Seminar Event Detail

Integrable Systems and Random Matrix Theory

Date:  Monday, November 01, 2021
Location:  ZOOM ID: 926 6491 9790 Virtual (4:00 PM to 5:00 PM)

Title:  Discrete Darboux Transformations And Orthogonal Polynomials

Abstract:   Two basic discrete Darboux transformations in the theory of orthogonal polynomials are called Geronimus and Christoffel transformations. The consistency relation for those two gives the discrete Toda equation, a discrete integrable system, and it can also be considered as a relation between the elements of the Padé table.

In this talk, we are going to review the basics of discrete Darboux transformations for orthogonal polynomials. Then we'll show how such transformations can lead to Sobolev orthogonal polynomials, exceptional orthogonal polynomials, and indefinite orthogonal polynomials. Some associated asymptotic results for orthogonal polynomials and convergence results for underlying Padé approximants will be presented as well.

A recording of the talk can be found here.


Speaker:  Maxim Derevyagin
Institution:  University of Connecticut

Event Organizer:   Ahmad Barhoumi


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