen Choi, and Peter 8-10 June 2002 University of Calgary Rosenthal of the University of Toronto, and Org.: P. Binding, T. Ware (University of Calgary) Heydar Radjavi of Dalhousie University. The 23th Annual Meeting of CAIMS/SCMAI was Other invited speakers from abroad included hosted by the University of Calgary and Professor D. Hadwin of the University of New attended by over ninety academics, postdoctoral Hampshire, who spoke on an approach to fellows and graduate students from across Voiculescu’s free entropy using covering Canada, but also from the United States and as numbers, and Professor Marius Dadarlat of far afield as Israel and the European Purdue University, whose topic was the problem Community. Despite the unusually wet weather, of uniformly embedding a group into a Hilbert the atmosphere at the meeting was very positive. space. There was a lively interaction amongst the In addition to the established researchers, the participants, whose interests included fluid conference also provided a forum for several dynamics, environmental mathematics, graduate students and postdocs from Canadian Hamiltonian dynamics, mathematical modelling, universities to present their work. computational finance and computer graphics. Invited speakers!: Adrian Ocneanu (Penn State U.), Man- There were five plenary talks, each of which was Duen Choi (U. of Toronto), Marius Dadarlat (Purdue U.), Ken Davidson (U. of Waterloo), George Elliott (U of followed by three parallel sessions each Toronto), Don Hadith (U. of New Hampshire), Heydar focussing on one of the above areas. The Radjavi (Dalhousie U.), Peter Rosenthal (U. of Toronto). presentations were of a consistently high standard, and the meeting provided an excellent CMS Summer Meeting showcase for the activities of Canadian applied June 2-4, 2001, University of Saskatchewan and industrial mathematicians. Org.: K.Taylor, C. Soteros, M. Bremner, Y. Cuttle and F.-V. Kuhlmann (Saskatchewan) Invited speakers: J. Marsden (Caltech), A. Gargett (Old Supported by the NPC (CRM, Fields, PIMS), and the Dominion), G. Swaters (Alberta), N. Dyn (Tel Aviv), and University of Saskatchewan H.!Ockendon (Oxford). The 2001 Summer Meeting of the Canadian 30th Annual Meeting of the Statistical Mathematical Society was both a scientific and Society of Canada (SSC) an organizational success. There are relatively May 26-29, 2002, McMaster University, Hamilton few mathematicians who live within easy Supported the NPC (CRM, Fields, PIMS) and McMaster traveling distance of Saskatoon, so the total of University. 279 registered participants exceeded most This meeting was an unequivocal success, with expectations and seems to be a record for a 379 registered participants. Three workshops regular summer meeting. were held: David Boyd, University of British Columbia, • Design and Analysis of Cluster gave the CMS Jeffery-Williams Lecture and Lisa Randomization Trials by A. Donner, Jeffrey, University of Toronto, gave the CMS University of Western Ontario, and N. Klar, Krieger-Nelson Lecture. The plenary lecturers Cancer Care Ontario. were Georgia Benkart, Wisconsin-Madison; Zoe • Design and Analysis of Computer Chatzidakis, Paris; Geoffrey Grimmett, Experiments for Engineering by J. Sachs, Cambridge; and Barry Simon, CalTech. Duke University, and W. Welch, University of Waterloo. There were also ten well-attended special • Handling Missing Data by K. Nobrega and sessions in Abstract Harmonic Analysis, D. Haziza, Statistics Canada. Geometric Topology, Graph Theory, Infinite Dimensional Lie Theory and Representation There were 46 scientific sessions in total, plus a Theory, Mathematical Education: Cognition in poster session. Topics ranged from theoretical Mathematics, Matrix Analysis, Model Theoretic probability, inference, and stochastic processes Algebra, Number Theory - in Honor of David to applied sessions on environmental issues, Boyd, Rigorous Studies in the Statistical
36 Annual Report 2001 - 2002 CRM Scientific Activities statistical genetics, and statistics and • Statistics for Microarray Data Analysis governmental policy. (Michael Newton, University of Wisconsin at Thanks in no small part to the funding from the Madison and Terry Speed, University of NPC, the meeting included a large number of California at Berkeley) internationally known speakers. The particular • Statistics and Brain Mapping (Pedro Valdes- speakers whose funding was wholly or partially Sosa, Cuban Neuroscience Center and Moo covered by the grant from NPC, by session, Chung, University of Wisconsin at Madison) were: • Statistics and Public Policy (Miron Straf, National Academy of Sciences) • Probability (Ilie Grigorescu, University of • Split Plot Experiments in Industry (Robert Miami), McLeod, PhD student at University of • Statistical Inference (Chris Klaassen, Manitoba) University of Amsterdam and William • New Research Findings in Analysis Methods Strawderman, Rutgers University) for Survey Data (Christian Boudreau, PhD student at University of Waterloo).
CRM Annual Report 2001 - 2002 37 Scientific Activities
Members’ Seminars and 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
Analysis Seminar CRM-ISM March 12, 2002 Org.: Paul Gauthier Olivier Rousseau, Univ. de Montéal (CRM & Univ. de Montréal) Théorie du degré topologique de Brouwer et théorème June 1, 2001 de Jordan Paul Gauthier, Univ. de Montéal March 19, 2002 La fonction zêta de Riemann et les cercles de Richard Fournier, Dawson College & Univ. de remplissage Montréal June 8, 2001 Inégalités différentielles et univalence Jie Xiao, Concordia Univ. March 26, 2002 Isoperimetric inequalities via Hausdorff content Rasul Shafikov, SUNY at Stony Brook n June 15, 2001 Equivalence of domains in C Alexandre Girouard, Univ. de Montéal April 2, 2002 Rétraction de boule en dimension infinie Richard Fournier, Dawson College & Univ. de June 21, 2001 Montréal Pierre-Olivier Rathé, Univ. de Montéal La suite universelle de Maurice Heins et autres Produits de Blaschke pathologies June 28, 2001 April 9, 2002 Jean-Phlippe Samson, Univ. de Montéal Sébastien Manka, Univ. de Montréal Surconvergence Le théorème d'approximation de Carleman July 19, 2001 April 16, 2002 Sébastien Manka, Univ. de Montéal Nabil Ayoub Un théorème de sélection pour les relations Théorème de Bloch et théorème de Landau August 2, 2001 April 30, 2002 Victor Havin, Saint Petersburg Paul Gauthier, Univ. de Montréal Sur la séparation des singularités de fonctions Propriété d'universalité de la fonction zêta de analytiques bornées Riemann August 6, 2001 May 7, 2002 Abel Schroeder, ORT Braude College, Israel Richard Fournier, Dawson College & Univ. de Equations for linear fractional maps of operator balls Montréal Sur un homeomorphisme de l'ensemble des fonctions February 5, 2002 analytiques bornées Paul Gauthier, Univ. de Montéal Théorème de Bloch conforme-faux pour May 14, 2002 quasiconforme Jean-Philippe Samson, Univ. de Montréal Une introduction aux séries de Dirichlet February 12, 2002 Jie Xiao, Concordia Univ. May 21, 2002 Corona theorem for conformal deformations Todor Fabian Une interprétation probabiliste de la fonction Zêta de February 19, 2002 Riemann, sa représentation spectrale et applications Nabil Ayoub La constante de Bloch Seminar in Non-linear Analysis February 26, 2002 Org.: Marlène Frigon (CRM & UdeM) André Boivin, Western Ontario Univ. September 19 and 26, 2001 Théorèmes d'approximation et applications Isidore Fleischer, CRM Sur les fonctions à variations bornées à valeurs dans les espaces métriques
38 Annual Report 2001 - 2002 CRM Scientific Activities
October 3, 2001 Special Lectures Nicolas Beauchemin, Univ. de Montréal Org.: Jean-Marc Lina (CRM) Introduction à la catégorie de Lusternik-Schirelman October 3, 2001 October 24 and 31, 2001 Noel Cressie, Ohio State Univ. Nicolas Beauchemin, Univ. de Montréal Fast spatial prediction via multi-resolution tree- La catégorie relative structured models November 14, 2001 October 4, 2001 Nicolas Beauchemin, Univ. de Montréal Noel Cressie, Ohio State Univ. Théorie des points critiques pour des fonctionnelles Fast spatial prediction via multi-resolution tree- multivoques structured models II November 28 and December 5, 2001 Alexandre Girouard, Univ. de Montréal March 13, 2002 Enlacement homologique Bradley J. Lucier, Purdue Univ. Wavelet Methods for Medical Tomography December 11, 2001 Donal O'Regan, National Univ. of Ireland Special Lectures Integral Equations Org.: J. Harnad (Concordia & CRM) January 11, 2002 September 26, 2001 Donald Violette, Univ. de Moncton A. N. Tyurin, Steklov Mathematical Institute Différentiabilité de type univoque pour une certaine Quantization and theta-functions classe d'applications multivoques October 3, 2001 January 30, 2002 A. N. Tyurin, Steklov Mathematical Institute Alexandre Girouard, Univ. de Montréal Symplectic geometry of moduli spaces of vector Axiomatisation des inégalités de Morse bundles February 6-13 and 20, 2002 October 10, 2001 Nicolas Beauchemin, Univ. de Montréal A. N. Tyurin, Steklov Mathematical Institute Introduction à la f-catégorie Non-abelian theta-functions March 13, 2002 Ron Stern, Concordia Univ. Special Lectures A necessary condition for state constrained Org.: John Taylor (McGill) stabilization September 28 and October 5, 2001 March 27, 2002 Francois Ledrappier, École Polytechnique Nicolas Beauchemin, Univ. de Montréal (Palaiseau, France) La catégorie relative au sens de Szulkin Brownian motion and negatively curved manifolds
April 25 and May 2, 2002 October 12, 2001 Nicolas Beauchemin, Univ. de Montréal Francois Ledrappier, École Polytechnique Application de la catégorie relative aux équations (Palaiseau, France) différentielles Ergodic properties of some linear actions Special Lectures October 19 and 26, 2001 Org.: N. Kamran & J. Hurtubise (CRM & Francois Ledrappier, Ecole Polytechnique McGill) (Palaiseau, France) Aspects de la rigidité pour les variétés à courbure September 10, 13, 14 and 17, 2001 négative Li Ma, Tsinghua Univ. Mean Curvature Flow for Lagrangian Submanifolds, I
Special Lecture Org.: Adam Sikora (CRM) July 13, 2001 Louis Kauffman, Univ. of Illinois at Chicago Virtual Knot Theory
CRM Annual Report 2001 - 2002 39 Scientific Activities
Special Lecture CRM-ISM Modélisation et design de pièces en composite: Org.: Dana Schlomiuk (UdeM) optimisation October 4, 2001 November 8, 2001 Jean-Paul Pier, Centre universitaire du Marc Thiriet, CNRS & Univ. Pierre et Marie Luxembourg Curie & INRIA, France L'analyse fonctionnelle, une théorie omniprésente Traitements endovasculaires. Des modèles dans les mathématiques du 20e siècle numériques aux outils médicaux November 29, 2001 Special Lectures Patrick Terriault, École de Technologie Org.: Peter Russell (McGill) Supérieure, Univ. du Québec à Montréal March 8, 2002 Conception de dispositifs médicaux en alliages à Vladimir Popov, Steklov Institute mémoire de forme Colloque CRM-ISM December 13, 2001 Modern developments in invariant theory Gérard Plante, Univ. de Sherbrooke March 13, 2002 Présentation des activités du à l'Université de Vladimir Popov, Steklov Institute Sherbrooke Self-dual algebraic varieties and nilpotent orbits February 7, 2002 March 13, 2002 Dominique Pelletier, École Polytechnique de Vladimir Popov, Steklov Institute Montréal Automorphism groups of finite dimensional simple Analyse de sensibilité et d'incertitude par la méthode algebras de l'équation des sensibilités March 20, 2002 February 21, 2002 Vladimir Popov, Steklov Institute Adel Blouza, Univ. de Rouen & Univ. Paris VI Generators and relations of affine coordinate rings of Une version du lemme de Friedrichs et applications semisimple groups au modèle de coque de Koiter March 20, 2002 February 21, 2002 Vladimir Popov, Steklov Institute Laurent Dumas, École Normale Supérieure de Discrete complex reflection groups Paris & Univ. Paris VI Optimisation de formes aérodynamiques dans Special Lectures l'industrie automobile Org.: Jacques Hurtubise February 28, 2002 March 19, 21, 26, 28 & April 2, 2002 Laurent Dumas, École Normale Supérieure de Nizar Touzi, Univ. de Paris I Panthéon-Sorbonne Paris & Univ. Paris VI Contrôle stochastique et applications à la finance Modèles de billard’étude asymptotique April 22, 2002 February 28, 2002 Jonathan Borwein, Simon Fraser Univ. Adel Blouza, Univ. de Rouen & Univ. Paris VI Why Math is (Still) Hard: Challenges in Réduction algorithmique des systèmes cinétiques Mathematical Computing raides March 21 and 28, 2002 Special Lecture (CCC 2002) Michel Delfour, CRM & Univ. de Montréal Org.: Jacques Hurtubise Modèles de coques minces et de coques asymptotiques H. Cohen, Univ. de Bordeaux Courbes elliptiques!: de la théorie à la pratique April 4, 2002 Annie Raoult, LMC & TIMC, IMAG, Univ. CRM-CERCA Joseph Fourier, Grenoble Org.: José Urquiza (CRM), Josée Manseau Nouveautés en modélisation hiérarchique de plaques (École Polytechnique), Donatien N’dri (École April 11, 2002 Polytechnique) Annie Raoult, LMC & TIMC, IMAG, Univ. October 18, 2001 Joseph Fourier, Grenoble Jean Deteix Modélisation de l'orientation des fibres cardiaques
40 Annual Report 2001 - 2002 CRM Scientific Activities
Seminar in Mathematical Physics November 27, 2001 Org.: J. Harnad (CRM & Concordia) & Pavel Eyal Markman, Univ. of Massachusetts Winternitz (CRM) (Amherst) September 18, 2001 Elliptic Sklyanin systems Ahmed Sebbar, Univ. de Bordeaux December 4, 2001 Capacities, Jacobi Matrices, & Jacobi Forms Ray McLenaghan, Univ. of Waterloo September 25, 2001 Group invariant classification of separable Misha B. Sheftel, St. Petersburg & Istanbul Hamiltonian systems in the Euclidean plane Method of group foliation, non-invariant solutions of December 11, 2001 the heavenly equationand heavenly metrics Zuzana Masakova, CRM September 26, 2001 Combinatorial properties of cut and project sequences A.N. Tyurin, Steklov Mathematical Institute, January 15, 2002 Russian Academy of Sciences, Moscow Pavel Winternitz, CRM & DMS Non-abelian theta-functions and spin networks I Systèmes intégrables et superintégrables dans les October 2, 2001 espaces avec courbure E.G. Kalnins, University of Waikato, New January 22, 2002 Zealand Dmitri Korotkin, Concordia Univ. & CRM Perturbations of Black holes and special functions Some integrable systems on Hurwitz spaces October 3, 2001 January 29, 2002 A.N. Tyurin, Steklov Mathematical Institute, Simon Gravel, CRM & Univ. de Montréal Russian Academy of Sciences, Moscow Systèmes superintégrables avec symétries du Non-abelian theta-functions and spin networks II troisième ordre October 9, 2001 February 5, 2002 Michel Grundland, UQTR & CRM Luis-Miguel Nieto, Univ. Valladolid Sur certains aspects géométriques des applications du Higher order supersymmetric periodic potential modèle sigma CP2 February 12, 2002 October 10, 2001 Mikhail Babich, Concordia Univ. & Steklov A.N. Tyurin, Steklov Mathematical Institute, Mathematical Institute, St.Petersburg, Russia Russian Academy of Sciences, Moscow Schlesinger system with 4 points, its symmetries, Non-abelian theta-functions and spin networks III connections with Painlevé VI system and the October 16, 2001 algebraic surface theory Aleksander Strasburger, Univ. de Bialystok February 19 and 21, 2002 On the ordering problem in QM and its connection Fréderic Lesage, CRM with certain classes of Orthogonal Polynomials Théorie des champs intégrables et dualité October 23, 2001 February 26, 2002 David Calderbank, Univ. of Edinburgh Jean-Louis Verger-Gaugry, Institut Fourier, Integrable background geometries in dimensions one Saint-Martin d’Hères, France to four Un théorème de compacité pour l'ensemble des n November 1, 2001 ensembles uniformément discrets de R et ses sous- Henrik Aratyn, Univ. of Illinois ensembles : réseaux, ensembles modèles, ensembles de Symmetries of Integrable Models and Applications to Delaunay, clusters. the Witten-Dijkgraaf-Verlinde Equations March 12, 2002 November 13, 2001 Charles P. Boyer, Univ. of New Mexico Decio Levi, Univ. Roma Tre Sasakian-Einstein Geometry Multiscale Reduction for Differential Difference March 19, 2002 equations and Integrability John Harnad, CRM & Concordia Univ. November 20 and 22, 2001 Matrix models, integrable systems, duality, and all Aleksander Orlov, Institute of Oceanology, that Moscow & CRM Hypergeometrical tau-functions
CRM Annual Report 2001 - 2002 41 Scientific Activities
March 26, 2002 Nicolae Vulpe, Académie des sciences de Maria Cristina Ciocci, Univ. of Gent Moldavie KAM for reversible systems Differential operators and multiplicity of singular April 2, 2002 points for polynomial differential systems Michel Racine, Univ. d’Ottawa Christiane Rousseau, UdeM & CRM Superalgèbres simples Points de selle normalisables et intégrables dans le April 4, 2002 système de Lotka-Volterra Jan Zich, Technical Univ., Prague & CRM Voronoi and Delone tiling of quasicrystals CRM Postdoctoral Fellows Seminar Org.: Pietro-Luciano Buono (CRM) April 9, 2002 G. Pogosyan, UNAM, Mexico & JINR, Dubna, January 16, 2002 Russia Marco Bertola, CRM Superintegrable potentials in N-dimensional The (Bi)-Orthogonal Polynomial Approach to Euclidean space Random (Two)-Matrix Models April 16, 2002 January 23, 2002 Marco Bertola, CRM Diego Matessi, CRM Fundamental systems of solutions for infinite Mirror Symmetry according to the SYZ-conjecture recurrence relations arising in two-matrix models; January 30, 2002 applications to the Riemann-Hilbert problem José Urquiza, CRM April 23, 2002 Contrôle d'équations des ondes Jacek Szmigielski, Univ. of Saskatchewan February 16, 2002 An Ansatz for the large n asymptotics of bi- Luciano Buono, CRM orthogonal polynomials. The genus zero case Bifurcations, G-Transversality and Stratifications April 25, 2002 February 20, 2002 Miroslav Englis, Mathematics Institute, Piergiulio Tempesta, CRM Academy of Sciences, Prague Superintegrability, Classical Lie theory and Exact A review of (Berezin and other) quantization methods Solvability in Quantum Mechanics April 30, 2002 Bertrand Eynard, Saclay (France) & CRM Statistics Seminars Discrete classical strings, Weyl functions, and Org.: Jean-François Angers (UdeM) & Roch integrable systems Roy (UdeM) May 7, 2002 July 4, 2001 T. A. Osborn, Univ. du Manitoba Guy Mélard, Univ. Libre de Bruxelles Magnetic Curvature of Quantum Phase Space Problèmes numériques relatifs aux processus VARMA May 14, 2002 Franco Magri, Univ. Milano-Bococca July 11, 2001 A geometrical characterization of separable systems Atanu Biswas, Indian Statistical Institute, according to Levi Civita: classical roots and modern Calcutta perspectives Adaptive designs for normal responses with prognostic factors Special Days in Dynamical Systems December 13, 2001 Org.: Dana Schlomiuk (UdeM & CRM) & Kilani Ghoudi, UQTR Christiane Rousseau (UdeM & CRM) Estimateurs non-paramétriques des distributions de November 29, 2001 valeurs extrêmes multivariées Dana Schlomiuk, UdeM & CRM December 21, 2001 Équations différentielles algébriques dans le plan Christian Robert, Univ. Paris Dauphine & projectif complexe CREST Estimation de mélanges de distributions!: Résultats Robert Roussarie, Univ. de Dijon récents et perspectives Intégrales abéliennes et cycles limites
42 Annual Report 2001 - 2002 CRM Scientific Activities
January 11, 2002 February 27, 2002 Jacques Carrière, Univ. of Alberta Denise A. Lievesley, Directrice de l’Institut de A Gaussian Process of yield rates calibrated with statistique, Unesco strips Le mandat et les activités de l'Institut de statistique February 6, 2002 de l'UNESCO Jean-François Angers, Univ. de Montréal March 27, 2002 Tests pour vérifier l'égalite de deux fonctions Alain Latour, UQAM February 13, 2002 Processus GARCH à valeurs entières Luc Perreault, Hydro-Québec April 3, 2002 Analyse bayésienne multisite d'une rupture dans des Alain Vandal, McGill Univ. séquences de variables aléatoires Utilisation des ondelettes pour élaborer des tests dans hydrométéorologiques les modèles autorégressifs dans les durées February 20, 2002 conditionnelles Racula Balan, Univ. de Sherbrooke April 10, 2002 Statistique bayésienne non-paramétrique dans le cas Pierre Duchene, HEC markovien Deux applications de la théorie des graphes à l'analyse de survie
CRM Annual Report 2001 - 2002 43 Scientific Activities
