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.
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.
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.
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.
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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