SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

Topic #4  ------------   OP-SF NET 7.6  -------------   November 15, 2000
From: Jasper V. Stokman ( and Erik Koelink
Subject: Report on Laredo Summer School

>From July 24th to 28th 2000, Renato Alvarez-Nodarse, Francisco Marcellan, Walter
Van Assche and Rafael Yanez organized the first SIAG OP-SF Summer School 2000 on
Orthogonal Polynomials and Special Functions in Laredo, Spain. The program
consisted of five courses of four hours each, together with two afternoons of
short presentations in which the participants could report on their research. In
total there were about 55 participants, of which the majority (about 34) came
from Spain.
The central theme of the courses was the theory of orthogonal polynomials. Each
course had its own characteristic approach to the subject. The combination of
courses gave a very nice impression of the various modern aspects and interests
in this broad research field. Antonio Duran gave a nice introductory course on
matrix orthogonal polynomials, in which he explained the extension of various
important properties of scalar orthogonal polynomials to the setting of matrix
orthogonal polynomials. Ken McLaughlin gave a very stimulating lecture series, in
which he explained the connections between Riemann-Hilbert problems and
asymptotics of orthogonal polynomials. Jurgen Prestin lectured on polynomial
wavelets, in which orthogonal polynomials are used to construct and study
wavelets in polynomial spaces. Erik Koelink gave a course on the spectral
analytic approach to the theory of special functions, emphasizing the nice
applications to indeterminate moment problems, as well as applications to special
functions associated with doubly infinite Jacobi matrices. Finally, Jasper
Stokman's course gave an introduction to the theory of multivariable orthogonal
polynomials, emphasizing both the connection with the theory of one-variable
orthogonal polynomials and the representation theory of affine Hecke algebras.

The courses of the two undersigned were accompanied by detailed lecture notes.
The sheets and the lecturer's personal notes for the courses of Antonio Duran and
Ken McLaughlin were handed out to the participants. More extensive notes of all
the courses will appear soon in a book to be published by Nova Science

The summer school was held in Laredo, a very pleasant village on the Atlantic
coast between Santander and Bilbao. The climate was amazingly moderate for the
time of the year, with daily temperatures around 22 degrees centigrade, and about
four hours sunshine each day: perfect for a summer-school! Hotel Cosmopol, where
the lecturers and most of the applicants stayed, was excellent.

The pleasant surroundings soon led to various off-schedule activities by the
participants, as well as the organizers and lecturers. To name a few: Francisco
Marcellan and Renato Alvarez-Nodarse organized a group who went jogging on the
beach daily. Your reporters joined the group at a certain point, despite the fact
that their ``running-days'' have been over for quite some time. The runs were
tough, but very pleasant, and soon we decided to keep on jogging back home, even
to participate in organized runs in Holland! But back in everyday reality, and
especially without the inspiring presence of Paco Marcellan, our good intentions
have disappeared into thin air.

The rumour reached us that some participants found a completely different kind of
off-schedule activity: bars and dancing-clubs stayed open throughout the night,
and it seemed that some participants enjoyed night-life until sun-rise...--in
contrast to the present writers, who regularly entered an almost completely
deserted bar with extremely loud music in the evening to play pool, but returned
to the hotel before the serious night activities started!

We enjoyed this well-organized summer school very much. The organizers did an
excellent job, which led to a pleasant atmosphere and a good and well-balanced
series of lectures. We sincerely hope that the participants also feel that the
summer school has been worthwhile, mathematically as well as socially! Let's hope
that the next OPSF summer school in Germany will be as successful!

Jasper V. Stokman and Erik Koelink.

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