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, organizes survey talks by distinguished mathematicians on topics of current interest. Fall 2001 Winter 2002 Organizers: D. Schlomiuk (CRM & UdeM) & Friday December 7 T. Tokieda (UQAM & UdeM) Andrzej Zuk, The Univ. of Chicago Friday September 21 Groups with property (T) Henri Darmon, McGill Univ Friday January 25 Elliptic curves and Hilbert's twelfth problem Izabella Laba, Univ. of British Columbia Wednesday September 26 A review of some tiling problems Louis Nirenberg, Courant Institute of Math. Sciences Friday February 1 A problem on differential forms coming from economics Martin J. Gander, McGill Univ. Friday October 5 The Jungle of Domain Decomposition Methods: Schwarz, Carolyn S. Gordon, Dartmouth College Schur, Feti, Neumann-Neumann and More Can you hear the shape of a manifold Friday February 22 Friday October 12 Boris Khesin, Univ. of Toronto Andrei N. Tyurin, Steklov Institute Trinity of Euler equations on the Virasoro group Three mathematical facets of SU(2) spin networks Friday March 1 Friday October 19 Hanspeter Kfrat, Univ. Basel Paul Gauduchon, École Polytechnique (France) Separation of Orbits in Varieties Variétés kählériennes ortho-toriques Friday March 8 Friday October 26 Vladimir Popov, Steklov Institute, Moscow Chris Sogge, Johns Hopkins Univ. Modern developments in invariant theory Riemannian manifolds with maximal eigenfunction growth Friday March 15 Friday November 2 Askold Khovanskii, Univ. of Toronto David Ruelle, IHES Newton polyhedra Nonequilibrium Statistical Mechanics: Entropy Production Friday March 22 for Quantum Spin Systems Ed Spiegel, Columbia Univ. Friday November 9 (CRM-Fields Prize 2001 Continuum Equations for Rarefied Gases William T. Tutte, Univ. of Waterloo Friday April 5 Some adventures in Graph Theory Yakov Eliashberg, Stanford Univ./IAS Friday November 16 Geometry of contact domains and transformations Claude LeBrun, SUNY Stony Brook Friday April 12 Promotional Materials for Infinite-Dimensional Lie Groups Goro Shimura, Princeton Univ. Friday November 23 The arithmeticity of Euler products and Eisenstein series on Juan Maldacena, Harvard Univ. a unitary group QCD, strings and black holes Friday April 19 Friday November 30 Bernard Malgrange, Institut Joseph Fourier, Univ. de Dorian Goldfeld, Columbia Univ. Grenoble 1 Multiple Dirichlet series and moments of zeta and L- Théorie de Galois différentielle non-linéaire functions Friday April 26 Kumar Murty, Univ. de Toronto Elliptic curves and Sieve methods Friday May 2 Hassan Aref, Univ. of Illinois at Urbana-Champaign Vortex crystals
44 Annual Report 2001 - 2002 CRM Coming Activities
Theme Year 2002-2003: Math in Computer Science
Organizing Committee mathematics. More recently, a recurrent theme in many of the domains examined are David Avis (McGill), Yoshua Bengio (Montréal), probabilistic methods; these have permeated the Gilles Brassard (Montréal), Luc Devroye whole of computer science, and so particular (McGill), Pierre L’Écuyer (Montréal), Pierre emphasis will be placed on the utilisation of McKenzie (Montréal), Prakash Panangaden these techniques, both in theoretical areas and in (McGill), Bruce Reed (McGill), and Denis more applied ones such as simulation and Thérien (McGill). machine learning.
Overview Summer School on Quantum The field of computation, formally born only last Information Processing century but with roots that stretch back to July 16-20, 2002 Euclid, is now a mathematical discipline in its Org.: Gilles Brassard (Montréal) own right, with solid theoretical foundations on Classical information theory is firmly rooted in which are based its spectacular development. the classical physics of Newton and Einstein. The CRM special year in the mathematics of But the world is quantum mechanical. This has computer science proposes to explore in depth a prevented us from tapping the full potential of significant spectrum of the many sub-areas that physical reality for information processing are core foundational material for modern purposes. For instance, quantum mechanics computer science, that exhibit significant and allows for unbreakable cryptographic codes and new mathematical content, and that have indeed such a high level of parallelism in computation influenced the development of mathematics. that a classical computer the size of the universe Mathematically, the areas with the earliest would be left behind. The goal of this school is to influence on computer science were logic and make the field of quantum information discrete mathematics. Since then, the theoretical processing accessible to a general audience of foundations of computer science have mathematicians and computer scientists who blossomed, and ideas from the area (like have little or no familiarity with quantum effectiveness, complexity and tractability) have mechanics. grown to occupy an ever more important role in Invited speakers: A. Ambainis, C.H. Bennett, G. Brassard, H. Buhrman, R. Cleve, C. Crépeau, D. Gottesman, N. Gisin,
CRM Annual Report 2001 - 2002 45 Coming Activities
P. Hoyer, R. Laflamme, A. Tapp, J. Watrous. Descriptive complexity Aisenstadt Chair lecture series June 10-14, 2002 There will be three series of conferences An area that has come to the fore in recent years, associated with the Aisenstadt Chairs by Manuel descriptive complexity gives a tool that Blum (Carnegie Mellon), Laszlo Lovasz (Microsoft Research), and Endre Szemeredi (Rutgers complements more classical approaches to University). complexity theory. After a survey of the area, the workshop will concentrate on links between CONCENTRATION PERIOD I branching programs and algebraic structures. Invited speakers: D. Barrington, P. Beame, P.L. Crescenzi, R. Complexity Theory, Analysis of Gavalda, N. Immerman, K.J. Lange, P. Pudlak, A. Razborov, Algorithms M. Sachs, R. Raz, P. Schnoebelen. May-June 2002 Org.: Pierre McKenzie (Montréal), Denis Thérien (McGill) CONCENTRATION PERIOD II In May 2002, the CRM will host two of the most Quantum Foundations in the Light of important international conferences in Quantum Information October 14 to November 2, 2002 theoretical Computer Science, namely the ACM Org.: Gilles Brassard (Montréal), Christopher A. Fuchs Symposium on Theory of Computing and the (Bell Labs, Lucent Technologies) IEEE Conference on Computational Complexity. Rolf Landauer’s best-known aphorism is In addition, there will be several one-week information is physical. This workshop is centred workshops on topics that lie at the core of the on the belief that physics is informational! Our theory of computing. Each workshop will bring long-term purpose is to reformulate the together a number of leading scientists who will foundations of quantum mechanics in the light present both expository lectures and state-of-the- of quantum information theory. Rather than art research. being counterintuitive, could it be that quantum mechanics was inevitable for information to Lecture series on branching programs behave as we understand it now? For instance, May 13-17, 2002 Org.: Ingo Wegener (Dortmund) what can we derive from the fact that unconditionally secure cryptographic key ACM Symposium on Theory of Computing distribution is possible but bit commitment is (STOC) not? May 19-21, 2002 Invited speakers: M. Appleby, H. Barnum, C.H. Bennet, G. IEEE Conference on Computational Brassard, H. Briegel, J. Bub, A. Cabello, C. Caves, R. Complexity Floreanini, C. Fuchs, N. Gisin, L. Hardy, P. Hayden, F. May 21-24, 2002 Markopoulou, D. Mayers, D. Mermin, D. Poulin, R. Schack, B. Schumacher, J. Smolin, R. Spekkens, C. Timpson. Randomness in Branching program May 27-31, 2002 CONCENTRATION PERIOD III Random techniques play an important role in Combinatorics, probability and computer science, through algorithms, which algorithms give an efficient solution to problems for which May 2003 no good deterministic solution is known, or Org.: David Avis (McGill), Luc Devroye (McGill), Bruce A. Reed (Waterloo) through the probabilistic study of complexity. A week will be devoted to this theme, starting with Leave nothing to chance. This cliché embodies the links between probabilistic methods and the common belief that randomness has no place branching programs. in well-planned methodologies, every i should be dotted and every t should be crossed. In Verification and model-checking discrete mathematics, at least, nothing could be June 3-7, 2002 further from the truth. Introducing random choices into algorithms can improve their In the past ten years, theoretical work in the area performance. The application of probabilistic of verification has started to bear fruit. The tools has led to the resolution of combinatorial workshop will cover the major areas of this problems which have resisted attack for decades. development, in particular those linked to model-checking. A month-long concentration period will take place around this general theme. Lecturers at the
46 Annual Report 2001 - 2002 CRM Coming Activities school will introduce participants to a number of WORKSHOPS weapons, mostly from the probabilistic arsenal, Random Number Generation and and their applications in combinatorics and in Highly Uniform Point Sets the study of algorithms. We anticipate a June 17-28, 2002 significant amount of collaboration between Org.: Pierre L’Écuyer (Montréal) participants at the school during the month. This workshop will bring together the world There will be five-hour mini-courses given by: V. Chvatal leaders in the theoretical and practical aspects of (Rutgers), A. Frieze (Carnegie-Mellon), L. Lovasz, (Microsoft), C. McDiarmid (Oxford), M. Molloy (Toronto), J. random number generation by computer and the Pach (City College New York et Hungarian Academy of design of highly uniform point sets for quasi- Sciences), E. Szemeredi (Rutgers). Monte Carlo integration. The general theme is the development of practical random number INTERNATIONAL ANNUAL MEETINGS generation software for various classes of ACM Symposium on Theory of applications, such as simulation, statistics, Computing (STOC) numerical analysis, computer games, lotteries, May 19-21, 2002 cryptology, etc. In simulation, highly uniform (or low-discrepancy) point sets can often IEEE Conference on Computational advantageously replace the traditional random Complexity numbers. Their construction and analysis can be May 21-24, 2002 based on ideas and tools that are very similar to Org.: Pierre McKenzie (Montréal), Denis Thérien (McGill) those used for random number generators and These two conferences are part of the we want to strengthen this connection. concentration period on Complexity theory, Invited speakers: P. Boyle, G.J. Chaitin, C. Crépeau, L.Y. analysis of algorithms. Deng, M. Evans, H. Faure, M. Fushimi, J. Gentle, M. Goresky, S. Heinrich, A. Keller, A. Klapper, C. Lemieux, G. Leobacher M. Mascagni, M. Matsumoto, H. Morohoshi, S. Ninomiya, T. Mathematical Foundations of Nishimura, A.B. Owen, W. Schmid, I. Sloan, H. Programming Semantics (MFPS) Wozniakowski. March 19-22, 2003 Org.: Prakash Panangaden (McGill) Mathematical Models and Techniques Conferences and workshops in this series, held for Analysing Systems annually since 1985, aim to provide a forum for September 30 to October 4, 2002 researchers in all areas surrounding semantics to Org.: Prakash Panangaden (McGill) present their latest research results, and to The analysis of systems has both diversified and improve communication and interactions deepened tremendously in the last few years. In between mathematicians and computer scientists terms of diversification, systems of interest now who work in these areas. The areas of relevance include stochastic systems, real-time systems include category theory, domain theory, logic and hybrid systems, that is, systems where the and topology on the mathematics side, and type state space is partly discrete and partly theory, semantics, and the design and continuous. Applications include flight implementation of programming languages on management systems for aircraft, process control the computer science side. systems, telecommunication systems and battle management systems. In all of these one has to IEEE Symposium on Logic in deal with continuous time evolution and usually Computer Science (LICS) with probabilistic aspects as well. Perhaps the June 20-26, 2003 most successful mathematical technique for Org.: Amy P. Felty (Ottawa), Philip Scott (Ottawa) dealing with these problems – now almost To be held at the University of Ottawa, the IEEE twenty years old – is model checking. This is Symposium on Logic in Computer Science now being extended to probabilistic systems and (LICS) is an annual international forum on the theory has advanced to the point where tools theoretical and practical topics in computer have been designed and built. In terms of the science that relate to logic in a broad sense. The general mathematical theory co-inductive CRM will be sponsoring four satellite workshops techniques, like bisimulation, have proved their for this conference. value repeatedly. The workshop would have two main speakers, who will each give five lectures: Prof. Marta
CRM Annual Report 2001 - 2002 47 Coming Activities
Kwiatkowska, U. Birmingham, Probabilistic been implemented and reduced to each other. Model Checking, and Dr. Jan Rutten, CWI Over the last few years, similar results are now Amsterdam, Coinductive Calculus. achieved in the context of adversaries equipped Additional invited speakers: R. Alur, P. Caines, with quantum computers. This workshop will R. Jagadeesan, and D. Precup. bring together specialists of both classical and quantum cryptographic protocols who will Finite Model Theory present the state of the art in this fascinating area March 2-9, 2003 of research. Org.: Denis Thérien (McGill) Invited speakers: D. Beaver, *C. Cachin, R. Cramer, C. This workshop will focus on the expressive Crépeau, I. Damgaard, P. Dumais, D. Gottesman, J. van de power of logics and on the deep relationship Graaf, *R. Impagliazzo, J. Kilian, D. Mayers, *M. Naor, *S. Rudich, L. Salvail, A. Smith, A. Tapp, S. Wolf, M. Yung. between logic and computational complexity. *to be confirmed. The principal speaker will be Phokion Kolaitis (U.C. Santa Cruz). The workshop will be held at Recent Advances in Machine Learning the Bellairs Research Institute of McGill June 2-13, 2003 University. Org.: Yoshua Bengio (Montréal), Balázs Kégl (Montréal), Doina Precup (McGill) Semigroups and Automata Probabilities are at the core of recent advances in March 9-16, 2003 the theory and practice of machine learning Org.: Denis Thérien (McGill) algorithms. The workshop will focus on three This workshop will discuss recent developments broad areas where these advances are crucial: in the theory of automata and semigroups, in statistical learning theory, learning algorithms, particular some dealing with long-standing open and reinforcement learning. The workshop will problems such as decidability of the dot-depth therefore bring together experts from each of hierarchy and decidability of Rhodes these three important domains. Among the complexity. sub-topics that will be covered, we note: variational methods, graphical models, the curse Cryptographic Reduction of Quantum of dimensionality, empirical methods to take and Classical Protocols advantage of theories of generalization error, April 28 to May 2, 2003 and some of the applications of these new Org.: Claude Crépeau (McGill) methods. Cryptographic protocols have been studied for Invited speakers: P. Bartlett, A. Barto, P. Frasconi, G. Hinton, two decades in the classical scenario under M. Jordan, V. Koltchinskii, Y. Le Cun, M. Littman, G. Lugosi, S. Roweis, B. Scholkopf, D. Schuurmans, S. Singh, R. Sutton. various computational assumptions. Such protocols as Bit Commitment, Oblivious Transfer and Multiparty Computations have
48 Annual Report 2001 - 2002 CRM Coming Activities
Theme Year 2003-2004: Geometric and Spectral Analysis
Organizing Committee courses are listed in the detailed program given below. E. Bierstone (Toronto), W. Craig (McMaster), F. Finster (MPI), P. Gauthier (Montréal), Aisenstadt Chair Lecture Series D. Jakobson (McGill), V. Jaksic (McGill), N. Kamran (McGill), R. Melrose (MIT), There will be two chairholders for the year: P.!Sarnak (Courant) and S. T. Yau (Harvard). P. Milman (Toronto), D.H. Phong (Columbia), and J. Toth (McGill). SPECTRAL ANALYSIS Analysis has traditionally stood at the centre of Contact geometry and analysis gravity of much of the research activity in July 2003 mathematics. In particular, the fields of Org.: R. Melrose (MIT), D. Auroux (MIT & École geometric and spectral analysis have played a Polytechnique, France) fundamental role in shaping the major themes of In the vigorous development of contact current research in differential geometry and geometry, which has taken place over the past mathematical physics, and they stand indeed at ten years or so, the notion of a tight (or the core of several of the deepest and most conversely an overtwisted) contact structure has spectacular advances in these fields. There is proved to be central, with many deep and now, for example a much deeper understanding important applications to three-dimensional of the eigenvalues and eigenfunctions of topology. On the analytic side, the notion of the manifolds than there was even five years ago. quantization of a contact manifold, that is the The thematic year in geometric and spectral existence of a generalized Szegö projection, has analysis will focus on a number of themes in come to play a central role in developments which this interaction has been particularly related to the algebra of pseudodifferential fruitful. The year is organized around two operators of Heisenberg type and related interconnected themes: the first, whose different homological questions. Both endeavours are subthemes cover the whole year, is principally related to embedding, or fillability, questions centered on various questions in spectral which remain substantially open, especially in analysis; it comprises what is in essence two the three dimensional case. It is hoped that by short programs, one on contact geometry and bringing this group together they will be able to the other on analysis on singular space, and a understand these relationships and their more extended period on spectral analysis in repercussions. The format is one of informal mathematical physics and number theory. The lecture series over two weeks, on subjects such two short programs have a particularly strong as: Contact Floer homology and symplectic field emphasis on developing new connections to theory, Approximate holomorphic geometry, other areas of mathematics. The second theme Gauge theory and symplectic fillings, relates to the analysis of the Einstein equations, a Heisenberg algebras, Toeplitz quantization, and subject on which there has been spectacular Powers of circle bundles. progress in recent years. It is concentrated in the fall of 2003. Analysis and Resolution of These themes have been chosen so as to have a Singularities balance between the geometric and spectral August 2003 components of the scientific program, and also Org.: E. Bierstone (Toronto), P. Milman (Toronto), D.H. with the objective of highlighting some of the Phong (Columbia) most interesting current applications of analytic Effective methods in resolution of singularities ideas to physics. are becoming central to a modern generation of There will be a strong emphasis on training problems from analysis and geometry – for through the short courses, which will precede example, spectral theory and Hodge theorem for the proposed workshops, as well as through the algebraic varieties, stability of oscillating coordination of the graduate course offerings in integrals, existence of Kähler-Einstein metrics, analysis and geometry in the Montréal sharp forms of Moser-Trudinger inequalities. universities. In particular, a minimum of eight The diversity of the problems and their very short courses is being planned in connection different origins and aims have led to a lack of with the various workshops. Some of these short communication among researchers on these and
