Centre de recherches mathématiques, Annual Report 1996-1997

A word from the director

It is gratifying to see that 28 years after its creation, the CRM consistently generates outstanding research programs and initiatives. Internationally renowned, the CRM is playing a leading role in the development of the mathematical sciences in Canada, by supporting research and training projects in both fundamental and applied mathematical sciences, by fostering interdisciplinarity, by reaching out to the business and industrial sectors and by contributing actively to the organization of mathematical research in the country. The year 1996-1997 has seen the CRM more active than ever in all these directions. The present report purports to reflect these activities, some of which I will now highlight.

Every year, a good fraction of the CRM's activities are organized under a special theme. This allows a concentration of expertise in areas of high interest so as to stimulate interactions and give young researchers first class training. It was certainly most opportune to devote 1996-1997 to Discrete Mathematics in view of the recent developments in this vast field and of the importance it has in domains such as computer science, management and engineering. Moreover, despite the presence in Canada of many specialists in Discrete Mathematics, the area had not yet been the object of a special program in this country. The CRM coordinated its activities with those of Berkeley's MSRI which was holding connected events under the same banner during the year. This allowed for an even greater impact of the programs on the discipline.

The CRM special year principally covered two subjects: Combinatorics and Group Theory. In addition to the CRM Summer School in Banff, ten workshops (nine in Montreal, one in Waterloo) focused on various aspects of these two topics. The Aisenstadt chair, which allows the CRM to play host each year to distinguished scientists, is traditionally integrated with the thematic activities. This year, it was held by László Babai from the University of Chicago and the Fields medallist Efim Zelmanov from Yale University. The whole year proved extremely fruitful and I wish to thank all those (organizers, speakers, participants, support staff) who enthusiastically contributed to making this special program such a success.

In 1997-1998, the CRM will be presenting another Canadian première: a full special year in Statistics. A distinguished scientific committee chaired by Nancy Reid is coordinating a program that promises to be very exciting and will involve a large number of the Canadian statisticians. To further develop its links with the Statistics community, the CRM, in collaboration with the Statistical Society of Canada, created the CRM-SSC prize in Statistics. It will be awarded for the first time at the 1998 Annual SSC meeting. The CRM also signed an agreement with Springer-Verlag to establish a CRM Series as part of their main Series in Statistics.

In addition to its thematic activities, the CRM also maintains a general scientific program consisting of timely events held in Montreal and elsewhere. With the cancellation of NSERC's conference grant program, the CRM, along with the other Canadian Institutes, has taken over the responsibility of sponsoring meetings across the country. Some thirteen events were thus organized and funded (in part) by the CRM during 1996-1997. I was proud to be personally involved in the Symposium in honour of Jií Patera and Pavel Winternitz, two of CRM's distinguished scientists who have contributed enormously to the life of our institute and its international reputation, and in the workshop organized (at no cost to the Canadian taxpayers) by the CRM at the Nankai Institute of Mathematics in China, in the framework of a collaboration agreement between this institute and the CRM.

Apart from the newly created prize in Statistics, three other prizes are sponsored by the CRM. The 1996-1997 recipients were: James Arthur (CRM-Fields Institute prize), Henri Darmon and Lisa Jeffrey (André-Aisenstadt prize) and Ian Affleck (CAP-CRM prize).

The CRM publishing division was very busy this past year with an output of almost one book per month. I would like to mention two titles in particular: Ioannis Karatzas' "Lectures on the Mathematics of Finance" already advertised as a best-seller by the AMS, and Donald Knuth's "Stable Marriage and its Relation to Other Combinatorial Problems," the English version of Knuth's Aisenstadt Lectures originally published in French by the CRM. As well, close to one hundred and fifty research reports were produced in 1996-1997 by the members of the CRM.

In retrospect, the year 1996-1997 will certainly be remembered for the creation of the Network for Computing and Mathematical Modeling (ncm2), a major and decisive event in the development of industrial mathematics in Canada. Founded in 1996, this university-industry consortium was awarded a five-year grant of $600 K per year by NSERC in the framework of its research network program. Only three such grants were awarded in this year's competition. The ncm2 brings together five major Montreal-based research centres working in related areas and some twenty industrial partners. Apart from the CRM with its tradition in applied mathematics, the research centres are: CERCA, CIRANO, CRT and GERAD. The integration of these research powerhouses in the ncm2 has taken their collective R & D capacity as a network to an extraordinary level. The research program of the ncm2 is organized around three themes: (i) risk management, (ii) information processing, (iii) transportation and telecommunications. The ncm2 has proved very attractive to non-university organizations as it provides a one-stop access to a broad and world class expertise. In leading this initiative, the CRM has shown that mathematical sciences can advantageously compete with other disciplines for the funding of large-scale projects. It also assumed its responsibilities towards the development of career opportunities for its trainees. In its report, the international site visit committee wrote: "With its impressive participant base, it (the ncm 2) can arguably become the outstanding industrial-university mathematical research program in the hemisphere." We also think that the potential of the ncm2 is enormous.

In spite of the regional tensions that the NSERC research network competition created, the CRM has remained committed to playing a leading national role in the development of Canadian Mathematics. This is reflected in the collaborative relations it has with the Fields Institute and PIms, with AARMS and CCARMS, with a number of universities and with various Canadian Associations, and professional societies. The coming year will see critical decisions being made for the future of Mathematical Sciences in Canada as the CRM and the other institutes seek refinancing in the framework of the reallocation exercise. A first step in this process has been the work of the Canadian Mathematics Review Committee whose visit in Quebec was steered by the CRM. In this context, I trust that the present report clearly illustrates how cost-efficient the CRM is. What this institute accomplishes with the level of funding it gets is remarkable. Yet this level is not optimal. For instance, let us consider the situation with postdoctoral fellowships. Thanks to collaboration with the ISM, the ncm2 research centres and contributions from its members, the CRM could count some twenty-two postdoctoral fellows in residence in 1996-1997. This is far from sufficient however for an institute of its calibre. In the same vein, there should be more funds to support long-term visitors the return would be enormous.

The past twenty-eight years have shown how great a vehicle the CRM is for the development of science in Canada. It owes its success to the goodwill and the generosity of the many who contributed in one way or another to its activities, and I wish to thank them again warmly. I also take the occasion to acknowledge the continued support of our contributors, in particular NSERC, the Université de Montréal, FCAR, the Canadian Institute for Advanced Research and the André and Nussia Aisenstadt Foundation. With the growing importance of knowledge in the global economy, it is clear that the CRM has the potential to play in the future an expanded strategic role in R & D. I trust that this, as well as its essential role in the promotion of research in mathematics in Canada, will be recognized more and more.

Luc Vinet, Director

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27 May 1998, webmaster@CRM.UMontreal.CA