SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

Topic #8   ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: OP-SF Net Editor (
Subject: Reports on SPOA VIII at Sevilla

The VIII Simposium sobre Polinomios Ortogonales y sus Aplicaciones was
held in Sevilla during 22-26 September 1997.  It is the eighth in a line
of symposia on orthogonal polynomials and their applications which are
held in Spain once a year. But it fits also into a series of major
European conferences on orthogonal polynomials (Bar-le-Duc, Segovia,
Erice, Delft, Sevilla). In particular, conferences of this last series try
to offer a state of the art, although no conference nowadays will cover
the whole are of orthogonal polynomials and special functions. Therefore
it seemed appropriate to ask a few people to report on the Sevilla
conference.  Bill Connett and Alan Schwartz describe the general setting. 
Next Arno Kuijlaars on the one hand and Margit Roesler and Michael Voit on
the other hand discuss, each from their own specialism and taste, the
scientific trends which became apparent from the lectures in Sevilla.

Topic #9   ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Bill Connett (
      and Alan Schwartz (
Subject: Report on SPOA VIII at Sevilla


Facultad de Matematicas
Universidad de Sevilla
Sevilla, 22-26 September 1997

This international conference had approximately 150 registrants. It
featured ten plenary talks and approximately 70 talks in the research
seminars. It also included the most memorable opening session in recent
memory. This session took place in the main university building which was
formerly the tobacco factory made famous in the opera Carmen. The Chairman
of the Organizing Committee, Professor Duran, entertained us with a list
of the organizations that had promised support for this conference, and
expressed his gratitude for that support, carefully titrated to reflect
the degree to which the organizations had fulfilled their promises.  This
candor was very much appreciated by those members of the audience that had
struggled with similar problems in the past. The Vice-Rector of the
University then gave an elegant and emotional speech comparing the
researchers' pursuit of mathematics to Don Pedro's pursuit of Carmen, with
a number of interesting asides about the complexity and volatility of our
beloved mathematics, and the dangers inherent in the pursuit of such a coy
and demanding muse. In any event, the audience was afire with passion, and
greeted the first plenary speaker, Herbert Stahl, as the young matador
leading the corrida. We were not disappointed, Professor Stahl gave an
elegant and enlightening performance. 

This was a very full meeting with sessions from 9:30 in the morning until
6:00 or 7:00 in the evening, but the organizers fitted in three very
pleasant events. The participants were treated to an evening tour of the
Cathedral (third largest in Europe), the Giralda tower (the bell tower,
formerly a mosque), Los Reales Alcazares (the Mudjehar Royal Palace) and
the Bario de Santa Cruz (former Jewish quarter), so we had ample
opportunity to contemplate Spain's Muslim, Jewish and Christian Heritage.
The conference dinner, a sumptuous affair, took place in the Gardens of
Villa Luisa. An evening of Flamenco was provided for Friday night. Of
course, many extracurricular excursions were mounted to sample the
delights of this wonderful city.  The program of plenary talks:

- Daniel Alpay, "Exact formulas for continuous and discrete orthogonal
polynomials with rational weights and applications to solutions of
inverse spectral problem"

- Alexandre Aptekarev, "Asymptotics of general multiple orthogonal

- Richard Askey, "Combinatorics of the classical orthogonal polynomials"

- T. H. Koornwinder, "A survey of symbolic computation for orthogonal
polynomials and special functions"

- A. L. Levin and D. S. Lubinsky (speaker), "Orthogonal polynomials for
exponential weights"

- A. Martinez, "Asymptotic properties of Sobolev orthogonal polynomials"

- E. A. Rakhmanov, "Constrained equilibrium measure and zero distribution
of discrete orthogonal polynomials"

- E. B. Saff, "Zeros of orthogonal polynomials"

- Herbert Stahl, "Spurious poles of Pade approximants"

- Vilmos Totik, "Orthogonal polynomials with respect to varying weights
and the so called universality law"

Special mention must be make of Professor Lubinsky's presentation, which
set a new and very high standard for multimedia presentations.  Every
theorem by a famous person was accompanied with an historic photograph or
drawing, and the mathematics wizard managed to place an interesting and
appropriate cartoon on every slide, frequently drawing attention to some
of the more surprising moments in the line of argument.  This sets the new
standard in presentation which Doron Zeilberger can now aim for.