CRM Annual Report 2001 - 2002 49 Coming Activities related topics. This program, bringing together Sub-theme: Spectral Analysis in leading experts in resolution of singularities, Mathematical Physics and Number Theory complex differential geometry, and real analysis All year and partial differential equations, may have ground-breaking impact. Integrable and Near-Integrable Hamiltonian Partial Differential Equations Week 1. Workshop on oscillatory integrals and May 2004 critical integrability exponents Org.: W. Craig (McMaster), P. Deift (Pennsylvania), H. Topics include degeneracy of holomorphic Flaschka (Arizona), S. Kuskin (Heriot-Watt), P. Olver functions in several variables, Legendre (Minnesota), P. Winternitz (CRM). distributions and multiplier ideal sheaves. This workshop will provide a cross-section of Week 2. Short courses the most significant current activity in the field Three short courses to be accessible to graduate of Hamiltonian PDEs, including integrability, students in analysis, given by the organizers or asymptotics in the small dispersion limit, KAM other participants. theory, and Arnol'd stability. This workshop is organized in conjunction with the special year in • Effective methods in resolution of analysis at the Fields Institute. singularities – ideas involved in desingularization algorithms, concrete Spectral Theory of Schrödinger examples with a view to applications in analysis and geometry. Operators July 2004 • Stability questions in real and complex Org.: V. Jaksic (McGill), Y. Last (Hebrew) analysis; for example, stable forms of the The spectral theory of Schrödinger operators has method of stationary phase, stability of been the stage of spectacular developments over critical integrability exponents, ascending the last ten years. The emphasis has shifted to chain conditions, stability problems for the problems involving semiclassical limits and degenerate Fourier integral operators. limits of large numbers of particles (e.g., atomic • Real and complex blow up, resolution of Hamiltonians) and to the problems involving metrics, configuration spaces and Lie quasi-periodic and random structures. The goal algebras of vector fields – leading to a of the workshop is to bring together the world description of harmonic forms and L 2 leading experts, young researchers and the cohomology of various singular spaces. graduate students in this fast developing field. The state of the art research and results will be Week 3. Workshop on resolution of described in an accessible way, and the new singularities, metrics and the Laplacian directions of research will be pointed out. The Hodge theorem, describing the harmonic forms on a smooth algebraic variety and relating Dynamics in Statistical Mechanics them to its cohomology, has had wide impact on July 2004 differential and algebraic geometry, and Org.: V. Jaksic (McGill), C.-A. Pillet (Toulon) differential analysis. In the more general case of The past ten years have witnessed some major a singular projective variety, a description of the new developments in the field of non- harmonic forms remains largely open, although equilibrium statistical mechanics, owing to an there are substantial conjectures. An approach influx of fresh ideas from probability theory and through resolution of singularities depends on C*-algebras. This progress is complemented by understanding the structure of the Fubini-Study the study of concrete, physically relevant models metric lifted to a resolution. The workshop will of infinite particle systems, for which the zeroth bring together researchers in geometric, and the second law have been now rigorously algebraic and analytic areas related to these established. The goal of the workshop is to bring questions. together the world’s leading experts in the field.
Semi-Classical Theory of Eigenfunctions and Partial Differential Equations June 2004, (to be held at the Fields Institute) Org.: D. Jakobson (McGill), J. Toth (McGill) Many questions in quantum chaos are motivated by the correspondence principle in quantum
50 Annual Report 2001 - 2002 CRM Coming Activities mechanics. These include asymptotic bounds for A number of major advances have been achieved the eigenfunctions, integrated and pointwise over the past few years in the analysis of the Weyl error terms, and scarring. Another Cauchy problem in general relativity. These fundamental question concerns the local and include the proof of the non-linear stability of global statistical properties of the eigenfunctions, Minkowski space, the proof of the Riemannian their nodal sets and critical points. These Penrose conjecture and the rigorous description questions will from the main theme of the of the asymptotic behavior at infinity of the workshop. admissible Cauchy data. This workshop will bring together some of the key players who have Spectral Theory and Automorphic been involved in these developments, and will Forms provide an opportunity for exploring some of Org.: Y. Petridis (CUNY), J. Toth (McGill) the remaining open problems. Analytic questions about families of L-functions Workshop on the Interaction of Gravity include the distribution of zeros and the generalized Riemann hypothesis, value with External Fields distribution, special values as well as October 2003 Org.: F. Finster (MPI), N. Kamran (McGill) connections with arithmetical questions such as the distribution of primes, size of class groups, The interaction of gravity with external fields is analytic ranks and elliptic curves. This workshop governed by highly coupled systems of partial will bring together some of the most active differential equations on manifolds. The analysis researchers in this rich and important area of of these systems has lead to surprising results on mathematics, which lies at the boundary of the role of external fields in the dynamics of analysis and number theory. gravitational collapse and singularity formation. These results include, in the spherically ANALYSIS OF THE EINSTEIN symmetric case, the existence of stable particle- EQUATIONS like solutions of the Einstein-Yang Mills equations, and the non-existence of black hole September-October 2003 solutions when the gravitational field is coupled Workshop on the Cauchy Problem for to a Dirac spinor field. One of the objectives of the Einstein Equations the workshop will be to review these September 2003 developments, and to discuss some of the Org.: F. Finster (MPI), N. Kamran (McGill) directions for future research. Short courses: H. Friedrich (MPI), F. Finster (MPI), J. Smoller (Michigan)
CRM Annual Report 2001 - 2002 51 Coming Activities
Theme Year 2004-2005: Mathematics of Complex Multiple-Scale Systems
Organizing Committee A. Bourlioux (Montréal), M. Delfour (Montréal), Aisenstadt Chair Lecture Series Weinan E (Princeton), M. Gander (McGill), There will be two or three Aisenstadt Chair T. Hou (Caltech), A.J. Majda (Courant), holders who will talk on topics relevant to the T. Souganidis (Texas), R. Sircar (Princeton), applications covered during the year, such as the C. Schuette (Berlin), and A. Stuart (Warwick). mathematics of climate modeling, multi-scale simulations, and non-linear analysis applied to The 2004-2005 thematic year will be dedicated to various domains. the applied mathematical tools (modeling, analysis, computational) needed to study Stochastic Partial Differential Equations complex systems in various domains of science and Models of Turbulence and engineering. Complexity is used generically Fall 2004 in a broad sense to encompass a wide range of Org.!: Weinan E (Princeton) scales to be accounted for, a large number of The workshop will focus on tractable models degrees of freedom, couplings between several which share some of the features believed to mechanisms in the model, general nonlinearities, occur in 3D turbulence, typically models which and much more. The domains for applications include advection of a passive scalar, and include climate modeling, turbulence, fronts randomly driven Burgers. The workshop will propagation, molecular dynamics, materials, continue this work and explore more realistic finances, bio-mechanical systems in medicine, problems, such as 2D turbulence and wave quantum control. Despite the diversity in the turbulence with the hope of firming up the applications, some of the challenges and mathematical formulation of the problem and strategies to face them have much in common: the expected result, and identifying critical how can one include any form of knowledge obstacles where numerical computations and regarding the dynamic of the solution so as to simplified models might help. produce an useful model which captures well the global behavior of the system? One Workshops particularly promising approach is based on Representing Unresolved Degrees of stochastic models: this will be the topic for the Freedom in the Atmosphere and Ocean summer school and will also be a recurring Fall 2004 theme throughout the various workshops. Those Org.: A.J. Majda (Courant) will be an opportunity for interaction between A central problem in attempts to understand and applied mathematicians specializing in predict the evolution of atmospheric or oceanic modeling and numerical simulation and flows is how best to represent the unresolved researchers in the various fields of applications scales: this is the parameterization problem in in science and engineering. dynamic meteorology or physical oceanography or the closure problem in turbulence. The most Summer School in Stochastic Methods in pertinent areas of analysis and applied Applied Mathematics mathematics are homogenization theory, July 2004 probability and non-linear stochastic PDEs. Org.: A. Bourlioux (Montréal), E. Vanden Eijnden (Courant) Extracting Low-Dimensional Effective This two-week intensive preliminary workshop Dynamics of Biomolecules will introduce graduate students and postdocs to Fall 2004 the basic stochastic tools to be used and Org.: C. Schuette (FU Berlin), J. Maddocks (EPF Lausanne), developed in the subsequent specialized A. Stuart (Warwick) workshops. General topics are: stochastic partial Complexity in biomolecular dynamics rises from differential equations, stochastic differential fast rotating or oscillating modes super-imposed equations/stochastic processes, numerical to the slow global motion of the molecule. methods for SDE/SPDE. Simply eliminating those fast modes would lead
52 Annual Report 2001 - 2002 CRM Coming Activities to a very bad approximation on the time scale of invasive procedures in medicine and surgery interest. This workshop will discuss progress in and identifying issues, problems, trends, and analysis and algorithmic realization of different mathematical and computing challenges. stochastic approaches to this problem. It will be structured around the following themes: medical imaging processing and Front Propagation, Homogenization geometrical modeling, fluid-structure interaction Theory and Fully Nonlinear Stochastic in health problems, static/dynamical design and Partial Differential Equations control of (implantable) medical devices, finite Fall 2004 element based computer aided manufacturing. Org.: T. Souganidis (Texas) Models in phase transitions and combustion give Integrative Multiscale Modeling and rise to interfaces moving with prescribed normal Simulation in Material Science, Fluids and velocities. The theory of viscosity solutions Environmental Science provides a very good framework for the Spring 2005 rigorous analysis of such models, in particular Org.: T. Hou (Caltech) Introductory short course for the stochastic cases due to random media, Potential lecturers: R. Phillips and M. Ortiz (Caltech) turbulent advection, etc. This workshop will This concluding workshop will focus on focus on the rigorous analysis of such systems as interdisciplinary interaction with the goal to well as its applications to designing develop some new tools that combine mathematical models and numerical algorithms mathematical analysis, multiscale modeling and for problems in reaction-diffusion, turbulent computational analysis in an integrative way combustion, particle systems, phase transitions, across many scientific disciplines such as Hamiltonian dynamics, etc. biology, chemistry, environmental science, fluid dynamics, geophysics, information science, and Stochastic Modeling in Financial materials science. There have been many Mathematics exciting recent, but problem-specific and Spring 2005 fragmented, advances in multiscale analysis, Org.: R. Sircar (Princeton), J.P. Fouque (North Carolina State) modeling, and simulation. Hosting this workshop will provide a unique opportunity to The theme of this week is emerging directions in make significant advances and bridge the gap in financial mathematics, with emphasis on research, training, and knowledge transfer stochastic modeling of market uncertainties, between mathematics and the application asymptotic and numerical approximations to disciplines. pricing and stochastic control problems, and data estimation issues. The goal is to bring Quantum Control: Mathematical and together researchers in a variety of disciplines Numerical Challenges II (mathematics, engineering, operations research Summer 2004 and economics, for example) to emphasise Org.: M. Delfour (Montréal), A. Bandrauk (Sherbrooke), different techniques and approaches. C.!Le Bris (Cermics, ENPC, Paris) This workshop will build on the one-week Mini-invasive Procedures in Medicine and workshop organized in October 2002 (see below) Surgery on the same topic and expand its scope to a Spring 2005 three-week program. Org.: M. Delfour (Montréal), A. Fortin (Laval), A. Garon (École Polytechnique, Montréal), C. Peskin (Courant), A. Even though it has a somewhat distinct flavour Quarteroni (École Polytechnique, Lausanne), M. Thiriet from the ones listed above, its definite (INRIA) interdisciplinary applied nature fits very well in This extended concentration period will be the overall philosophy of the thematic year. concerned with complex medical biomechanical systems, bringing together several facets of mini-
CRM Annual Report 2001 - 2002 53 Coming Activities
Interdisciplinary and Industrial Program
Joint IMA-NCM2 Workshop on particular in transportation logistics and in Computational Methods for telecommunications planning. Large-Scale Integer Programs The theory of location is evolving, with October 14-19, 2002, Minneapolis, Minnesota questions such as competitive location or the Org.: W. Cook (Rice University), M. Gendreau (CRT, location of non-punctual or structured objects Montréal), George Nemhauser, M. W. P. Savelsbergh being studied; in routing, the advent of better (Georgia Institute of Technology) communication devices and increased In the past decade there have been significant computational power make real-time dynamic theoretical and computational advances in the routing a possibility. These changes imply that field of integer programming. As a result there new problems with different mathematical has been a greatly increased use of integer properties must be tackled and new algorithmic programming software in industry. However, strategies devised. the need to solve even larger and more complex This workshop will include a series of ten problems continues to grow. In this workshop, surveys, covering both the more traditional and we will bring together experts in various areas of the newer subject areas, with additional integer programming and its applications. contributions by conference participants. Areas Theoretical and methodological topics included covered include routing; location; economic aspects, pricing, e-commerce; fleet management; in the workshop are approximation algorithms telecommunications; network design. for large-scale linear programs, stochastic integer Invited speakers: G. Laporte, A. Corberan, J.J. Salazar, D. programming, branch-and-cut and branch-and- Vigo, M. Salomon, S. Nickel, T. Lowe, P. Hansen, O. Berman, price, algebraic and combinatorial methods, G. Wesolowsky, J. Thisse, P. Marcotte, B. Gavish, M. decomposition, constraint programming and Gendreau, M. Savelsbergh, J.Y. Potvin, A. Balakrishnan, M. O. Ball, B. Jaumard, M. Labbé, C. Colbourn, T. Crainic, T. parallel implementation. Application areas Magnanti 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 and operations researchers working in discrete Org.: A. Bandrauk (Sherbrooke), M. Delfour (Montréal), C.!Le Bris (ENPC, Paris) and combinatorial optimization, computational Sponsors: NSERC, CRM, Ministère de la recherche, France scientists working in parallel computing, search, 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-NCM 2 Workshop on Coherent Control of Molecular Processes following Distribution Systems: Location and the pioneering work of theoretical chemists such Vehicle Routing as Paul Brumer (Toronto), Moshe Shapiro December 2-6, 2002, Montréal (Weizmann Institute), Stuart A. Rice (Chicago), Org.: Michel Gendreau (CRT, Montréal) & Gilbert Laporte and other international and Canadian (CRT, HEC) distinguished scientists is steadily making an The questions surrounding distribution systems impact on the experimental and technological are of prime economic importance. The scale of world. these systems is increasing at a fast rate because of the growth of international commerce and This new field of research is dedicated to “using travel. The advent of e-commerce will only current state of the art laser technology to increase their scale, as well as change their control and manipulate the quantum behaviour nature; goods purchased over the Internet must and motion of matter at the molecular level”. be delivered; also, they often get returned. The basis of this new science is the encoding and Related to these questions is the rich field of control of quantum information at the molecular network design problems, which arise in level in order to control the time evolution of
54 Annual Report 2001 - 2002 CRM Coming Activities molecular processes, such as guiding the final Quantum Computing output of a reaction to a desired target. Most of Invited speakers: M.Y. Ivanov (NRC-Ottawa), S. Lacelle the research in this area has been numerical and (Sherbrooke), R. Laflamme (Waterloo), D. Lidar (Toronto). theoretical, involving multidimensional time- dependent Schrödinger equations, TDSEs. Numerical Methods Coupling these molecular processes to the laser Invited speakers: T. Carrington (Montréal), M. Fortin (Laval), W. Hager (Gainesville), C. Le Bris (CERMICS, ENPC, Paris), field equations, Maxwell’s equations, results in Y. Maday (UPMC, Paris), A. Peirce (UBC), M. Schoenauer coupled parabolic (TDESs) and hyperbolic (INRIA, France), G. Turinici (INRIA-Rocquencourt), R. Wyatt (Maxwell) partial differential equations. There (Texas). are outstanding problems, both numerical and mathematical, which this workshop will address Summer School in Computational by bringing together mathematicians, theoretical Biology July 2003 chemists and physicists working in the area of Org: N. El-Mabrouk (Montréal) and D. Sankoff (Ottawa) control and optimization of systems subject to quantum laws. The school will deal with recent progress in computational biology: cellular networks, The workshop will involve 20-30 international structural molecular biology, and comparative experts in laser molecule interactions, genomics. optimization, theory and control of molecular dynamics. It will emphasize participation of Stochastic Networks graduate students in applied mathematics, Summer 2004 theoretical chemistry and physics. Org.: D. Dawson (Carleton), P. Glynn (Stanford), D. Macdonald (Carleton) Molecular and Electron Control Stochastic modelling of communications and Invited speakers: O. Atabek (Orsay), A. D. Bandrauk processing networks is playing a significant role (Sherbrooke), T. Brabec (Ottawa), P. Brumer (Toronto), R. de in enhancing our understanding of now to Vivie-Riedle (MPI, Garching, Germany), R. Kosloff (Hebrew University), R. Kosut (Sc Solutions Inc.), H. Lefebvre-Brion engineer and manage complex systems ranging (Paris-Sud), Y. Ohtsuki (Tohoku, Japan), H. Rabitz from the Internet to high volume wafer (Princeton). fabrication facilities. These new technologies are leading to an array of new mathematical Quantum Control: Mathematical problems and model formulations that have Problems & Theory brought new intellectual stimulation to the area, Invited speakers: G. Chen (Texas A&M), M. Delfour (Montréal), S. K. Mitter (MIT), V. Ramakrishna (Texas, and have created new opportunities for Dallas), J.-P. Zolésio (École des Mines), E. Zuazua applications impact. (Complutense, Madrid).
