Centre de recherches mathématiques, Annual Report 1995-1996

Centre de recherches mathématiques
Annual Report 1995-1996

Table of Contents

A word from the director

Recent thematic years at the CRM have alternated between fundamental domains of the mathematical sciences and applied ones. The year 1995-96 was decidedly under the applied banner. The first semester was devoted to numerical analysis and the second to applied topics in analysis (spline functions, wavelets, special functions, neural networks and finance). The scientific meetings were praised and extremely well received by the scientific community: more than 700 researchers visited the CRM for these events. We trust that the years to come (combinatorics and group theory (96-97), statistics (97-98) and number theory (98-99)) will maintain this level of popularity and scientific quality.

The industrial program at the CRM, started in 93-94, is still expanding. Four of our conferences and workshops were organized jointly with the CERCA and the CIRANO, two liaison and transfer research centres based in Montreal. The CIRANO/CRM conference on mathematical finance was supported by a number of firms and financial institutions. Four industrial postdoctoral fellowships, jointly sponsored by the CRM and non-academic partners, were given to young scientists working on applied problems. Finally, the numerical physics group PHYSNUM has joined the CRM. Because of its industrial contacts, this group has successfully helped Ph.D.'s with backgrounds in fundamental fields make the transition to industrial settings. Many PHYSNUM/CRM postdoctoral fellows have indeed found positions in industry, often before the end of their stipend.

The Canadian mathematical scene is always changing. A consortium of several universities in western Canada has created the Pacific Institute for the Mathematical Sciences (PIms) and the CRM wishes this new institute well. The CRM, the Fields Institute and the PIms are about to present a grant application to NSERC which, in addition to supporting PIms, would include funds to launch new initiatives of national scope. This national network NNCMS (National Network for Collaboration in the Mathematical Sciences) will offer a postdoctoral fellowship program for Ph.D.'s making the transition to industry (complementary to the one at the CRM), financial support for the organization of schools and conferences, a program for meetings on mathematical problems from industry and various programs for graduate students. The CRM would assume the chairmanship of the NNCMS management board during its first year of operation.

The recent growth of the CRM and its expanding (national) responsibilities have required the appoint ment, this past year, of a second deputy director. Yvan Saint-Aubin has assumed this function.

Whoever is involved in science nowadays knows how scarce funding is becoming. Therefore CRM is proud to have received, this year, a 15% increase in its three-year FCAR grant (programme Centre) for 1996-1999. The Fonds FCAR has supported the CRM since the early seventies and its role has always been crucial in maintaining the diversity of our activities. In 1994 NSERC recommended the creation of a CRM-Fields coordinating committee and established a formula for the funding of activities outside Québec. This committee first visited the CRM in October 95 and was favourably impressed by our efforts in pursuing our national mission. Indeed the budget for 94-95 (already committed when the rule was established) showed significant progress toward the goal set by NSERC. And the predictions for 95-96 indicated that the target would be met; in fact, these have been exceeded. Finally, in spite of severe budget cuts, the Université de Montréal has maintained its substantial financial support to the CRM.

The year 95-96 has been marked by several events highlighting the leadership of the CRM at the local, national and international level. We hope that this report will convey the diversity of the Centre's accomplishments. I take the opportunity to thank all those who have made them possible: the deputy directors Martin Goldstein and Yvan Saint-Aubin; the regular, associate and visiting members; the graduate students; the members of our various committees; the organizers of the scientific events; the great staff of the CRM; the administration of the Université de Montréal; all our partners and of course, André Aisenstadt.

Luc Vinet, Director


Presenting the CRM

The Centre de recherches mathématiques (CRM) was created in 1969 by the Université de Montréal through a special grant from the NRC. It became an NSERC national research centre in 1984. It is currently funded by NSERC (Natural Sciences and Engineering Research Council), by the Government of Québec through the Fonds FCAR pour l'aide et le soutien à la recherche and the Université de Montréal, and by private donations. The mission of the CRM is to do research in mathematics and closely related disciplines and to provide leadership in the development of the mathematical sciences in Canada.

The CRM accomplishes its mission in several ways:

  • it maintains a local group of researchers chosen mainly from departments of mathematics and statistics, but also from departments of computer science, physics, economics, engineering, etc.;
  • it organizes a series of scientific events each year, around a given theme (distinguished lecture series, workshops, conferences, summer schools, visitor programs, etc.);
  • it works actively at developing contacts with industry through joint activities with liaison and transfer research centres (CERCA and CIRANO), research centres doing applied research (CRT, GERAD and the LACIM) and directly with indus tries. Activities range from the organisation of sci entific conferences to an industrial postdoctoral fel lowship program;
  • it publishes some 150 technical reports and about 6-8 books per year. Some of its collections are published jointly with the AMS and with Springer Verlag. In addition it produces videos and software;
  • each year it invites, through the Chaire Aisenstadt, one or two prestigious mathematicians to give advanced courses;
  • it awards three prizes yearly: the CRM-Fields Prize recognizing major contributions to mathematics, the Aisenstadt Prize given for outstanding work done by a young Canadian mathematician, and the CAP-CRM Prize for exceptional achievement in theoretical and mathematical physics;
  • it has signed protocols of collaboration with other national institutes: the Steklov Institute (Moscow) and the Nankai Institute of Mathematics (Tianjin);
  • it informs the community of its activities through its Bulletin (2 or 3 issues per year) and through its rich web page www.CRM.UMontreal.CA;
  • it offers first class computer services to its visitors. It is currently working on expanding the network links among the local community.
  • The CRM fulfils its national mission by involving the largest possible number of Canadian mathematicians in its scientific programs, both as participants and as organizers. It also supports many events taking place outside Montréal and the Province of Québec. It is recognized worldwide as one of the major institutes in the mathematical sciences. The director of the CRM is supported by two managerial structures: the Board of Directors and the Scientific Advisory Committee. The Scientific Advisory Committee is a prestigious group of internationally renowned mathematicians, both Canadian and non-Canadian, who approve scientific programs and thematic years, choose recipients of the CRM-Fields and the Aisenstadt prizes, and suggest new scientific ventures to explore. The president of the Canadian Mathematical Society is a member ex officio. This structure is augmented by the CRM-Fields committee that oversees the collaboration and coordination between the two institutes and assures the truly national role of both. The members are representatives of the Canadian scientific community.

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