Extract from OP-SF NET

Topic #8 --------------- OP-SF NET --------------- July 13, 1995

From: Tom H. Koornwinder thk@fwi.uva.nl
Subject: Reports on Mini-Program Toronto

The Mini-Program on Special Functions, q-Series and Related Topics (see OP-SF Net 2.2, Topic #5) was held during 12-23 June, 1995 at the University of Toronto. I solicited short reports of the Miniprogram from Marcel de Jeu and Doug Bowman, and I added one myself. All these reports give impressions rather than detailed and formal accounts. Finally, George Gasper communicates a short note.

Report by Marcel de Jeu jeu@math.mit.edu

From June 12 to June 23, 1995, a workshop on special functions, q-series and related topics was held at the University of Toronto, under the auspices of the Fields Institute For Research In Mathematical Sciences. As the title already indicated, a great variety of subjects were to be expected, both in the five minicourses during the first week and in the contributed lectures during the second week. Roughly speaking, the minicourses and the lectures could be divided into three groups. The first group was concerned with special functions and q-series as such (mostly in one variable), the second group concentrated on the relationship between special functions, q-series and representation theory (not necessarily in one variable), and the third group treated miscellaneous aspects of special functions, as diverse as e.g. connections with computer algebra, combinatorics, probability theory and superbly converging algorithms for approximations of pi. The topics in the latter category had the virtue of appealing easily to a general uninitiated audience, but it did not go unnoticed that the audiences for the first and second group of topics appeared to be somewhat disjoint. Even though the theory of special functions and the representation theory of (quantum) groups are related, this has apparently not encouraged too many people to be engaged in both fields - although there are of course exceptions. At any rate, anyone interested in special functions must have found something to choose from at this workshop - the diversity of the program was a guarantee for that.

Report by Doug Bowman bowman@math.uiuc.edu

The weather in Toronto for the Fields Institute session on q-series and special functions was quite nice making attendance quite a pleasure. The first week talks were tutorials which I think were moderately successful, some drifted into the informal talk category, some were quite competent introductory surveys of their subject, while others were aimed at students and were replete with exercises. I understand that one person even handed in solutions! I think that I gained something from all that I attended. I found the atmosphere among the international participants friendly, especially the second week, when I think people had relaxed somewhat. The talks during the second week were in general well presented, and toward the end a disagreement even broke out after one talk livening up the atmosphere. One fellow could be counted on throughout the conference to provide comic relief, but I'm not sure that this was intentional. Another highlight for me was attending planning sessions on a Bateman project revision. I have always loved tables of special functions.

Report by Tom Koornwinder thk@fwi.uva.nl

The Toronto workshop was great for me, first of all because I could meet there so many colleagues in my field. Concerning the program, I was in particular excited by the last week, which was more research oriented than the first week and was also more intensive. The regular program (9-12 a.m. and 1.30-5.00 p.m.) was already quite tough in the second week, but moreover there was a busy fringe program: two business meetings on a possible Askey-Bateman book project and two evening sessions on Multivariable Special Functions, Algebraic Structures and Mathematical Physics, organized by Luc Vinet. Some of the lectures I heard there were among the most memorable things of my two weeks in Toronto.

Compared to the Columbus NATO Advanced Study Institute of 1989 there was less emphasis on classical analysis aspects and much more on multi-variable, algebraic, formal and combinatorial aspects. In this respect Toronto may not have given a completely balanced survey of the state of the art in the theory of orthogonal polynomials and special functions, but this will be easily compensated by some other meetings in the past (e.g. Delft 1994) or in the future.

The first week was devoted to introductory minicourses. Then the program was much more relaxed, starting only at 9.30 a.m. and often ending at 3 p.m. It is my feeling that we might have been slightly more effective here if we had defined better for each course what knowledge could be assumed and if some or all of the courses would have comprised four rather than three one-hour lectures. There were some tutorial sessions in connection with the minicourses. For one topic this was given by an advanced PhD student, for the other topics it was done by the lecturers themselves. Since this was kind of an experiment, I am curious to hear from participants whether they appreciated these tutorials. Another event in the first week, which I personally liked very much, was a demonstration by Christian Krattenthaler of his Mathematica package implementing part of the book by Gasper and Rahman on Basic hypergeometric series.

The setting of the workshop, at the Oxford and Cambridge modeled St. George campus in central Toronto, was superb. The lectures were in University College, the building where the University of Toronto started in the 19th century. Never before at a conference have I had registration and refreshments service in such a nice room as here. It was surprising that this historic building housed such well-equipped lecture rooms, although better air conditioning would have been welcome when outside temperatures rose to 36 degrees Celsius. The lecture room for the main lectures in the second week compensated for this by having all doors open, including a door to the street. Sometimes, a concert on nearby bells enlivened the lectures. This room was very special by its high balcony and by the long stairs coming down to the ground level. There was something very theatrical about this room, and indeed, some of the lectures and subsequent discussions were theater.

Social events included a barbecue in the first week in the pleasant Hart House quadrangle and a banquet in the second week in the splendid Great Hall of Hart House. Both occasions were also an opportunity for fraternizing with the people of the parallel PDE workshop of the Fields Institute. The banquet concluded with a piano recital by Christian Krattenthaler, a man with many-sided talents.

The Fields Institute organizational machinery had some trouble getting off the ground in the first week, but gradually everything went quite smoothly, the congress secretary was kind and efficient, and the refreshments in the breaks were delicious. David Masson, coordinator of the scientific program (and of much more) has really done a great job.

Note by George Gasper george@math.nwu.edu

On June 16th, for submitting the "best" set of solutions to three exercises in the "q-Series" Minicourse by George Gasper, Dennis Eichhorn was awarded an autographed copy of the N.M. Atakishiyev and S.K. Suslov Russian translation of the Gasper and Rahman "Basic Hypergeometric Series" book. It was autographed by the authors, translators, and R. Askey who wrote the Foreword in the book.
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