CRM Annual Report 2001 - 2002 55 Coming Activities
General Program
Topology of Moduli Spaces need in order to tackle some of the mainstream July 2003 problems in the area. Topics to be covered Org.: E. Markman (U. Mass.) & H. Nakajima (Kyoto) include special holonomy, homogeneous and There have been many deep results in recent cohomogenity one methods, comparison years concerning the topology of moduli space, techniques. whether of curves, vector bundles, instantons or Hilbert schemes. One recurrent theme has been Week 3: Curvature and topology. The the discovery of deep algebraic structures which relationship between positive or negative aspects govern the topology: an early prototype is the of curvature and the global structure of operad structure developed for loop spaces and manifolds is a well-established one, and interacts applied with success to moduli problems. A with the special properties of metrics (e.g., in the particular emphasis will be put on the Einstein case, the boundedness of the Ricci exploration of these underlying structures. Many curvature from below). deep links have been discovered, and they have attracted much interest. Short Program on Integrable Systems Summer 2005 Group Theory and Numerical Analysis Org.: J. Harnad (Concordia), A. Its (IUPUI), P. van Moerbeke (Louvain), C. Tracy (UC Davis) May 2003 Org.: P. Winternitz (Montréal), D. Levi (Rome), A. Iserles The topic of integrable systems has many (Cambridge), R. Quispel (La Trobe) ramifications throughout geometry, Topics to be covered include Lie group methods mathematical physics, dynamical systems and in numerics, symmetries of numerical nonlinear PDE. This program will survey some differential equations (discretization preserving of the most important recent developments in symmetries), symmetries of discrete systems, three related sub-areas: 1. the geometry of symbolic algebra calculations, discrete integrable systems, 2. isomonodromic differential forms, the Hopf algebra structure, deformations, 3. random matrices and related infinite-dimensional algebras of vector fields and problems. These subjects have seen some of the groups of integrators, dynamical systems. most interesting developments in recent years, with ties to theoretical physics (duality in string Short Program on Riemannian theory), number theory, geometry (for example, Geometry in mirror symmetry), as well as Lie theory. The Summer 2004 organizing committee consists of international Org: V. Apostolov (UQAM), A. Dancer (Oxford), N. Hitchin leaders in the area. (Oxford), M. Wang (McMaster) Each week there will be a series of lectures of an Metrics whose curvature satisfies constraints, as expository nature given in the mornings, and well as the relations between curvature and seminar type talks in the afternoons. topology have been of interest ever since the beginning of differential geometry. More Week 1: The geometry of integrable systems. recently, such metrics have come to the fore in Topics covered include isospectral flows, loop physical problems related to string theory. algebras, moduli spaces, Hitchin systems, classical and quantum R matrices, Darboux- Week 1: Special metrics. The workshop will Bäcklund transformations, separation of focus on three types: 1. Einstein metrics. Studied variables, applications of integrable systems to since the 1920s in the context of relativity; a gravitation, conformal theory, Yang-Mills, recent source of interest has been the concept of Seiberg-Witten theory, hydrodynamic equations, holography in physics. 2. Self-dual geometry. Frobenius manifolds. Due to the applicability of holomorphic methods, an important source of examples. Week 2: Isomonodromic deformations and 3. Special holonomy. Not only the Calabi-Yau applications. Topics covered include the inverse metrics, but also the G2 and Spin(7) examples are monodromy method, Riemann-Hilbert problem, of physical interest. nonlinear WKB approximation, asymptotics of solutions, Hamiltonian structure, duality, Week 2: Short courses. The aim is to present Painlevé transcendents, Garnier systems, material, which graduates students, and others Schlesinger transformations, birational
56 Annual Report 2001 - 2002 CRM Coming Activities transformations, relations to root lattices, there are intimate links between descent algebras reductions to linear systems, classical solutions. and non-commutative symmetric functions, as Week 3: Random matrices and related problems. defined by Gelfand, Lascoux, et al., with bases Topics covered include the spectral theory of naturally indexed by compositions. Problems random matrices, relations to orthogonal under study include the explicit computation of polynomials, asymptotics, scaling limits, bases in these algebras underlying the Fredholm determinants, Riemann-Hilbert corresponding combinatorial structures. methods, Toeplitz determinants, Hankel determinants, random sequences and growth Week 1: Short courses. The aim is to present rates, number-theoretic correlates. basic notions in a format accessible to graduate students. Subjects for lectures include: descent Short Program on Non-commutative algebras, quasi-symmetric functions, non- Combinatorics commutative symmetric functions, and quasi- Summer 2005 determinants. Org.: F. Bergeron (UQAM), N. Bergeron (York), and C. Reutenauer (UQAM) Weeks 2 and 3: Workshop. There is to be an The understanding of certain non-commutative extended two-week workshop, with plenty of structures in algebra is intimately linked to opportunity for interaction. Part of the program certain combinatorial problems. For example, the will include survey lectures on subjects actually characters of finite Coxeter groups and Iwahori- or potentially related to the topic of the Hecke algebras tie in to Young tableaux, workshop, such as hyperplane arrangements or partitions and compositions. In a parallel vein, non-commutative geometry.
CRM Annual Report 2001 - 2002 57 CRM Collaborative Network
Within its general mandate of promoting Commitee, 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 John B. A NATIONAL INSTITUTE Friedlander of University of Toronto. The The CRM is strongly committed to its national administrative responsibility in this matter mission. The CRM takes measures to ensure that alternates each year between the CRM and the the largest possible number of scientists across FI. Scientific collaboration continues between the Canada benefits from its activities and become FI and the CRM, with a close coordination of the involved in their planning. For instance, it activities for the theme year 2003–2004 in appoints to its Advisory Committee eminent analysis and partial differential equations. One Canadian scientists from various parts of the major common initiative this year was the set-up country; it is present at all important forums of a sound financial basis for the Atlantic where the future directions of the Canadian Association for Mathematical mathematical sciences are discussed; it urges its Sciences/Association des chercheurs en sciences organizers to make efforts to ensure the mathématiques de l’Atlantique (AARMS/ participation of the Canadian specialists in their ACSMA). activities; it organizes and supports scientific events across the country; it collaborates with CANADIAN ASSOCIATIONS AND Canadian institutes, societies and associations. A PROFESSIONAL SOCIETIES specific budget is set aside each year for the The CRM maintains close ties with the different participation of Canadian graduate students in professional societies in the mathematical its programs. The CRM is the only national sciences: CMS, CAIMS, SSC, and CAP. The institute that operates in the two official president of the CMS is an ex-officio member of languages of Canada and it is highly visible on the CRM advisory committee, and together with the international scene. In keeping with its the other institutes, the CRM organizes special national role, it coordinates its activities with the sessions at CMS meetings. The SSC meetings have been funded through the national program; Fields Institute, PIMS, the Canadian as well, the CRM gives out a prize each year Mathematical Society (CMS), the Canadian jointly with the SSC; similarly, together with Applied and Industrial Mathematics Society CAP, it awards a prize each year in (CAIMS), the Statistical Society of Canada (SSC), mathematical and theoretical physics. There is a the Canadian Association of Physicists (CAP), section on this year’s prize-winners elsewhere in and other societies as well as with other this report. institutes abroad. INTERNATIONAL COLLABORATION THE FIELDS INSTITUTE (FI) AND THE The CRM has exchange protocols with Osaka PACIFIC INSTITUTE FOR THE University, with Seoul's Asia-Pacific Center for MATHEMATICAL SCIENCES (PIMS) Theoretical Physics, with the Institute of Since the early 1990’s two other research Mathematical Sciences at Nankai University, institutes have joined the CRM on the Canadian with the Czech Technical University of Prague scene: Toronto’s Fields Institute (FI), and the and the University of Rome. Pacific Institute for Mathematical Sciences In its publications, the CRM is continuing its (PIMS). As well as coordinating their scientific partnership with the American Mathematical activities, the three institutes have worked Society, in particular with its two series of joint closely on a variety of initiatives, the most publications, the CRM Monograph Series and important of which has been the Mathematics of the CRM Proceedings and Lecture Notes. It also Information Technology and Complex Systems, has two series with Springer-Verlag, in statistics of which more is described elsewhere in this and in mathematical physics. It has publications report. exchange agreements with Fields Institute, There are several other initiatives worthy of PIMS, MSRI (Mathematical Sciences Research Institute), the Institute for Mathematics and its mention. One of these is the National Program
58 Annual Report 2001 - 2002 CRM CRM Collaborative Network
Applications, École Normale Supérieure Montréal area. This network has just been (France), and the Isaac Newton Institute. formalized with the recent constitution of the “Regroupement Neuro-imagerie Québec” (RNQ) OUR ACADEMIC PARTNERS under the umbrella of the Institut Universitaire All this activity rests on a solid base of de Gériatrie in Montréal. RNQ, with its 70 cooperation with universities in the region, in researchers, has just been awarded a very large particular the Montréal universities, and most grant ($11M) towards the purchase of equipment particularly the Université de Montréal, whose in neuro-imaging. One of the strongest alliances support for the CRM has been indefatigable. The of CRM within that network is its association Université de Montréal releases each year five of with the INSERM laboratory for brain-imaging its faculty members to work at the CRM, and the support of these faculty members is an essential at Jussieu, France (director: Habib Benali). asset for the CRM’s scientific activities. There is in addition a regular program of teaching release INSTITUT DES SCIENCES with the other Montréal universities, bringing MATHÉMATIQUES the equivalent of another two positions to the One important vehicle for collaboration with the CRM each year. On an ad-hoc basis linked to the Québec universities is the Institut des sciences theme program, the CRM has also been mathématiques. This institute, which arranging release of research personnel from encompasses most of Québec’s universities, is nearby universities such as Laval, Sherbrooke, principally concerned with coordinating Queen’s and Ottawa; some of these graduate training. The links with research are arrangements are being put on a more obvious, and indeed, the CRM and the ISM have permanent footing. The partnerships of the CRM a long-standing partnership, in particular in with the other research institutes in the Montréal offering postdoctoral fellowships, in organizing area have been very profitable. More will be said the CRM-ISM colloquium, and in organizing about these in the next section. special courses for the CRM’s thematic programs. NEURO-IMAGING INITIATIVE IN QUÉBEC In recent years, CRM’s PhysNum laboratory has developed a strong collaborative network with various partners in neuro-imaging in the
CRM Annual Report 2001 - 2002 59 AARMS/ACSMA
One of the great success stories this year was the AARMS is already organizing a variety of constitution of a sound financial basis of a activities, partially funded through the National regional association for mathematical research, Program Committee of the institutes. Here are the Atlantic Association for Research in some recent activities: Mathematics/Association des chercheurs en • International Workshop on Groups, Rings, Lie sciences mathématiques de l'Atlantique. and Hopf Algebras (Memorial, May 28 to June Founded in 1995, AARMS brings together 1, 2001). university researchers from the Atlantic region. • International Workshop on Dynamical Systems This community, after several years of struggle, and Their Application to Biology (Cape Breton, is experiencing a rebirth with twenty new August 2-6, 2001). researchers hired in the past two years. • Workshop on Modelling and Scientific During a visit past June, the three Canadian Computation (University of New Brunswick, mathematics institutes’ directors, along with September 28-30, 2001). AARMS director, Professor Hermann Brunner, • APICS Meeting 2001 (St. Francis Xavier met with the top administrators of the three University, September 19-21, 2001). most important Atlantic universities: Memorial, Dalhousie, and the University of New This year’s scientific program was also funded Brunswick. A formula for co-sponsorship was by NPC and included a summer school on set-up with each of the six partners contributing algebra, fractal geometry, graph theory and 30K$ to AARMS activities. The MITACS differential equations, that took place July 22 to network has also offered to the Atlantic August 6, 2002, as well as two workshops: community important financial resources for • Combinatorial Methods in Polynomial Identity industrial mathematical research. This new Theory (Memorial, August 2002). version of AARMS will be run by a board of • 31st Annual Canadian Operator Theory and directors and an advisory committee with the Operator Algebras Conference (University of participation of the three Canadian institutes New Brunswick, May 20-24, 2003). and of the Atlantic mathematical community.
