SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

CRM Workshop on Special Functions:
CRM, May 21-26, 1996

This is a report on the Atelier sur les méthodes algébriques et q-fonctions spéciales (Workshop on Algebraic Methods and q-special Functions), Centre de recherches mathématiques, Université de Montréal, Montréal, Québec, Canada, May 21-26, 1996.

Monday, May 20, was a national holiday in Canada (Victoria Day) and this pushed the start of the workshop to Tuesday morning. Luc Vinet, co-organizer with Pavel Winternitz and director of the Centre, opened the session at 9:00, welcomed the participants and dedicated the workshop to the memory of Waleed Al-Salam, who passed away April 14 of this year (see obituary). There were approximately seventeen invited speakers who gave hour-long talks; there were about fourteen contributed half-hour talks. David and Gregory Chudnovsky were invited but were unable to attend and their time on the program was taken by other events. Sergei Suslov was invited, could not attend, but Dick Askey delivered his lecture. Dick also gave his own lecture (more details later). There was indeed a heavy emphasis on q-special functions, both of one-variable Askey-Wilson type and of several-variable Macdonald type. The algebraic methods were highly refined and sophisticated, mostly based on root systems and associated mathematical objects such as double affine Hecke algebras. Here is an alphabetical list of the invited speakers and the titles of their lectures:

Contributed talks were given by N. Atakishiyev, R. Chouikha, P. Floris, A. Grünbaum, K. Kadell, M. Kapilevich, J. LeTourneux, K. Mimachi, A. Odzijewicz, V. Spiridonov, A. Strasburger, N. Takayama, F. van Diejen, L. Vinet. Ian Macdonald started his lecture Tuesday morning and finished it on Wednesday. Dick Askey gave an extra half-hour talk on Wednesday containing an overview of Askey-Wilson polynomials. Tom Koornwinder used another one of the hours originally scheduled for the Chudnovsky's to discuss René Swarttouw's web site which gives access to a vast collection of formulas and references for the polynomials contained in the Askey tableaux (q=1 and general q). The URL is\symbol{126}renes/index.html; see also the software announcement on Askey-Wilson computer algebra mini-project.

There were approximately sixty participants; as well, some members of the Centre dropped in on the lectures. The languages spoken at coffee and in the hallways appeared to be English, Russian, French, Japanese, Dutch, Polish. The weather was mostly delightful with a few evening showers. The University is in a scenic location near Mont Royal; the Pavillon André-Aisenstadt, which houses the Centre, is a beautifully designed and equipped academic building, with a wonderful view of the northwest of the city. Ian Macdonald gave the first lecture on Tuesday, Adriano Garsia gave the last one on Saturday, thus bracketing an intense period of leading-edge mathematics. It was generally agreed that the workshop was excellent both in organization and inspiration to the participants for future work. At the conclusion all applauded and thanked the organizers for this exciting conference.

Charles Dunkl

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