Centre de recherches mathématiques, Annual Report 1996-1997


The CRM is strongly committed to its national mission. In this direction, it takes measures to ensure that the largest possible number of scientists across Canada benefit from its activities and become involved in their planning. For instance, it appoints to its Advisory Committee eminent Canadian scientists from various parts of the country; it is present at all important forums where the future directions of the Canadian mathematical sciences are discussed; it urges its organizers to make efforts to ensure the participation of the Canadian specialists in their activities; it seeks Canadian graduate students and postdocs to take part in its programs; it has made the hiring of Canadian postdocs from outside Quebec a priority; it organizes and supports scientific events across the country; and it collaborates with Canadian institutes, societies and associations.

The CRM also plays a major national role through the leadership it exerts in the selection of its scientific programs, the infrastructure it offers, the interactions it has developed with various disciplines as well as with the business and the industry sectors. Finally, it collaborates with the Montréal Universities in organising scientific activities in the Montréal area such as the CRM-ISM colloquium, and through its partnership agreements.

The CRM operates in the two official languages of Canada and is highly visible on the international scene. In keeping with its national role, it is coordinating its activities with the Fields Institute, PIms, CMS, CAMS, SSC, CAP, AARMS, CCARMS, and collaborating with technology transfer centres as well as with other institutes abroad. These aspects of the CRM's national role are described below.

Fields Institute

The importance of coordinating the scientific activities of the CRM and the Fields Institute (FI) was stressed when the FI was created. Since the beginning communication between the two centres has been excellent. Thus, the directors have always been in regular contact; also, the CRM has appointed to its Advisory Committee (AC) R. Moody who was then on the FI's Scientific Advisory Panel (SAP); D. Dawson has been on this CRM AC for the last four years and has remained a member during his first year as director of FI. Thus he is very well informed of the CRM plans; similarly, the FI nominated F. Lalonde who is on our AC to its SAP. In 1994, at the request of NSERC, the CRM-FI coordinating committee was formed to monitor and facilitate the coordination between the two institutes.

As a result there has been little repetition in the scientific programs of the two institutes and more importantly, beyond the coordination, much collaboration has developed. In this vein let us mention the following.

The CRM-FI prize awarded in recognition of outstanding accomplishments in the mathematical sciences in Canada was created in 1994. This year's winner is James Arthur of the University of Toronto. The administrative responsibility in this matter alternates each year between the CRM and the FI. Nominations for the 1997 prize are currently being received.

The CRM and the FI have jointly sponsored many scientific events. J. Patera from the CRM co-organized a yearlong theme program at the FI. The CRM is publishing the proceedings of a workshop held at the FI and vice versa. Some postdocs have shared their time between the CRM and the FI and there have been many exchanges and visits between the scientific personnel of the two institutes.

The CRM and the FI were both involved in the development of the National Network for Collaboration in the Mathematical Sciences (NNCMS). Moreover, in 1995, the CRM took the initiative of bringing together the FI and PIms in an effort to develop a national network for computing in the mathematical sciences. A proposal was presented to NSERC in the framework of its Major Facility Access Program. Although the project was not funded, $75K was given as seed money.

It is certainly the intent of the CRM and the FI to continue their collaboration in the future. In 1997, the CRM and the FI co-sponsored 9 scientific meetings, and collaboration in this area should remain this high in the years to come. A good example is the 1998 Conference on Formal Power Series and Algebraic Combinatorics which will take place at the FI and to which the CRM has already committed funds. In line with a recommendation of the CRM-FI coordinating committee, this meeting will have the additional merit of extending to 1998 and outside Montréal, the 1996-1997 theme year in combinatorics of the CRM. In 1998 CRM regular member D. Sankoff will organize one of the events to be held at FI in their theme year on probability.

Pacific Institute for the Mathematical Sciences

The CRM has a long tradition of collaboration with the western universities that are now part of the PIms consortium and with many of the scientists that are much involved in the management of this institute. We want and will do all we can to maintain and expand such collaborations through the new PIms.

In recent years the CRM has given substantial support to activities organized by people and universities that are today part of PIms. In some cases, these were important elements of CRM thematic programs. To name a few: the summer school of 1993 on mathematical biology organized at UBC by R. Miura this school actually launched the 1993 CRM theme program on dynamical systems; the summer institute in mathematical physics also organized at UBC in the following year by J. Feldman and L. Rosen; the workshop on organic mathematics organized by J. Borwein through the Centre for Experimental and Constructive Mathematics (CECM at SFU) and connected to the 1995 CMS winter meeting at Simon Fraser University; the first CRM summer school in Banff had G. Semenoff, the 1996-97 director of the UBC site of PIms, as its main organizer, etc.