60 Annual Report 2001 - 2002 CRM Industrial Collaborations
The main vehicles for the CRM’s efforts in this • Integration of real-time weather data and area are the research networks to which it Geographic Information System (GIS) for use in belongs. There are two of these, one the Network transportation. for Computing and Mathematical Modelling Charles Lin, CERCA (ncm2), involving eight research centres in the • Modélisation et test d’Ipv6 Montréal area in a multidisciplinary consortium, Rachida Dssouli, CRM and MITACS, a national network focussing on • The Real Options Approach to Risk Management the mathematics of information technology and Pierre Lasserre and Andrey Pavlov, complex systems. CIRANO NETWORK FOR COMPUTING AND • Ingénierie des réseaux de distribution MATHEMATICAL MODELLING (NCM2) multifournisseur The CRM serves as the organizational centre for André Langevin and Diane Riopel, GERAD the Network for Computing and Mathematical • Planification et confection d’horaires en milieu
Modelling, ncm2 (in French: Réseau de calcul et hospitalier de modélisation mathématique, rcm2), a Brigitte Jaumard, CRT collaboration which allows the network to • Gestion des risques financiers: critères respond to the needs of industry in a large prudentiels, décentralisation et contrôle de number of fields related to a common area of performance computing and mathematical modelling, mostly René Garcia, CIRANO around five major themes: (1) risk management, • Localisation des sources d’activité en magnéto- (2) information processing, imaging and parallel encéphalographie par maximum d’entropie en computing, (3) transport and moyenne et modèles graphiques hiérarchiques telecommunications, (4) health and (5) electronic Bernard Goulard, CRM commerce. Overall, the projects have involved the The five centres that established the network participation of 70 researchers in the network were the CRM, the Centre de recherche en calcul centres, and 63 postdoctoral fellows and appliqué (CERCA), the Centre interuniversitaire graduate students. The total value of the de recherche en analyse des organisations contributions of our partners in 2001-2002 was (CIRANO), the Centre de recherche sur les $602,000 in cash and $500,000 in kind. The transports (CRT), and the Groupe d’études et de industrial partners involved at some point with recherche en analyse des décisions (GERAD). ncm ’s research projects are: ADOPT Since then, three new members joined the 2 Technologies Inc., Air Canada, ANIQ R&D Inc., network: the Cooperative Centre for Research in AstraZeneca Banque nationale du Canada, Bell Mesometeorology (CCRM), the Centre de Mobilité, Biochem-Pharma, Boehringer- Recherche Informatique de Montréal (CRIM) Ingelheim, CardiaNove, Centre universitaire de and the Institut National de la Recherche santé McGill (MUHC), CHUM Informatique Scientifique – Télécommunications. (Centre hospitalier de l’Université de Montréal), NSERC funding for ncm2 with a yearly grant of CLSC Côte-des-Neiges, Royal Victoria Hospital, about $650,000 came to an end this year. The Santa Cabrini Hospital, Hôpital Sainte-Justine, new projects funded in the last phase of the Hydro-Québec, IFM2, Merck Frosst, Société de NSERC grant included: l’assurance automobile du Québec, Société • Analyse des écarts de rendements à échéance canadienne des postes. entre les obligations corporatives et In December 2001, ncm 2 was the host of Joe gouvernementales Keller (Stanford) as part of the lecture series G. Gauthier, GERAD Grandes Conférences. He gave a talk on the • Receptor-ligand molecular associations Mathematics of Visual Perception: Color vision. François Major, CERCA and Yoshua As part of a series of breakfast meetings, the Bengio, CRM directors of the network were able to meet Pavel Hamet (research director for the “Centre de Recherche du Centre hospitalier de l’Université
CRM Annual Report 2001 - 2002 61 Industrial Collaborations de Montréal”), Réal Decoste (director of electronic commerce and experimental Ouranos), and Marc Garneau (president of the economics. The other component is located at Canadian Space Agency). the Université de Montréal, and is devoted to A special day on health care issues titled multimedia research. Comment les techniques d'optimisation peuvent ameliorer la gestion dans le domaine de la santé was LABORATOIRE UNIVERSITAIRE SUR organized by Brigitte Jaumard (GERAD) and LE TEMPS EXTRÊME (LUTE)
Bernard Gendron (CRT), with about forty The summer of 2001 saw the birth of a new ncm2 participants. laboratory, the Laboratoire Universitaire sur le Bernard Larrouturou, president-director of Temps Extrême (LUTE). The laboratory involves INRIA (France), visited Montréal in January. His a contribution of $300,000 per year from talk focussed on INRIA’s research program in Environment Canada, a significant contribution computer science and applied mathematics, with ($1M) in computer time, as well as the presence a particular emphasis on life sciences. in the university environment of a good number of Environment Canada’s researchers. The Two special days were organized in April by laboratory will involve not only meteorological Fahima Nekka and Jean-Marc Lina from CRM research but also an extensive study into impacts on the topic of Fractals, wavelets and medical as well as mitigating measures. LUTE’s official imaging with Jacques Lévy-Vehel (INRIA) as a launch took place on December 6, 2001, with keynote speaker for a workshop on Multifractal above 130 participants in attendance at McGill analysis of signals and images, followed by a University. Four speakers presented talks on conference on Multifractal image denoising. extreme weather and its impact on society: There was also a workshop-conference Isztar Zawadzki, Director, Marshall Radar organized in May by Pierre Lasserre and Audrey Observatory, McGill University and Lead Pavlov (CIRANO, IFM2) on real options. Scientist Canadian Weather Research Program Nowcasting and Climatology of Extreme Weather. LABORATOIRES UNIVERSITAIRES BELL Gordon McBean, Chair, Policy, Institute for Catastrophic Loss Reduction Chair, Canadian The CRM is an active participant in the ncm ’s 2 Foundation for Climate and Atmospheric Laboratoires universitaires Bell, part of a joint Sciences (CFCAS) project between the ncm and Bell. The 2 Dangerous Weather – What Canadians Need to laboratories aim at creating innovations in the Know. field of multimedia research and applications (mainly interactive applications aimed at the Georges Beauchemin, Ministère de la Sécurité general public, electronic commerce applications Publique, Gouvernement du Québec, Président and new generations of evolved networks) as du conseil, Projet OURANOS well as at promoting the training of a highly Affronter le temps extrême: faits saillants de la qualified, international calibre workforce in nouvelle loi sur la sécurité civile et ses défis. these areas. Richard Anthes, President, University The guiding principles of the Bell University Corporation for Atmospheric Research (UCAR), Laboratories are: a deep integration with the Colorado university environment; a balance between Global Weather Services in 2025: An Update. exploratory research, applied research and applications development; a multidisciplinary INSTITUTE FOR MATHEMATICS AND approach. ITS APPLICATIONS These objectives and guiding principles are The ncm2 has arranged for an exchange program made possible thanks to a $12M investment with the Institute for Mathematics and its which is used to finance research projects, to Applications in Minnesota. This institute is the endow chairs and to finance a research US’s major research institute in Applied infrastructure. The laboratory has two locations, Mathematics. As part of the IMA’s 2002 the main one being in downtown Montréal, next program, the ncm2 will be hosting a workshop to CIRANO. As well as offices, it contains a on distribution networks in the fall of 2002. As state-of-the-art simulation laboratory for
62 Annual Report 2001 - 2002 CRM Industrial Collaborations
well, the IMA will host a certain number of ncm2 the second prize winners, were C. Voisin, from postdoctoral fellows during the year. École Polytechnique de Montréal, supervised by MITACS B.!Jaumard from Université de Montréal, and This network of centres of excellence on A.!Boukhtouta, supervised by B.!Lamond, from Mathematics of Information Technology And Université Laval. Complex Systems (MITACS) is one of 22 such Several important administrative changes took networks set up by the federal government. place this past year. Since March 2002, MITACS MITACS was put together by the three Canadian is a non-profit corporation. Also, on September mathematical institutes (CRM, Fields, PIMS) in 1, 2002, John Schwenk was appointed as Chief 1998, and research began in the spring of 1999. Operating Officer and Network Business The MITACS network covers the whole country, Manager. A position for an associate scientific with the participation of 300 researchers, 400 director was also created. students and postdoctoral fellows, and more than 75 companies. MITACS Activity at CRM: The 31 research projects are spread among Spring School on Optimization. universities across Canada. Following the review May 14 – 18, 2001 of the report presented by MITACS to the NCE This joint CRM-CRT-MITACS activity was in March 2001, a new grant of $10.8M was started in 2001 by Pierre Hansen of the École des announced by Brian Tobin, who was then the Hautes Études Commerciales and Patrice minister for industry, for each of the year Marcotte from the Université de Montréal. A 2003-2004 and 2004-2005. second edition took place in 2002 with a spring The third annual meeting took place at the school on logistic and distributic, which took University of British Columbia in Vancouver, in place May 8-10 at HEC, with Gilbert Laporte as May 2002. This was a large-scale event, with its director. The school was an opportunity for over 350 participants from Canada and the US, students to enlarge their horizons in the area of including many of the network’s researchers, a deterministic optimization and mathematical large number of students (whose travel expenses programming, with an emphasis on industrial were partly covered by MITACS) and numerous applications. industrial partners. Other MITACS activities involving the CRM These meetings play a key role to establish new included: collaborations and to maintain a strong cohesion Séminaires CRM-MITACS sur l’apprentissage between the researchers working on different statistique sub-domains in applied mathematics: bio- September 2001 - February 2002, CRM medical research, industrial and business 4eInternational Conference on Information applications, information technology, Fusion manufacturing, and financial mathematics. Each August 7-10, 2001, Montréal MITACS project belongs to one of those themes; Theme Meeting of Information Technology in addition to the general annual meeting, each November 10-12, 2001, CRM theme leader organizes specialized annual Colloque CRDE-MITACS sur les Méthodes de meetings where technical details can be rééchantillonnage en économétrie October 13-14, 2001, Université de Montréal discussed in more details. Journée Finance CIRANO-MITACS!: New During the annual meeting, each research group Statistical Methods for Old Financial Problems reported on their progress. There were also October 19, 2001, CIRANO many interesting presentations by industry Emerging Market Risk Management researchers describing their more pressing November 9, 2001, CIRANO mathematical needs and describing the links that Financial Derivatives have already been established between MITACS December 7, 2001 researchers and industrial partners. Conférence CIRANO-MITACS sur les The poster session was the opportunity for the Méthodes de Monte Carlo et numériques en students affiliated with MITACS to present their finance work relevant to MITACS themes. Awards were March 15, 2002, CIRANO given to the best among the 70 posters, including three first prizes and five second prizes. Among
CRM Annual Report 2001 - 2002 63 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.
Francis Clarke was elected senior member of Alexei Miasnikov from McGill University was the Institut Universitaire de France (September awarded the Canada Research Chair in 2001). combinatorial algebra.
Henri Darmon of McGill University received Christophe Reutenauer from UQAM has been the prestigious Steacie Memorial fellowship appointed as the Canada Research Chair in from NSERC. combinatorial algebra and mathematical computing. Andrew J. Granville was awarded the Canada Research Chair in number theory. Christiane Rousseau from the Université de Montréal started her mandate as president of the Michel Grundland of the Université du Québec Canadian Mathematical Society in June 2002, for à Trois-Rivières was awarded the Alan Richards a term of two years. Fellowship from Durham University. David Sankoff from the University of Ottawa Dmitry Jakobson from McGill University has been named the Canada Research Chair in received a Sloan Fellowship (May 2001). Mathematical Genomics.
Niky Kamran was elected member of the Royal John Toth has been appointed as a Dawson Society of Canada. scholar at McGill (May 2001).
François Lalonde of Université de Montréal, Pavel Winternitz from the Université de was awarded the Canada Research Chair in Montréal received the 2002 ACP-CRM prize in differential geometry and topology. mathematical physics. The Czech newspaper Lidove Noviny also named him as one of the ten John McKay from Concordia University was most cited Czech scientists since 1980 elected member of the Royal Society of Canada (September 21, 2002). in 2000. He also received the faculty excellence award in 2001.
64 Annual Report 2001 - 2002 CRM Research Laboratories
The CRM now covers several research laboratories at the heart of the Québec mathematical community. These research centers act as focal points for local scientific activity and participate actively in the scientific direction of the CRM.
CICMA
This centre comprises researchers working in Iovita, Kisilevsky and Ramakrishna. On the number theory, group theory and algebraic group theory side, Kharlampovich and geometry. Contemporary number theory follows Miasnikov are world-renowned specialists on two major courses. On the one hand, there is the group varieties and McKay is one of the theory of special values of L-functions attached originators of the moonshine program. to arithmetic objects, originating in the work of Gauss and Dirichlet and leading to the modern Among the problems to be studied by the group conjectures of Deligne, Beilinson and Bloch-Kato. in the coming years include the construction of On the other hand, the Langlands program rational points on elliptic curves both from postulates a close link between arithmetic L- algorithmic and theoretical viewpoints; Zeta functions and automorphic representations. An functions of varieties over finite fields on the area where these two currents intersect is the algorithmic approach; canonical lifting of elliptic study of elliptic curves. The center is particularly curves and Abelian varieties; cryptography and well represented in this regard with Darmon, Abelian varieties.
Members of the Laboratory
Director: A. Granville (UdeM) J. McKay (Concordia) H. Darmon (McGill) Algebraic number theory, Computational group theory, Algebraic number theory, arithmetic geometry, sporadic groups, computation geometry, arithmetic, L- combinatorics. of Galois groups. functions, diophantine equations, elliptic curves. A. Iovita (Concordia) A. Miasnikov (McGill) Number theory. Group theory. Director: H. Kisilevsky (Concordia) O. Kharlampovich (McGill) R. Ramakrishna (McGill) L-functions, Iwasawa theory, Combinatorial theory of Galois representations, elliptic curves, class field groups and Lie algebras. modular forms, elliptic theory. curves. C. Lévesque (Laval) C. David (Concordia) Algebraic number theory, P. Russell (McGill) Elliptic curves, Drinfeld units, class number, Algebraic geometry. modules. cyclotomic fields. F. Thaine (Concordia) E. Goren (McGill) M. Makkai (McGill) Cyclotomic fields, cyclotomy, Arithmetic geometry, moduli Mathematical logic. rational points, rational spaces of Abelian varieties, points on curves. Hilbert modular forms, p- adic modular forms.
CRM Annual Report 2000 - 2001 65 Research Laboratories
Highlights of the activities of the Laboratory and of its members in 2001-2002. Among the numerous activities in which members of the centre were involved, either as participants or as organizers, is the concentration period on the Langlands program on function fields, organized by H. Darmon and J. Hurtubise in April-May 2002. As part of the program, there were a graduate course, a three-week workshop including a series of lectures by R. Langlands himself and a special day in his honour.
This period was immediately followed by the 2002 Conference of the Canadian Number Theory Association. E. Goren was one of the organizers.
Several ISM lectures were offered to Montréal graduate students in the context of this thematic year, as for example, an introduction to automorphic forms (H. Darmon) and an introduction to algebraic geometry (E. Goren).
In the course of the year, the Québec-Vermont Number Theory Seminar (http://www.crm.umontreal.ca/fr/niveau2/index_gro.html) took place alternately in Montréal and Burlington, totalling about forty talks.
66 Annual Report 2000 - 2001 CRM Research Laboratories
CIRGET (Le Centre inter-universitaire de géométrie différentielle et de topologie)
Geometry and topology in point are mathematical physics and number are fundamental theory. During the last fifteen years, a group of disciplines of researchers of international calibre in geometry mathematics. Their and number theory has been hired by Québec richness and vitality universities. The research centre based at UQAM throughout human now comprises fourteen professors-researchers history is reflected by and one research associate. their deep link to our experience of the The main themes to be pursued in the coming universe. They are at a years include Dehn surgery and geometrization crucial crossing point of à la Thurston; quantization of Hitchin systems modern mathematics and geometric Langlands program; classification and in effect several domains of mathematics of special Kähler metrics; the study of symplectic have recently shown a strong trend towards a invariants, especially in dimension 4; geometrization of ideas and methods: two cases Hamiltonian dynamical systems.
Members of the Laboratory Director!: O. Collin (UQAM) F. Lalonde (UdeM) S. Boyer (UQAM) Gauge theory and topology of Symplectic geometry and Knot theory, geometry of 3- 3-dimensional manifolds. topology, Hamiltonian dimensional manifolds, Dehn mechanics surgery, character manifolds. J. Harnad (Concordia) Integrable systems, I. Polterovich (UdeM) S. T. Ali (Concordia) symplectic geometry, random Heat equation, Riemannian Mathematical physics, matrices. manifolds, asymptotic quantization, coherent states. developments, combinatorial J. Hurtubise (McGill) identities. V. Apostolov (UQAM) Integrable systems, gauge Riemannian geometry, theory, moduli spaces. K. P. Russell (McGill) general relativity, complex Affine algebraic geometry, and symplectic 4-dimensional A. Joyal (UQAM) group actions. manifolds, (almost) Homotopy, categories, Hermitian, Kähler and algebraic topology. J. Toth (McGill) Einstein metrics. Spectral theory, semi-classical N. Kamran, (McGill) analysis, micro-local analysis, A. Broer (UdeM) Differential geometry, Hamiltonian mechanics. Algebraic transformation differential systems, groups and invariant theory. geometric integrability, D. Wise (McGill) conservation laws, spectra of Residually finite groups, low operators, Lie algebras. dimensional topology, 3- dimensional manifolds.
CRM Annual Report 2000 - 2001 67 Research Laboratories
Highlights of the activities of the laboratory and of its members in 2001-2002. The CRM just ended a thematic year in Groups and Geometry, which considerably pushed forward the CIRGET in several important domains: during the 2001 summer, a concentration period on 3- dimensional manifolds and geometric group theory attracted more than a hundred participants during three weeks, of whom one half were graduate students, to the most important conference in the subject in several years. During the fall, a conference on infinite dimensional Lie groups shed some light on a difficult and diverse subject. The second semester was devoted to the study of the links between group theory and algebraic geometry, with an extended period on Langlands theory for function fields, which focussed attention on a leading subject to which access is quite difficult.
Aside from these events, thirty talks (twenty of which by speakers from outside Montréal) were given in the context of the weekly CIRGET seminar (http://www.math.uqam.ca/cirget/seminar01-02.html) organized by Olivier Collin. Also, two CIRGET workshops took place at UQAM in April 2002: Casson’s Invariant: 17 years on (April 13-14, organized by Olivier Collin) and The hyperbolic volume conjecture (April 20-21, organized by Steven Boyer and Adam Sikora).
In conclusion, we wish to congratulate Niky Kamran for his election to the Royal Society of Canada.
68 Annual Report 2000 - 2001 CRM Research Laboratories
LACIM (Laboratoire de combinatoire et d’informatique mathématique)
LACIM is a research networks and research engines, of which the use st laboratory of the is growing exponentially in this 21 century. Université du Québec à Montréal, which was The researchers officially established The laboratory is comprised of twelve principal in 1989. Its research researchers, all professors at UQAM, four activities concentrate associate members in North America and on enumerative algebra, thirteen in Europe. Notably, Christophe algebraic combinatorics, Reutenauer (regular member) and Nantel computer science and their Bergeron (associate member, York University) applications to other scientific domains, such hold Canadian research chairs. A team of four as the analysis of algorithms, statistical LACIM members is supported by a grant from mechanics and computational biology. FCAR. André Joyal, past member of LACIM and current member of CIRGET, is involved in Research areas several activities at LACIM, both formal and Discrete mathematics has lately become an informal. LACIM is the largest research group in important field of practical research, witness the combinatorics in Canada and is known new heading in Mathematical Reviews 05E of worldwide in its field. The UQAM team has algebraic combinatorics with subheadings contributed to the emergence and establishment indicating interactions with the newest areas of of combinatorics as a mathematical discipline. mathematics, such as group representations, For example, several LACIM members have quantum groups, discrete algebraic geometry, played and continue to play an important role in special functions. Combinatorics benefits from the organization of the international colloquium the revival of the concrete computational aspect Séries formelles et combinatoire algébrique, which is in mathematics after decades of abstract bilingual and is held yearly, alternately in structuralism. Algebra is enriched in a Europe and North America. Its success is fundamental manner by combinatorics, as the without question. commutative algebra book by Eisenbud demonstrates, highlighting constructive Research activities at LACIM geometric methods. Moreover, combinatorics A.!Joyal enriched the counting theory of Polya applies to computer sciences (theory of by including the theories of group automata, analysis of algorithms), to statistical representations and symmetric functions. Under physics (computation of configuration spaces the name of theory of species, this theory and of critical exponents, discrete models), bio- marked the emergence of the UQAM informatics (combinatorics of words applied to combinatorics group about twenty years ago. genomic sequences). The youth, dynamism, From that time research has diversified greatly at utility and applicability of this research domain LACIM: a) classical enumerative combinatorics are highlighted in the modern world, where and its applications (counting of discrete discrete structures (trees, graphs, permutations) configurations and planar maps); b) algebraic are more and more present in communications, combinatorics; c) theoretical computer science; d) bio-informatics.
CRM Annual Report 2000 - 2001 69 Research Laboratories
Members of the Laboratory
Director!: S. Brlek (UQAM) P. Leroux (UQAM) C. Reutenauer (UQAM) Combinatorics of words, Combinatorics. Algebraic combinatorics, non- algorithmics. commutative algebra, V. Makarenkov (UQAM) automata, codes, free C. Chauve (UQAM) Computational biology, algebras. Enumerative combinatorics, mathematical classification. trees, bio-informatics. R. Bédard (UQAM), O. Marcotte (UQAM) Representations of finite G. Labelle (UQAM) Operational research, groups, Lie theory. Enumerative combinatorics, combinatorial optimization, analysis. graph theory. A. Bergeron (UQAM) Bio-informatics. J. Labelle (UQAM) T. Walsh UQAM) Combinatorics, topology. Algorithmics, enumerative F. Bergeron (UQAM) combinatorics, graphs. Combinatorics, algebras, L. Laforest (UQAM) representations of finite Data structures, groups. combinatorics, asymptotical analysis, quaternary trees.
Highlights of the activities of laboratory and of its members in 2001-2002. Since January 2001, C. Reutenauer has held a senior Canada Research Chair. The 57e Colloque des Sciences mathématiques du Québec was organized in April 2002 by R. Bédard, P. Bouchard and L. Bélair (the latter two being collaborating members at LACIM).
R. Bédard also co-organized the CRM winter school on Coxeter groups in January 2002.
A special AMS session on combinatorial Hopf algebras was organized in May 2002, by F. Bergeron, C. Reutenauer and M. Aguiar (the latter being a collaborating member at LACIM).
A session parallel to the 2002 SMC summer meeting was organized by C. Chauve, P. Leroux and Sylvie Corteel (the latter being a collaborating member at LACIM). C. Reutenauer was one of the plenary speakers at this meeting.