All the participants were grateful for the efforts made by the organizing
committee A.J. Duran, P. Lopez-Rodriguez, and J.C. Medem of the University
of Sevilla. The gratitude extended beyond their efforts in organizing the
meeting, providing comfortable accommodations, and arranging the cultural
events. We are all grateful for the opportunity to visit this beautiful
old city.

William C. Connett and Alan L. Schwartz

Topic #10  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Arno Kuijlaars (
Subject: New trends in OP from the Sevilla conference

New trends in orthogonal polynomials from the Sevilla conference

    The impression from the Sevilla meeting is that the field of
orthogonal polynomials is still very much alive.  A number of new
directions have appeared where new results were obtained and more
developments are to be expected.  Of course, my impression is biased by my
own interests, which is in asymptotics. This area was very well
represented in Sevilla and in the plenary talks in particular. 
    E.A. Rakhamnov reported on his very elegant results on asymptotics for
polynomials satisfying a discrete orthogonality. This work has already
attracted a number of follow-up papers, and the interest is continuing to
grow, especially in the direction of strong asymptotics. 
    Another direction that has grown in importance over the last few
years, is the theory of matrix orthogonal polynomials, as witnessed by the
plenary talks of D. Alpay and E.B. Saff. 
    There is continuing interest in the theory of Sobolev orthogonal
polynomials, with main contributions from the large and active Spanish
school. A review on asymptotic results was presented by A. Martinez. It is
clear that progress has been made in recent years. 
    Multiple orthogonality has been a favourite with the Russian school.
It deserves wider interest, because of its connections with simultaneous
Pade approximation and irrationality proofs in number theory. The topic
was reviewed by A. Aptekarev. 
    Of basic importance remain the applications of orthogonal polynomials
in mathematical physics. Relations with integrable systems and random
matrices were discussed in a number of talks (e.g. Chen, Grunbaum,
Kaliaguine, Totik). One of the highlights of the Sevilla meeting was V.
Totik's announcement of a proof of the universality conjecture in random
matrices using clever estimates on orthogonal polynomials. This kind of
interaction with other areas keeps our field alive. 

Arno Kuijlaars

Topic #11  ------------   OP-SF NET 4.6  ------------ November 15, 1997
From: Margit Roesler ( and Michael Voit
Subject: Impressions from the Sevilla conference

Impressions from the Sevilla conference

This symposium has its roots in a series of Spanish meetings during the
1980's. Since then, it has become a constantly growing international
meeting ground for scientists working on special functions and their
applications. The present meeting was attended by about 150 participants
from all over the world.

There were 10 one-hour plenary talks (see the list in the report of Bill
Connett and Alan Schwartz), and about 70 research talks which were held in
four parallel sessions. In fact, the program was quite dense, and it was
often difficult for us to decide in which session we should attend.
Nevertheless, we had the impression that the arrangement of the sessions
was carefully planned; as far as possible, the afternoon sessions were
dedicated to particular topics. Here the variety was very broad: there
were sessions on more classical aspects of orthogonal polynomials
including asymptotics, zeros, and moment problems, as well as Sobolev
orthogonal polynomials, q-special functions, and multivariable aspects.
Several sections were devoted to applications in approximation theory,
differential equations, mathematical physics, and probability theory.
Finally, a special computer algebra session was organized by SCAGOP
(Spanish Computer Algebra Group on Orthogonal Polynomials). 

Compared to earlier conferences of this kind (like Delft or Granada), we
here in particular enjoyed a growing emphasis on multivariable structures
and a strong impact from problems in mathematical physics and probability
theory. As usual at conferences of this size, the scientific level of the
talks was varied. Among the plenary lectures, we were in particular
impressed by the opening lecture of Herbert Stahl and the excellent
performance of Doron Lubinsky.

The organization of the symposium was almost perfect - except for the
queues at the computer facilities. Most participants were conveniently
accommodated at the Residence Hernando Colon. Besides the intense
scientific part of the conference, an extraordinary program of social
activities was offered; here we especially remember the conference
dinner in the Gardens of Villa Luisa and the (almost?) authentic
Flamenco show on Friday night. The organizing committee, consisting of
A.J. Duran, P. Lopez-Rodriguez, and J.C. Medem, has really done a great

Margit Roesler and Michael Voit

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