Among activities to come that are largely supported by the CRM and organized by PIms members, we should like to mention the 1st Vancouver Meeting in Probability which is being organized by M. Barlow and E. Perkins from UBC and which will take place this summer as well as the 1998 Summer School in Banff on Algebraic Cycles organized under the chairmanship of J. Lewis from the University of Alberta and an important part of the CRM 1998-1999 program in Number Theory and Algebraic Geometry.

It is the CRM's wish to maintain and expand collaboration of that sort with PIms and to encourage and support activities organized by PIms that would prolong and complement the theme programs of the CRM. We also envisage exchanges of postdocs between PIms and CRM (S. Kallel who is currently a postdoc at CRM will move to PIms next year) and a joint internship program in business and industry for undergraduates. This last project could be a step towards connecting our respective networks for research in industrial mathematics.

Canadian Associations and Professional Societies

With the development of the NNCMS project, two regional university associations have been created: the Atlantic Association for Research in the Mathematical Sciences (AARMS) and the Central Canada Association for Research in the Mathematical Sciences (CCARMS). The CRM is already involved with these organizations and looks forward to developing closer ties. Of the 1997 CRM-sponsored activities, three will be held at universities that are part of AARMS (Memorial [1] and Dalhousie [2]) and one at an institute that is part of CCARMS, namely the IIMS of the University of Manitoba.

The CRM is also much involved with a number of professional societies (CMS, CAMS, CAP, SSC) related to the mathematical sciences. Over the years and particularly recently, the CRM has funded many meetings that were held under their ægis.

An important segment of the Canadian mathematical community gathers at the winter and summer meetings of the Canadian Mathematical Society (CMS). This year the CRM subsidized the session on Complex Analysis and Geometry at the winter meeting (Western Ontario, December 1996). It is supporting the International Linear Algebra Society Symposium on "Fast Algorithms for Control, Signal and Image Processing" connected to the session on Linear Algebra of the CMS Summer Meeting in June 1997 (Winnipeg). The president of the CMS is an ex-officio member of the CRM Advisory Committee and is thus able to make the case directly for activities that the CMS would wish the CRM to support.

The CRM and the Canadian Association of Physicists (CAP) have jointly created the CAP-CRM Prize recognizing outstanding work in theoretical and mathematical physics. (CRM is responsible for seeking nominations and managing the international committee that chooses the yearly winner.) The CRM is subsidizing this summer (1997) the CRM-Fields-CAP Summer Workshop in Theoretical Physics to be held at Queen's University. The Kingston Summer Workshops have been organized and held at Queen's for many years. However, with the cancellation of the NSERC non-core programs, support for this event had disappeared. With this summer workshop, the CRM joins the effort to revive this tradition.

Each year the Canadian Applied Mathematics Society (CAMS) holds a general meeting which takes place this summer at the Fields Institute. The CRM is supporting this conference. J. Bélair from the CRM is vice-president of the Society.

The 1997-1998 theme year in statistics has given the CRM the opportunity to collaborate with the Statistical Society of Canada (SSC). In particular, the CRM will be supporting the SSC annual congress of 1998 (and possibly of subsequent years). The CRM has also proposed to the SSC the creation of a prize to recognize important work by Canadians in Statistics.

Foreign Institutes and Organizations

The Université de Montréal is part of the 3x3 Canada-China Consortium with UBC, Toronto and McGill in Canada; Beijing, Nankai and Tsing Hua Universities in China. The CRM took the lead in writing the mathematics component of the multi-million proposal presented last Summer to CIDA by the four Canadian universities. (The final answer from CIDA has not yet been released but it is believed that, unfortunately, it will be negative.) To further develop these collaborations a protocol of exchange between the CRM and the Institute of Mathematical Sciences at Nankai University has been signed. A first week-long joint meeting was held in Tianjin in August 96. Efforts are being made to find funding to carry on and develop these exchanges.

The CRM and the Mathematical Sciences Research Institute (MSRI) in Berkeley had part of their 96-97 theme year devoted to combinatorics. Coordination between the two institutes prevented conflicts and flavoured complementarity in the programs. Several scientists attended events at both institutes.

This fall, the CRM will host a regional meeting of the American Mathematical Society (AMS). In addition to the plenary talks there will be 12 parallel sessions, and more than 200 participants are expected.

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27 March 1998, webmaster@CRM.UMontreal.CA