F. Bergeron was an invited speaker at the SIAM colloquium in San Diego in August 2002.
70 Annual Report 2000 - 2001 CRM Research Laboratories
Mathematical Analysis Laboratory
At the same time classical and central to modern random waves and quantum chaos, Hamiltonian mathematics, analysis involves studying formalism in statistical mechanics far from continuous systems from dynamical systems to equilibrium, asymptotic properties of wave solutions of partial differential equations and functions, Hilbert 16th problem and Hardy spectra of operators. The Québec group of conjecture. analysts has lately recruited an impressive Besides two active seminars, the program of the number of researchers. The creation of a laboratory includes a plan of intense activities, a laboratory allowing them to pursue their thematic year in analysis, focussing on spectral development will be welcome. The group analysis and geometric analysis, including a members belong to six Québec universities with short program on contact geometry and contact a particular concentration at Laval and McGill. analysis, a short program on the analysis of Many of the main currents of modern analysis singular spaces, two workshops in analysis of are studied by the group. Among the research general relativity and five workshops on subjects of the group, one finds conjectures on different aspects of spectral analysis.
Members of the Laboratory
Director!: R. Fournier (Dawson) T. Kaczynski (Sherbrooke) D. Jakobson (McGill) Complex analysis, univalent Topological methods, Conley Harmonic analysis, spectral functions, conformal index, applications to geometry. transformations. dynamical systems.
L. Baribeau (Laval) M. Frigon (UdeM) I. Klemes (McGill) Complex and functional Nonlinear analysis, Harmonic analysis, analysis, Banach algebras, differential equations, fixed trigonometric series. holomorphic iterations, point theory, critical point, discrete groups. theory. P. Koosis (McGill) Harmonic analysis. F. Clarke (Univ. Lyon I) P. Gauthier (UdeM) Nonlinear and dynamic Complex analysis, J. Mashreghi (Laval) analysis, control theory, holomorphy, harmonicity, Complex analysis, harmonic calculus of variations. analytic approximation. analysis, Hardy spaces.
G. Dafni (Concordia) P. Gora (Concordia) I. Polterovich (UdeM) Harmonic analysis, partial Ergodic theory, dynamic Partial derivative equations, derivative equations, complex systems, fractal geometry. spectral theory, differential variables. geometry. F. Gourdeau (Laval) D. Dawson (McGill) Banach algebras, T. Ransford (Laval) Probability, stochastic cohomology, amenability, Complex analysis, functional processes. functional analysis. analysis, spectral theory, potential theory, Jensen S. Drury (McGill) K.N. GowriSankaran measures. Harmonic analysis, matrix (McGill) theory. Potential theory. D. Rochon (UQTR) Numbers, analysis, dynamic R. Duncan (UdeM) V. Jaksic (McGill) complexes. Ergodic theory, probability. Mathematical physics.
CRM Annual Report 2000 - 2001 71 Research Laboratories
C. Rousseau (UdeM) D. Schlomiuk (UdeM) R. Stern (Concordia) Dynamical systems, Global analysis, dynamical bifurcations, qualitative systems, singularities, theory, polynomial systems, bifurcations, algebraic curves, analytic invariants, integrable primary integral. systems.
Highlights of the activities of the laboratory and of its members in 2001-2002.
The members of the laboratory worked as participants and organizers at numerous conferences. For example: • NATO Advances Study Institute, CRM, July 2002: Normal forms, bifurcations and finiteness problems for differential equations, organized by C. Rousseau. • Session in Analysis, CMS meeting, Laval, June 2002, organized by T. Ransford. • AMS meeting, UdeM, May 2002: ß Session in Potential Theory, organized by P. Gauthier, K.N. GowriSankaran et al. ß Session in Functions Spaces in Harmonic Analysis and Partial Derivative Equations, organized by G.!Dafni, J. Xiao. ß Session in Spectral Geometry, organized by D. Jakobson, Y. Petridis. • Workshop on Spectral Statistics and High Energy Eigenstates at CRM, Aug. 25-Sept. 2 2001, organized by J. Toth, D. Jakobson, Y. Petridis. • 55th Quebec Mathematics Colloquium at Bishop’s University, April 28, 2001 • Special day on Dynamic Systems, organized yearly by C. Rousseau and D. Schlomiuk. As a complement of these activities, regular seminars are co-organized at McGill by G. Dafni, D. Jakobson, V. Jaksic, at Université de Montréal by P. Gauthier and at Laval by T. Ransford. Moreover, D. Schlomiuk is co-organizer of the CRM-ISM Colloquium. Concerning prizes, we note the Sloan Fellowship held by D. Jakobson and the Dawson Fellowship held by J. Toth both obtained in May 2001.
72 Annual Report 2000 - 2001 CRM Research Laboratories
Applied Mathematics Laboratory
The new Montréal laboratory in applied Another notable characteristic of this group is mathematics and scientific computation reflects the intensive use of cutting edge computer an expanding domain as many of its members science means for advanced numerical have been recruited lately. It is characterized by computations. The augmentation of the number of researchers in this domain in Montréal reflects the intensity of its multidisciplinary indeed the spectacular expansion of the collaborations, since all its researchers are computation power in Montréal. working on the development of mathematical models and numerical methods for multiple applications to science and engineering.
Members of the Laboratory
Director: A. Bandrauk (Sherbrooke) S. Maslowe (McGill) A. Bourlioux (UdeM) Quantum chemistry. Asymptotic methods, fluid Modeling, numerical mechanics. simulation in turbulent P. Bartello (McGill) combustion. Turbulence, CFD. N. Nigam (McGill) Applied analysis, numerical Director!: M. Delfour (UdeM) methods in M. Gander (McGill) Control, optimization, design, electromagnetism. Domain decomposition, pre- shells, calculus, bio- conditioning. mechanics. G. Schmidt (McGill) Control of partial differential P. Arminjon (UdeM) A. Humphreys (McGill) equations. Numerical methods in fluid Numerical analysis, mechanics. differential equations. J.P. Zolésio (INRIA) Control, optimization.
Highlights of the activities of the laboratory and of its members in 2001-2002.
The members of the laboratory maintained an extensive complete calendar of seminars in Montréal: applied mathematics seminar at Université de Montréal, organized by M. Delfour; computational science and engineering seminar at McGill University (see http://www.math.mcgill.ca/~chang/CSE), organized by Martin Gander, twelve speakers; applied mathematics seminar at McGill (see http://www.math.mcgill//nigam/AMCSEseminar.htm), organized by Nilima Nigam, 18 speakers.
A. Bourlioux and M. Gander were scientific directors of the Séminaire de Mathématiques Supérieures in July 2001, on the theme Modern methods in scientific computation and applications.
Martin Gander and Nilima Nigam were members of the McGill team that won the first prize at the competition in numerical analysis organized by N. Trefethen, Decimal Decathlon, and publicized by SIAM.
Michel Delfour and André Bandrauk in collaboration with C. LeBris from CERMICS, Paris, co-organized a group of activities in quantum control, which was the theme of a workshop in fall 2002. Furthermore, M. Delfour also collaborates with André Garon and his group of engineers at École Polytechnique of Montréal and with Marc Thiriet and his team at INRIA on a major initiative in mathematical modeling and numerical simulation in medicine.
André Bandrauk was given a Canada Research Chair in computational and photonic chemistry.
CRM Annual Report 2000 - 2001 73 Research Laboratories
Mathematical Physics Laboratory
Mathematical physics represents one of the The group carries out research in several traditional strengths of the CRM ever since the scientific domains among the most active ones in arrival of J. Patera and P. Winternitz at the mathematical physics, for example: nonlinear Centre at the beginning of the 1970’s. The group coherent fluids systems, plasmas and optics, has considerably grown in the last years through integrable systems and classical and quantum the hiring of new researchers with a total of supranaturalisms, analysis of partial differential twenty academic researchers affiliated to seven equations via symmetry, spectral theory of Québec universities. Schrödinger operators and random matrices, Mathematical and theoretical physics has quasi-crystals, percolation, theory of conformal broadened its spectrum of activities in the last fields, statistical quantum mechanics and twenty years and has become an important symmetry of finite different equations. source of conjectures in pure mathematics.
Members of the Laboratory
Director : V. Hussin (UdeM) J. LeTourneux (UdeM) J. Harnad (Concordia) Quantum mechanics, Symmetry properties of Geometric methods, differential equations, systems, special functions. integrable systems, groups, Lie algebras, group isospectral flows, loop deformations, P. Mathieu (Laval) algebras. supersymmetries. Conformal field theory, classical and quantum S. T. Ali (Concordia) D. Jakobson (McGill) integrable systems, affine Lie Coherent states, wavelets. Quantum chaos, spectral algebras. geometry, harmonic analysis. M. Bertola (Concordia) J. Patera (UdeM) Axiomatic quantum field V. Jaksic (McGill) Applications of group theory, theory, invariant theory of Quantum mechanics, quasi-crystals, Lie algebras. discrete groups. statistics, random Schrödinger operators. Y. Saint-Aubin (UdeM) C. Cummins (Concordia) Conformal field theory, Group theory, modular N. Kamran (McGill) statistical mechanics, 2- functions, Moonshine. Differential geometry, partial dimensional phase transition differential equations. model. S. Durand (É.-Montpetit) D. Korotkin (Concordia) J. Toth (McGill) M. Grundland (UQTR) Integrable systems, classical Spectral theory, semi-classical Symmetry of differential and quantum gravity. analysis, micro-local analysis, equations in physics. Hamiltonian mechanics. F. Lalonde (UdeM) R. Hall (Concordia) Symplectic topology and L. Vinet (McGill) Quantum mechanics, geometry, global analysis on Symmetric properties of geometry, spectral inversion, manifolds, infinite systems, special functions. many-body problem. dimensional transformation groups. P. Winternitz (UdeM) J. Hurtubise (UdeM) Methods of group theory in Integrable systems, gauge R. Langlands (Princeton) physics, nonlinear theory, moduli spaces. Automorphic forms, critical phenomena, symmetries of phenomena, Ising models, difference equations, percolation, phase transition, superintegrability. finite models in statistical physics. C. Van Vliet (Miami)
74 Annual Report 2000 - 2001 CRM Research Laboratories
Highlights of the activities of the laboratory and of its members in 2001-2002.
S.T. Ali was part of the organizing committee of the 21st workshop on Geometrical Methods in Physics, in Bialowieza, Poland, July 2002. John Harnad was a plenary speaker there for a series of three talks on the theme of random matrices, isomonodromic deformations, duality, and so on. S.T Ali was also co- organizer of the 4th workshop on Wavelets, Quantization and Differential Equations, which found place in La Havana, Cuba, in February 2002.
C. Cummins organized the Moonshine session of the SMC winter meeting 2001.
John Harnad co-organized several CRM workshops, beginning in May 2000 with a workshop on isomonodromic deformations and their applications to physics, the proceedings of which will be published by the CRM. Then in September 2002, he was member of the organizing committee (together with P. Winternitz, C.!S. Lam and J. Patera, the former being in charge of it) of the workshop on symmetries in physics to the memory of R.!T. Sharp. Later in the month, another workshop on superintegrability in classical and quantum systems was organized in collaboration with P. Winternitz, P. Tempesta, W. Miller, G. Pogosyan and M. Rodriguez.
Niky Kamran gave a plenary talk at the 2001 AMS meeting. Together with B. Khesin, he organized a workshop at the CRM on the geometry of Lie groups in infinite dimension in October 2001.
P. Mathieu was invited to participate to an IPAM (UCLA) workshop on conformal fields, where he presented four talks and lectures.
Pavel Winternitz received the 2001-2002 ACP-CRM prize in mathematical and theoretical physics. He was also acknowledged by the Czech journal Lidove Noviny of September 21, 2002, as belonging to the very prestigious club of the ten most quoted Czech scientists since 1980. He was invited many times to give plenary talks, as for example at the SYMPHYS conference in Yerevan, Armenia, July 2001; to the NEEDS conference, Cadiz, June 2002, and to the European Conference of the Newton Institute, Cambridge, August 2001 (two talks in the subject What is Integrability?).
John Harnad and Niky Kamran are very involved in NSERC committees. Harnad is a member of the physics committee and responsible for the membership committee. Kamran heads the B committee in pure and applied mathematics.
CRM Annual Report 2000 - 2001 75 Research Laboratories
PhysNum Lina and F. Lesage) as well as graduate students (E. Lapalme, F. Levac, MD). Another direction of research concerns the analysis of wavelets applied to the study of one- dimensional signals (turbulence, EEG) and mammography imaging. In this direction, one studies random process attached to nodes of a tree or a graph whose depth is different resolution, from the coarser to the finer scale. During the last year, the PhysNum group This work is lead by the researchers of PhysNum developed its research activities in brain imaging (J.M. Lina, B. Goulard) together with PhD by pursuing the study of the inverse problem in students (P. St-Jean, D. Clonda) and the Master’s MEG (magneto-encephalography) and students (G. Sitzia). Notable is the presence of a beginning the study of problems of the same junior analyst (Y. Basile-Belavance) who is in type in optical imaging. This work involves the charge of the developpement, for the group, of main researchers of the group (B. Goulard, J.M. some of the computation libraries used in this research.
Members of the Laboratory
B. Goulard (UdeM) F. Lesage (CRM) F. Nekka (UdeM) Brain imaging. Conformal theory, integrable Fractal analysis. systems, inverse problems. H. Benali (INSERM, France) K. Worsley (McGill) Brain imaging. J.M. Lina (CRM) Geometry of random images Imaging, statistical inference, in medicine and astrophysics. wavelets.
Highlights of the activities of the laboratory and of its members in 2001-2002. The ability of visualizing in vivo cerebral regions used in cognitive tasks by the human brain has modified deeply most of the domains in neurosciences. Until recently, the study of human cognition was mostly founded on the analysis of cerebral lesions. With the help of new techniques in functional imaging (IRM, MEG, NIRS, etc.), this discipline made remarkable progress in the comprehension of the spatial-temporal mechanisms managing the operation of the brain. It remains that the problems of detecting cerebral activity and connectivity, between the cerebral regions spatial as well as temporal, remain important subjects of research, the main concern of neuroscientists being to solve these problems beyond any doubt as to the hypotheses guaranteeing the uniqueness of the solution. The mathematical and statistical approaches studied by the PhysNum group, in collaboration with the INSERM U494 unit tend to define a methodology based only on reliable hypotheses and knowledge at the anatomical and physiological levels. Two domains are principally concerned by this study: Magneto-Encephalography and optical imaging.
Cerebral imaging (MEG) In the context of Magneto-Encephalography applied to the study of cerebral functional connectivity, this subject acknowledged important developments can be summarized in the following way: • Probabilistic model based on graphic models applied to hidden Markov variables and resolution of the inverse problem by maximal entropy, • MiniMax approach on entropy and reduction of the space of features (space of data) MEG.
76 Annual Report 2000 - 2001 CRM Research Laboratories
• PCA approach on the direct problem and reduction of the space of sources (space of dipoles distributed on the cortical surface) of activation. This study was conducted mostly by the members of the U494 unit headed by H. Benali at the INSERM. This collaboration between CRM-INSERM (U494) was formalised by the nomination of H. Benali and J.M. Lina to the status of member researchers at both institutions. Notable is the emergence of another international collaboration with the Center of Excellence in Taiwan, which invited one of the group members (J.M. Lina) to give a series of seminars at the Central National University of Taipei.
Cerebral imaging (NIRS) Optical imaging offers possibilities of analysis of how the brain operates on objects usually difficult to observe with conventional tools (IRM, MEG, EGG). At the moment, there exists no strong method for detecting the active cortical zones from the infra-red (IR) optical signal interacting with the brain. Such a method, as it is the case with MEG, must take into account certain knowledge about the solution. One speaks of the regularization of the inverse problem through a priori knowledge. The approach developed in MEG (see preceding section) is certainly transposable into the context of optical imaging. The stake being probably more interesting for neuroscientists because of the flexibility of the technique used (compared to IRM or MEG imaging), PhysNum has defined of a research axis devoted to the resolution of the inverse problem for this kind of imaging. Up to now, the researchers involved in this direction of research have concentrated their efforts in understanding the problem in terms of the physics of interactions between laser beam and biological material and the transport equations that describe the progression of the laser beam trough the gray and white matter, starting from the source (placed on the surface of the scalp) to the detectors (situated on the surface of the scalp).
Graphical models and wavelets The PhysNum group made its name in the context of multiresolution analysis in studying and applying the Daubechies complex wavelets. During the last year, the work of one of its students (D. Clonda) have underlined the role of the phase of the coefficients in complex wavelets in the multiresolution treatment of images. Two typical applications were considered: estimation (denoising) and classification (textures segmentation). In both cases, the study proved that a modeling of the signal taking into account the phase of the coefficients in wavelets gives better results.
Models in cascade Some members of the PhysNum group (J.M. Lina, B. Goulard, P. St-Jean, D. Clonda, G. Sitzia) are involved in work related to analysis through continuous wavelets and particularly to analytical tools in imaging for breast cancer.
Most of this research is conducted in collaboration with academics (J. Doyon, F. Lepore, UdeM), foreign research organizations (H. Benali, INSERM; L. Garnero, CNRS, France) and a hospital (L. Lalonde, CHUM).
Scale invariance and fractal analysis F. Nekka and her students have pursued their work of classification of complex structures, in particular those representing a spatial scale invariance through derived tools of fractal analysis. This team perfected a method based on the spectrum of Hausdorff measures (when the Lebesgue measure degenerates) in order to distinguish the sets that are not via fractal dimension. This method was validated on sets called thin fractals. One obtains in this way one index allowing not only to distinguish sets of the same dimension, but also to classify them with respect to their homogeneity degree. The use of this method was extended to sets known as fat fractals. These sets have a practical interest, since they are considered as synthetic models of porous material. The whole method was written into a Matlab software. This software allows also the analysis of real images for classification.
CRM Annual Report 2000 - 2001 77 Research Laboratories
Statistics Laboratory
Statistics is undergoing a revolution in its This structure will also allow the Québec techniques and its approaches. This revolution community to benefit from a new pan-Canadian has been driven by the need to analyze very program in analysis of complex data organized large complex data sets and by the advent of by the three Canadian mathematics institutes. powerful computers. For example, statistical The laboratory is composed of the leaders of the methodology is central to the analysis of genome Québec school of statistics who work on subjects data generated by micro-array images. Data- such as statistical learning and neuronal mining is one of the tools used. The laboratory networks, analysis of functional data, statistical aims at structuring the Québec community in analysis of images, dependence structures, order to engage with this revolution at a time of Bayesian analysis, analysis of chronological an important renewal of academic personnel. series, of financial data and resampling methods.
