Topic #4 ------------ OP-SF NET 7.6 ------------- November 15, 2000 ~~~~~~~~~~~~~ From: Jasper V. Stokman (firstname.lastname@example.org) and Erik Koelink (email@example.com) 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 Publishers. 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.