Modern Approaches in Asymptotics of Polynomials (07w5032)
Peter Borwein (Simon Fraser University)
Doron Lubinsky (Georgia Institute of Technology)
Edward Saff (Vanderbilt University)
The focus of the conference will be on sequences of polynomials, their zeros, and asymptotic behavior – as well as related potential theoretic issues, such as distribution of points on a sphere. The aim is to bring together experts who have different approaches to these questions – for example those using potential theory, those mixing approximation and number theoretic techniques on integer polynomials, and those using Riemann-Hilbert techniques for asymptotics of sequences of (mainly orthogonal) polynomials. There has not been any meeting focusing on this cross-section of researchers in the past few years. We expect the communication of ideas and methods from these different approaches will encourage new techniques and research across several topics.
We also expect that the young researchers present will benefit from exposure to the leading different approaches.
PROPOSED PROGRAM OF THE WORKSHOP
There will be 15 hour long talks and 15 half hour talks, and perhaps up to three short courses of three lectures. There will be ample time in between for questions, and discussion. There will be a focused problem session during the conference – probably half way though, so that participants can consider these for a few days during their stay in Banff.
RELEVANCE, IMPORTANCE AND TIMELINESS
In recent years, asymptotics of orthogonal polynomials have been used to study random matrices, combinatorial questions such as the longest increasing subsequence in a given sequence, Toda lattices, and weighted approximation. The potential theory that underlies some of these asymptotics has been used in distributing points on spheres and manifolds and in studying the distribution of zeros of sequences of polynomials. Zeros of integer polynomials, and the behavior of integer polynomials has been explored with a view to applications in number theory. The problems within the focus of the conference are widely applied, highly regarded, and very active areas of research. The conference would be timely, and have a different focus from any other that we know of.
Between 5 and 10 of the participants will be young researchers (including some graduate students and postdocs).