Members of the Laboratory
Director : René Ferland (UQAM) Bruno Rémillard (HEC) Christian Léger (UdeM) Probability, stochastic Probability, empirical Resampling methods, processes, applications to processes, time series, adaptive estimation, model financial mathematics. non-linear filtering, selection, robustness, data applications to finance. mining applications. Christian Genest (Laval) Multivariate analysis, Louis-Paul Rivest (Laval) Jean-François Angers measure of dependence, Linear models, robustness, (UdeM) nonparametric statistics, directional data, sampling, Decision theory, Bayesian decision theory, applications diverse applications. statistics, robustness with to actuarial sciences, finance respect to prior information, and psychology. Roch Roy (UdeM) function estimation. Time series analysis, Nadia Ghazzali (Laval) forecasting methods, Yoshua Bengio (UdeM, Multivariate analysis, neural applications to econometrics DIRO) networks and genetic and epidemiology. Algorithms for statistical algorithms, applications to learning, neural networks, astrophysics and biostatistics. David Wolfson (McGill) Kernel methods, probabilistic Change points problems, models, data mining, Brenda MacGibbon (UQAM) survival analysis, Bayesian applications to finance, Mathematical statistics, analysis, optimal design, applications to statistical decision theory, bio-statistics. applications to medicine. modeling of language. François Perron (UdeM) Keith Worsley (McGill) Martin Bilodeau (UdeM) Decision theory, multivariate Geometry and analysis of Multivariate analysis, analysis, Bayesian statistics. random images in medicine decision theory, asymptotic and astrophysics. methods. Jim Ramsay (McGill) Functional data analysis, Yogendra Chaubey smoothing and (Concordia) nonparametric regression, Sampling, linear models, curves scaling. resampling, survival analysis.
78 Annual Report 2000 - 2001 CRM Research Laboratories
Highlights of the activities of the laboratory and of its members in 2001-2002. The researchers of the laboratory were very busy this year and several distinguished themselves. Yoshua Bengio has held the Canada Research Chair on algorithms of statistical learning since 2001. Moreover, Keith Worsley is the first Killam Fellow in statistics. The academic and scientific leadership of the group was acknowledged in several ways this year. For instance, in 2002, Jim Ramsay was president-elect and Louis-Paul Rivest was past-president of the Statistics Society of Canada. Christian Genest and Bruno Rémillard were members of the statistics and probability committee in the context of the reallocations exercise at NSERC. Yoshua Bengio is a member of the selection committee of the discovery grants committee of NSERC in computer science. Even our students distinguished themselves: Alexis Gerbeau, Masters student of Roch Roy, was recipient of the gold medal of the Governor General.
The laboratory took part in the organization of the conference Statistics 2001 Canada at Concordia University, in the presentation of the third public conference of the Canadian Journal of statistics in March 2002, as well as to the conference Statistique mathématique 2002 the honour of the 75th anniversary of Constance van Eeden. Yoshua Bengio was a member of the organizing committee of the conference Learning 2002. Roch Roy organized a session at the Joint Statistical Meetings 2001 in Atlanta and Christian Léger was part of the program committee of the Joint Statistical Meetings 2002 in New York. Among the main conferences to which the researchers of the laboratory were invited, there are the International Conference and Instructional Workshop on Wavelets and their Applications in Chennai, India (Jean-François Angers) and Neural Networks for Signal (Yoshua Bengio). The researchers gave talks around the world, notably at UCLA (Christian Genest) and at the Université Montpellier II (Martin Bilodeau). Finally, four research seminars series were organized by members of the laboratory, namely the CRM Statistics Seminar, the Statistics Seminars of McGill and Laval Universities and the joint UQAM-Concordia Statistics Seminar.
CRM Annual Report 2000 - 2001 79 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 2001-2002 or that will be published soon.
Recent Titles
AMS: CRM Monograph Series Springer-Verlag: CRM Series in • Eyal Z. Goren, Lectures on Hilbert Modular Mathematical Physics Varieties and Modular Forms, vol. 14, 2002 • Yvan Saint-Aubin & Luc Vinet (eds.), • Jose I. Burgos, The Regulators of Beilinson and Theoretical Physics at the End of the XXth Borel, vol.15, 2002 Century. 2001. • Joel Feldman, Horst Knörrer & Eugene • Roman Jackiw, Lectures on Fluid Dynamics, Trubowitz, Fermionic Functional Integrals and 2002. the Renormalization Group, vo. 16, 2002. • David Sénéchal, André-Marie Tremblay & • Michael Barr, Acyclic Models, vol. 17, 2002. Claude Bourbonnais, Theoretical Methods for Strongly Correlated Electrons, (to appear). AMS: CRM Proceedings & Lecture Notes CRM Subseries of the Springer-Verlag • Israel M. Sigal & Catherine Sulem, Nonlinear Series: Lecture Notes in Statistics Dynamics and Renormalization Group, vol. 27, 2001. • S. Ejaz Ahmed & Nancy Reid (eds.), Empirical Bayes and Likelihood Inference, 2001. • J.C. Taylor (ed.), Topics in Probability and Lie Groups: Boundary Theory, vol. 28, 2001. • Marc Moore (ed.), Spatial Statistics, 2001. • Alan Coley, Decio Levi, Robert Milson, Colin Les Publications CRM Rogers & Pavel Winternitz (eds.), Bäcklund and Darboux Transformations: The Geometry of • Nadia El-Mabrouk, Thomas Lengauer & Soliton, vol. 29, 2001. David Sankoff (eds.), Currents in Computational Molecular Biology 2001. • John McKay & Abdellah Sebbar (eds.), Proceedings on Moonshine and Related Topics, • Armel Mercier, Fonctions de plusieurs vol. 30, 2001. variables!: Différentiation, 2002. • John Harnad et Alexander R. Its (eds.), Isomonodromic Deformations and Applications in Physics, vol. 31, 2002 . • Vadim B. Kuznetsov (éd.), The Kowalevski Property, vol. 32, 2002.
80 Annual Report 2000 - 2001 CRM Publications
Previous Titles
AMS: CRM Monograph Series • Michel Fortin (ed.), Plates and Shells, vol. 21, • Michael Baake & Robert V. Moody (eds.), 1999. Directions in Mathematical Quasicrystals, vol. • Katie Coughlin (ed.), Semi-Analytic Methods 13, 2000. for the Navier-Stokes Equations, vol. 20, 1999. • Masayoshi Miyanishi, Open Algebraic • Rajiv Gupta & Kenneth S. Williams (eds.), Surfaces, vol. 12, 2001. Number Theory, vol. 19, 1999. • Spencer J. Bloch, Higher Regulators, Algebraic • Serge Dubuc & Gilles Deslauriers (eds.), K-Theory, and Zeta Functions of Elliptic Curves, Spline Functions and the Theory of Wavelets, vol. 11, 2000. vol. 18, 1999 • James D. Lewis, A Survey of the Hodge • Olga Karlampovich (ed.), Summer School in Conjecture, 2e Édition (with an appendix by Group Theory (Banff, 1996), vol. 17, 1998. B. Brent Gordon), vol. 10, 1999. • Alain Vincent (ed.), Numerical Methods in • Yves Meyer, Wavelets, Vibrations and Scaling, Fluid Mechanics (Montréal, 1995), vol. 16, vol. 9, 1997. 1998. • Ioannis Karatzas, Lectures on Mathematics of • François Lalonde (ed.), Geometry, Topology Finance, vol. 8, 1996. and Dynamics, (Montréal, 1995), vol. 15, 1998. • John Milton, Dynamics of Small Neural • John Harnad & Alex Kasman (eds.), The Populations, vol. 7, 1996. Bispectral Problem (Montréal, 1997), vol. 14, • Eugene B. Dynkin, An Introduction to 1998. Branching Measure-Valued Processes, vol. 6, • Michel Delfour (ed.), Boundaries, Interfaces 1994. and Transitions (Banff, 1995), vol. 13, 1998. • Andrew M. Bruckner, Differentiation of Real • Peter G. Greiner, Victor Ivrii, Luis A. Seco & Functions, vol. 5, 1994. Catherine Sulem (eds.), Partial Differential • David Ruelle, Dynamical Zeta Functions for Equations and their Applications (Toronto, Piecewise Monotone Maps of the Interval, vol. 4, 1995), vol. 12, 1997. 1994. • Luc Vinet (ed.), Advances in Mathematical • V. Kumar Murty, Introduction to Abelian Sciences: CRM’s 25 Years (Montréal, 1994), Varieties, vol. 3, 1993. vol. 11, 1997. • Maximilian Ya. Antimirov, Andrei A. • Donald E. Knuth, Stable Marriage and its Kolyshkin, & Rémi Vaillancourt, Applied Relation to Other Combinatorial Problems. An Integral Transforms, vol. 2, 1993. Introduction to the Mathematical Analysis of • Dan V. Voiculescu, Kenneth J. Dykema, & Algorithms, vol. 10, 1996. Alexandru Nica, Free Random Variables, vol. • Decio Levi, Luc Vinet, & Pavel Winternitz 1, 1992. (eds.), Symmetries and Integrability of Difference Equations (Estérel, 1994), vol. 9, AMS: CRM Proceedings & Lecture Notes 1995. • John Harnad, Gert Sabidussi & Pavel • Joel S. Feldman, Richard Froese, & Lon M. Winternitz (eds.), Integrable Systems: From Rosen (eds.), Mathematical Quantum Theory Classical to Quantum, vol. 26, 2000. II: Schrödinger Operator (Vancouver, 1993), • Decio Levi & Orlando Ragnisco (eds.), SIDE vol. 8, 1995. III - Symmetry and Integrability of Difference • Joel S. Feldman, Richard Froese, & Lon M. Equations, vol. 25, 2000. Rosen (eds.), Mathematical Quantum Theory I: • B. Brent Gordon, James D. Lewis, Stefan Many-Body Theory and Group Theory Müller-Stach, Shuji Saito & Noriko Yui (Vancouver, 1993), vol. 7, 1994. (eds.), The Arithmetic and Geometry of • Guido Mislin (ed.), The Hilton Symposium Algebraic Cycles, vol. 24, 2000. 1993 : Topics in Topology and Group Theory • Pierre Hansen & Odile Marcotte (eds.), (Montréal, 1993), vol. 6, 1994. Graph Colouring and Applications, vol. 23, • Donald A. Dawson (ed.), Measure-valued 1999. Processes, Stochastic Partial Differential • Jan Felipe van Diejen & Luc Vinet (eds.), Equations and Interacting Systems (Montréal, Algebraic Methods and q-Special Functions, vol. 1992), vol. 5, 1994. 22, 1999.
CRM Annual Report 2000 - 2001 81 Publications
• Hershy Kisilevsky & M. Ram Murty (eds.), Raman Scattering (Montréal, 1993), Montréal, Elliptic Curves and Related Topics (Sainte- 1994. Adèle, 1992), vol. 4, 1994. • Jacques Gauvin, Theory of Nonconvex • Andrei L. Smirnov & Rémi Vaillancourt Programming, Montréal, 1994. (eds.), Asymptotic Methods in Mechanics, vol. • Rémi Vaillancourt, Compléments de 3, 1993. mathématiques pour ingénieurs, Montréal, • Philip D. Loewen, Optimal Control via 1993. Nonsmooth Analysis, vol. 2, 1993. • Robert P. Langlands & Dinakar • M. Ram Murty (ed.), Theta Functions. From Ramakrishnan (eds.), The Zeta Functions of the Classical to the Modern, vol. 1, 1993. Picard Modular Surfaces (Montréal, 1988), Montréal, 1992. Springer-Verlag: CRM Series in • Florin N. Diacu, Singularities of the N-Body Mathematical Physics Problem, Montréal, 1992. • Yvan Saint-Aubin & Luc Vinet (eds.), • Jacques Gauvin, Théorie de la programmation Algebraic Methods in Physics - A Symposium mathématique non convexe, Montréal, 1992. for the 60th Birthday of Jíri Patera and Pavel • Pierre Ferland, Claude Tricot, & Axel van de Winternitz, 2000. Walle, Analyse fractale: Application W indows • Jan Felipe van Diejen & Luc Vinet (eds.), ™ 3.x d’initiation aux ensembles fractals, Calogero-Moser-Sutherland Models, 1999. Montréal, 1992 (software and user guide). • Robert Conte (ed.), The Painlevé Property: One • Stéphane Baldo, Introduction à la topologie des Century Later, 1999 ensembles fractals, 1991. • Richard MacKenzie, Manu B. Paranjape & • Robert Bédard, Groupes linéaires algébriques, Wojciech J. M. Zakrzewski (eds.), Soliton: Montréal, 1991. Properties, Dynamics, Interactions, Appli- • Rudolf Beran & Gilles R. Ducharme, cations, 1999 Asymptotic Theory for Bootstrap Methods in • Luc Vinet & Gordon Semenoff (eds.), Statistics, Montréal, 1991. Particles and Fields (Banff, 1994), CRM Series • James D. Lewis, A Survey of the Hodge in Mathematical Physics, Springer, New Conjecture, Montréal, 1991. York, 1998. • David W. Rand & Tatiana Patera, Concorder: Concordance Software for the Macintosh, Les Publications CRM Montréal, 1991 (software and user guide). • James G. Huard & Kenneth S. Williams • David W. Rand & Tatiana Patera, Le (eds.), The Collected Papers of Sarvadaman Concordeur: un logiciel de concordances pour le Chowla, I, II, III, 2000. Macintosh, Montréal, 1991 (software and user • Michael Barr & Charles Wells, Category guide). Theory for Computing Science, 1999 • Véronique Hussin (ed.), Lie Theory, • Maximilian Ya. Antimirov, Andrei A. Differential Equations and Representation Kolyshkin & Rémi Vaillancourt, Theory (Montréal, 1989), Montréal, 1990. Mathematical Models for Eddy Current Testing, • John Harnad & Jerrold E. Marsden (eds.), 1998. Hamiltonian Systems, Transformation Groups • Xavier Fernique, Fonctions aléatoires and Spectral Transform Methods (Montréal, gaussiennes, vecteurs aléatoires gaussiens, 1989), Montréal, 1990. Montréal, 1997. • M. Ram Murty (ed.) Automorphic Forms and • Faqir Khanna & Luc Vinet (eds.), Field Analytic Number Theory (Montréal, 1989), Theory, Integrable Systems and Symmetries, Montréal, 1990. Montréal, 1997. • Wendy G. McKay, Jirí Patera & David W. • Paul Koosis, Leçons sur le théorème de Beurling Rand, Tables of Representations of Simple Lie at Malliavin, 1996. Algebras. I. Ex-ceptional Simple Lie Algebras, • David W. Rand, Concorder Version Three: Montréal, 1990. Concordance Software for the Macintosh, • Anthony W. Knapp, Representations of Real Montréal, 1996 (software and user guide). Reduc-tive Groups, Montréal, 1990. • Decio Levi, Curtis R. Menyuk, & Pavel • Wendy G. McKay, Jirí Patera & David W. Winternitz, Self-Similarity in Stimulated Rand, SimpLie User’s Manual–Macintosh Software for Representations of Simple Lie
82 Annual Report 2000 - 2001 CRM Publications
Algebras, Montréal, 1990 (software and user • Yuval Ne’eman, Symétries, jauges et variétés de guide). groupe, Presses de l’Université de Montréal, • Francis H. Clarke, Optimization and 1979. Nonsmooth Analysis, Montréal, 1989. • R. Tyrrell Rockafellar, La théorie des sous- • Hedy Attouch, Jean-Pierre Aubin, Francis gradients et ses applications à l’optimisation, Clarke & Ivar Ekeland (eds.), Analyse non fonctions convexes et non convexes, Presses de linéaire (Perpignan, 1987), Montréal & l’Université de Montréal, 1979. Gauthiers-Villars, Paris, 1989. • Jacques-Louis Lions, Sur quelques questions • Samuel Zaidman, Une introduction à la théorie d’analyse, de mécanique et de contrôle optimal, des équations aux dérivées partielles, Montréal, Presses de l’Université de Montréal, 1976. 1989. • Donald E. Knuth, Mariage stables et leurs • Lucien Le Cam, Notes on Asymptotic Methods relations avec d’autres problèmes combinatoires, in Statistical Decision Theory, Montréal, 1974. Presses de l’Université de Montréal, 1976. • Robert Hermann, Physical Aspects of Lie AMS/International Press Group Theory, Presses de l’Université de • Duong H. Phong, Luc Vinet & Shing-Tung Montréal, 1974. Yau (eds.), Mirror Manifolds and Geometry, • Mark Kac, Quelques problèmes mathématiques AMS/IP Studies in Advanced Mathematics, en physique statistique, Presses de l’Université Amer. Math. Soc., Providence, RI, Internat. de Montréal, 1974. Press, Cambridge, MA, & CRM, Montréal, • Sybreen de Groot, La transformation de Weyl 1998(vol.10). et la fonction de Wigner: une forme alternative de la mécanique quantique, Presses de Aisenstadt Chair Collection l’Université de Montréal, 1974. • Yuri I. Manin, Quantum Groups and Noncommutative Geometry, Les Publications Miscellaneous CRM, 1988. • Pierre Ferland, Claude Tricot, & Axel van de • Laurent Schwartz, Semimartingales and Their Walle, Fractal analysis user’s guide. Stochastic Calculus on Manifolds, Presses de Introduction to fractal sets using Windows ™ l’Université de Montréal, 1984. 3.x., Amer. Math. Soc., Providence, RI & Centre de recherches mathématiques, Montréal, 1994.
CRM Annual Report 2000 - 2001 83 Publications
Research Reports
[CRM-2746] S. Allen, L. Gagnon & F. Lesage, pour l’optimisation de portefeuilles, une approche Hydrous area segmentation in radar imagery by level bayésienne, September 2001. set-based snakes, June 2001. [CRM-2762] L.-S. Guimond, Z. Masáková & E. [CRM-2747] S. Allen. Signal based features with Pelantová. Combinatorial properties of infinite applications to ship recognition in FLIR imagery, words associated with cut-and-project sequences, June 2001. October 2001. [CRM-2748] S. Tremblay & P. Winternitz. [CRM-2763] L.-S. Guimond, Z. Masáková & E. Invariants of the nilpotent and solvable triangular Lie Pelantová. Arithmetics on beta-expansions, October algebras, June 2001. 2001. [CRM-2749] M. Bertola, B. Eynard & J. Harnad. [CRM-2827] S. Durand. Non-local indeterministic Duality, biorthogonal polynomials and multi-matrix quantum behaviors modeled by wormhole-based time models, July 2001. travel, November 2001. [CRM-2750] S. Durand. Non-local wave function [CRM-2828] M. Bertola, B. Eynard & J. Harnad. reduction modeled by wormhole-based time travel, Duality of spectral curves arising in two-matrix August 2001. model, November 2001. [CRM-2751] P. Duchesne & R. Roy. Robust tests [CRM-2829] P. Winternitz. Lie point symmetries for independence of two time series, August 2001. and commuting flows for equations on lattices, [CRM-2752] J. Karrakchou. Linear quadratic November 2001. optimal control of linear time invariant systems with [CRM-2830] J. Patera & R. Twarock. Affine delays in state, control, and observation variables, extension of noncrystallographic Coxeter groups and September 2001. quasicrystals, November 2001. [CRM-2753] P. Bracken & A. M. Grundland. On [CRM-2831] D. Schlomiuk & N. Vulpe. Geometry complete integrability of the generalized Weierstrass of quadratic differential systems in the neighbourhood system, September 2001. of the line at infinity, December 2001. [CRM-2754] A. M. Grundland & W. J. [CRM-2832] P. Bracken & A. M. Grundland. Zakrzewski. Some geometric aspects of CP2 maps, Affine extension of noncrystallographic Coxeter September 2001. groups and quasicrystals, January 2002. [CRM-2755] B. Eynard. A concise expression for the [CRM-2833] J.-F. Angers. Curves comparison using ODE’s of orthogonal polynomials, September 2001. wavelet, February 2002. [CRM-2756] É. Marchand & F. Perron. On the [CRM-2834] A. Leblanc & J.-F. Angers. Prior minimax estimator of a bounded normal mean, density estimation via Haar deconvolution, February September 2001. 2002. [CRM-2757] J.-F. Angers & A. Biswas. A Bayesian [CRM-2835] R. Fournier & P. Mocanu. analysis of the four-year follow-up data of the Differential inequalities which imply starlikeness, Wisconsin epidemiologic study of diabetic March 2002. retinopathy, September 2001. [CRM-2836] A. Atoyan & C. D. Dermer. High- [CRM-2758] P. Valin. Unified framework for energy neutrinos from photomeson processes in information fusion, September 2001. blazars, October 2001. [CRM-2759] P. Valin. Reasoning frameworks for [CRM-2837] P.-L. Buono & J. Bélair. Restrictions fusion of imaging and non-imaging sensor and unfolding of double Hopf bifurcation in information, September 2001. functional differential equations, March 2002. [CRM-2760] M. J. Gander. Frequency [CRM-2838] F. H. Clarke & R. J. Stern. State decomposition and subspace iteration for nonlinear constrained feedback stabilization, March 2002. evolution equations, September 2001. [CRM-2839] R. J. Stern. Brockett’s condition for [CRM-2761] M. Haddou, J.-F. Angers & R. stabilization in the state constrained case 2839, Cléroux. Utilisation de modèles linéaires dynamiques March 2002.
84 Annual Report 2000 - 2001 CRM Publications
[CRM-2840] F Nekka & J. Li. Investigation of [CRM-2881] P. Jacob & P. Mathieu. Parafermionic intersection of triadic Cantor sets with their quasi-particle basis and fermionic-type characters, translates for a classification purpose, March 2002. August 2001. [CRM-2841] M. Bertola, B. Eynard & J. Harnad. [CRM-2882] E. G. Kalnins, J. M. Kress & P. Partition functions for matrix models and Winternitz. Superintegrability in a two-dimensional isomonodromic tau functions, April 2002. space of non-constant curvature, August 2001. [CRM-2842] M. Bertola. Bilinear semi-classical [CRM-2883] L. Martina, M. B. Sheftel & P. moment functionals and their integral representation, Winternitz. Group foliation and non-invariant May 2002. solutions of the heavenly equation, August 2001. [CRM-2843] A. M. Grunland, P. Tempesta & P. [CRM-2884] V. Apostolov, J. Armstrong & T. Winternitz. Weak transversality and partially Draghici. Local models and integrability of certain invariant solutions, May 2002. almost Kahler 4-manifolds, September 2001. [CRM-2844] J. Hurtubise & E. Markman. Elliptic [CRM-2885] J.-C. Aval & N. Bergeron. Catalan Sklyanin integrable systems for arbitrary reductive paths, Quasi-symmetric Functions and Super- groups, March 2002. Harmonic Spaces, September 2001. [CRM-2846] N. Alvarez & V. Hussin. [CRM-2886] R. L. Hall, N. Saad & A. B. von Generalized coherent and squeezed states based on Keviczky. Spiked harmonic oscillators, September the h(1) ⊕ su(2) algebra, December 2001. 2001. [CRM-2847] M. Daoud & V. Hussin. General sets [CRM-2887] L. Bégin, C. Cummins, L. Lapointe of coherent states and the Jaynes-Cummings model, & P. Mathieu. Fusion bases as facets of polytopes, May 2002. September 2001. [CRM-2872] A. Granville & K. Soundararajan. [CRM-2888] F. Gungor & P. Winternitz. Upper bounds for |L(1,c)|, June 2001. Generalized Kadomtsev-Petviashvili equation with an [CRM-2873] S. Twareque Ali, H. Fuehr & A. E. infinite dimensional symmetry algebra, September Krasowska. Plancherel Inversion as Unified 2001. Approach to Wavelet Transforms and Wigner [CRM-2889] A. Granville, I. Laba & Y. Wang, A Functions, June 2001. characterization of finite sets that tile the integers, [CRM-2874] N. Bergeron & M. Zabrocki. q and October 2001. q,t-Analogs of Non-commutative Symmetric [CRM-2890] R. L. Hall, N. Saad & A. B. von Functions, June 2001. Keviczky. Closed-form sums for some perturbation [CRM-2875] D. Korotkin. Matrix Riemann-Hilbert series involving associated Laguerre polynomials, problems related to branched coverings of CP1, June October 2001. 2001. [CRM-2891] R. L. Hall, W. Lucha & F. F. [CRM-2876] J.-C. Aval & N. Bergeron. Vanishing Schoberl. Relativistic N-Boson Systems Bound by ideals of Lattice Diagram determinants, July 2001. Oscillator Pair Potentials, October 2001. [CRM-2877] R. L. Hall & Qutaibeh D. Katatbeh. [CRM-2892] M. A. Rodriguez & P. Winternitz. Spectral bounds for the Hellmann potential, July Quantum superintegrability and exact solvability in 2001. N dimensions, October 2001. [CRM-2878] J. Hurtubise & E. Markman. Surfaces [CRM-2893] J.-C. Aval & N. Bergeron. Schur and the Sklyanin bracket, July 2001. Partial Derivative Operators, November 2001. [CRM-2879] F. Finster, N. Kamran, J. Smoller & [CRM-2894] M. Bertola, B. Eynard & J. Harnad. S.-T. Yau. Decay Rates and Probability Estimates for Duality of spectral curves arising in two-matrix Massive Dirac Particles in the Kerr-Newman Black models, December 2001. Hole, July 2001. [CRM-2895] A. Kokotov & D. Korotkin. Some [CRM-2880] L. Bégin, C. Cummins, L. Lapointe integrable systems on Hurwitz espaces, December & P. Mathieu. Fusion bases as facets of polytopes, 2001. August 2001. [CRM-2896] A. E. Krasowska & S. Twareque Ali. Wigner Functions for a Class of Semidirect Product Groups, January 2002.
CRM Annual Report 2000 - 2001 85 Publications
[CRM-2897] R. L. Hall & Q. D. Katatbeh. Spectral [CRM-2902] R. Fintushel, J. Park & R. J. Stern. bounds for the cutoff Coulomb potential, January Rational surfaces and symplectic 4-manifolds with 2002. one basic class, February 2002. [CRM-2898] V. Apostolov, D. M. J. Calderbank & [CRM-2903] N. Saad & R. L. Hall. Closed-form P. Gauduchon. Hamiltonian 2-forms in Kahler sums for some perturbation series involving geometry I, February 2002. hypergeometric functions, March 2002. [CRM-2899] J.-C. Aval, F. Bergeron & N. [CRM-2904] A. Granville & K. Soundararajan. Bergeron. Ideals of Quasi-Symmetric Functions and The distribution of values of L(1, c_d), June 2002. Super-Covariant Polynomials for Sn, February 2002. [CRM-2905] E. Kerman & F. Lalonde. Length [CRM-2900] A. Kokotov & D.Korotkin. Tau- minimizing Hamiltonian paths for symplectically function on Hurwitz spaces in genus zero and one, aspherical manifolds, June 2002. February 2002. [CRM-2906] S. Gravel & P. Winternitz. [CRM-2901] G. Labelle, C. Lamathe & P. Leroux. Superintegrability with third order invariants in A classification of plane and planar 2-trees, February quantum and classical mechanics, June 2002. 2002.
86 Annual Report 2000 - 2001 CRM Financial Report at 31 May 2002
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 organizations 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 The various sources of funding are presented in As one of the three mathematics institutes in Table 1. In 2001-2002, the CRM received the third Canada that jointly established the Mathematics instalment of $874,650 of a four-year NSERC of Information Technology and Complex institutes grant. This grant enables the Centre to Systems Network of Centres of Excellence fulfil its national mandate focussed on the (MITACS), the CRM supervises the activities of annual organization of scientific activities (postdoctoral fellowships, student scholarships, six of the Network’s research projects. It also visiting researchers, thematic scientific program promotes networking activities. The CRM as well as a general program of scientific received $97,000 in 2001-2002 for these tasks activities, and research support personnel). (For from the overall NCE funding provided to more details, see below the section titled MITACS. In addition, the research projects just “Financial statements”.) mentioned received $623,000 in NCE funding in the fiscal year. This last amount is not accounted The Comité d’étude et d’administration de la in the financial statement of the Centre because it recherche (CÉDAR) of the Université de is awarded directly to the researchers. Montréal provided an operating grant of $820,000 in 2001-2002. This budget is principally The CRM’s André Aisenstadt endowment allocated for the remuneration of the scientific contributed revenues of $76,206 in 2001-2002. personnel of the Centre. The budget also covers the release time of the faculty members who These funds serve for the Centre’s scientific direct the CRM and a part of the salary of activities, particularly the annual André administrative staff as well as some operating Aisenstadt Prize and Aisenstadt Chairs. The and computer expenses. CRM also received in fiscal year 2001-2002 (with the university’s departments of mathematics and The Fonds FCAR also supports the operations of computer science) revenue from the estate of the the CRM. The Centre received the final late Serge Bissonnette ($4,527). In addition the instalment of $210,000 of a three-year operating Centre received a grant from the Canadian grant in 2001-2002. This grant covers a part of Institute for Advanced Research (CIAR). the salary expenditures for the research support personnel, the publications personnel, the The CRM received other contributions totalling administrative personnel and operating costs. $420,181 from universities and partner An annual amount of $14,000 from this grant is organizations. The Institut des sciences set aside for the research activities of two college mathématiques (ISM) contributed funds for joint (CEGEP) researchers on release time to the CRM. CRM-ISM postdoctoral fellowships ($64,467) and the joint colloquium series ($7,685). Researchers The CRM manages the collective scientific from other Montréal and Québec universities activities and the general administration of the contributed $290,825 for joint postdoctoral Network for Computing and Mathematical fellowships, student scholarships, research
Modeling (ncm2). A budget of $83,894 was fellows, research professionals and invited allocated for these tasks in 2001-2002. In scholars. In addition, there were sponsorships addition, the CRM received $110,000 from the for two international conferences, RECOMB2001 Network to finance the research projects of three and STOC 2002, and a contribution of $4,500 for of its members. These amounts come from the the 2001 annual conference of the Canadian Network’s annual NSERC grant of $648,894. The Number Theory Association” The three events balance of this amount goes to the research were held in connection with the CRM’s projects of the four other founding centres of thematic years.
CRM Annual Report 2000 - 2001 87 Financial Report
The CRM generated revenues of $51,646 from its professors and researchers from other publishing programs (sales and royalties from institutions for prolonged periods; travel the CRM’s series with the American and accommodation expenses of invited Mathematical Society and Springer-Verlag New researchers (this includes the Aisenstadt York, and from the CRM’s in-house collection). Chairs and the visiting researchers taking Revenue from registrations to scientific activities was much higher than usual in 2001-2002 part in the scientific activities of the Centre); because three international conferences were postdoctoral fellowships and student accounted during fiscal year. These conferences scholarships; were RECOMB2001 (registrations totalling • scientific programs, that is, the annual $265,200), STOC2002 ($129,155) and CCC2002 thematic program; the general scientific ($29,980). Other scientific events generated program made up of events organized by registration revenue of $31,615. Other funds the CRM and of contributions to off-site came from compensation for services rendered scientific activities and events, mini- and operating costs ($12,724). programs on particular topics, colloquia Table 1 organized jointly with the ISM, and expenses associated with the four prizes of excellence Main sources de funding of the CRM, 2001-2002 in the mathematical sciences (the André Source $ Amount Aisenstadt Prize, the CRM-Fields Institute NSERC (Institutes and Initiatives Program) 874!650 Prize, the CAP-CRM Prize in Theoretical and Université de Montréal (CÉDAR) 820!000 Mathematical Physics, and the CRM-SSC FCAR (Research Centres Program) 210!000 Prize in Statistics); and finally, the scientific NSERC (Research Network Program, ncm ) 193!894 2 programs of the two networks, MITACS and National Centres of Excellence (MITACS) 97!000 ncm (workshops, seminars, lectures, Contributions from universities & partners 420!181 2 conferences); Other grants et revenue from endowments 201!535 Sales, registrations & other revenues 520!320 • the personnel involved directly in the Total 3!337!581 organization and management of the scientific programs; and Funding for Research • the research support personnel delivering In addition to the CRM’s grants, its researchers computer services and electronic-publishing obtain in funding for their research projects in services for the preparation of research the form of grants and contracts. Total funding for the research projects of CRM members was reports. about $2.5M in 2001-2002. The CRM directly managed about $672,000 in research grants. The rubric Publications includes production costs associated with the CRM’s publishing programs Financial Statement (remuneration of personnel preparing The following financial statement presents, on a publications as well as direct costs such as cash accounting basis, the revenues and printing of in-house collection publications). expenditures of the CRM for the fiscal year that Finally, the rubric Administration covers the ended on May 31, 2002. The financial statement remuneration of the CRM’s executive, the does not include the research funding of administrative personnel, the computer systems individual researchers. analysts (who support the Centre’s network, Expenditures are divided in three broad hardware and software used in its scientific, categories: Scientific Activities, Publications, and management, communications and administra- Administration. tive activities), and the communications personnel (Web, newsletter and annual report), The main line items under Scientific Activities are: as well as expenses related to executive and advisory business meetings, current operating • scientific personnel, that is, remuneration of costs, and computer equipment and professors and research fellows at the maintenance costs. Université de Montréal who undertake research on a full-time basis at the CRM; The 2001-2002 year-end surplus is minimal. expenses associated with the release of
88 Annual Report 2000 - 2001 CRM Financial Report
Financial Statement 2001-2002
NSERC- NSERC- FCAR- NCE- Univ. de Other Overall
Centre ncm2 Centre MITACS Montréal sources Total Scientific activities ! ! ! ! ! ! ! Scientific Personnel ! ! ! ! ! ! ! Visitors and Chairs 67 682 - 1 561 - - 21 955 91 198 Partnerships - - - - 15 000 45 000 60 000 Université de Montréal - - - - 690 498 50 559 741 057 Postdoctoral fellows 135 825 22 013 - - 2 427 280 871 441 136 Research professionals - - - - - 18 645 18 645 Students 3 127 83 995 - - - 17 700 104 821 Subtotal: Scientific personnel 206 633 106 008 1 561 - 707 925 434 730 1 456 857 Scientific Programs ! ! ! ! ! ! ! Thematic Years ! ! ! ! ! ! ! Math. Methods in Biology and Medicine 42 - - - - 258 092 258 133 Groups and Geometry 169 681 - - - - 61 404 231 085 Math in Computer Science 13 456 - - - - 104 415 117 871 Subtotal: Thematic years 183 179 - - - - 423 910 607 089 General scientific program 148 678 - - - - 40 174 188 852 Network activities - 8 436 - 38 989 - 200 47 625 Other 12 719 - 6 631 - 9 892 14 181 43 422 Subtotal: Scientific programs 344 576 8 436 6 631 38 989 9 892 478 465 886 988 Personnel - Scientific programs 155 637 - - - - - 155 637 Personnel – Direct research support 81 112 - 35 527 - - - 116 639 Total: Scientific Activities 787 957 114 444 43 719 38 989 717 817 913 195 2 616 121 Publications ! ! ! ! ! ! ! Personnel - - 88 668 - - - 88 668 Direct publication expenses - - - - - 6 143 6 143 Total: Publications - - 88 668 - - 6 143 94 811 Administration ! ! ! ! ! ! Personnel ! ! ! ! ! ! Executive 42 450 15 000 - 181 46 536 - 104 168 Administration and research 57 513 42 914 76 454 57 401 71 406 6 699 312 388 Systems experts & communications - 5 969 - - 31 437 861 38 267 Subtotal: Personnel 99 964 63 883 76 454 57 583 149 379 7 560 454 822 Advisory and other committees 13 919 - - - - 3 724 17 643 Operating expenses 37 231 1 321 8 914 2 213 12 353 11 656 73 688 Computer equipment 8 469 2 193 16 181 - 3 168 14 271 44 282 Total: Administration 159 583 67 397 101 548 59 795 164 901 37 211 590 435 Total Expenditures 947 540 181 841 233 936 98 784 882 717 956 548 3 301 367 Revenues ! ! ! ! ! ! ! Operating grants 874 650 - 210 000 - 820 000 - 1 904 650 Research networks, equipment and other grants - 193 894 - 97 000 - 201 535 492 429 Contributions from universities and partners - - - - - 420 181 420 181 Sales, registrations and other revenues - - - - - 520 320 520 320 Total Revenues 874 650 193 894 210 000 97 000 820 000 1 142 037 3 337 581 Surplus (Deficit) (72 890) 12 053 (23 936) (1 784) (62 717) 185 489 36 214
CRM Annual Report 2000 - 2001 89