### A promenade on r-fold symmetric multiple orthogonal polynomials

Mathematical Physics Seminar

28th October 2022, 1:45 pm – 3:30 pm

Fry Building, 2.04

The talk is about sets of polynomials satisfying a linear recurrence relation of order higher than 2 involving three terms only, with the last recurrence coefficient always nonzero. For positive recurrence coefficients in such recurrence relation, one can define a vector of measures with respect to which the original polynomial sequence is (multiple) orthogonal. The (multiple) orthogonality measures are then supported in a star in the complex plane. So the talk will start with a promenade in the domain of multiple orthogonality including their importance, its usefulness, along with a brief discussion on their applicability to number theory, spectral theory and random matrix theory. The main focus will be on a vector of multiple orthogonality measures whose components are all supported on the same star set in the complex plane. I will discuss on the asymptotic properties for the ratio of consecutive polynomials as well as on the asymptotic zero distribution.

*Biography:*

Talk recording: https://mediasite.bris.ac.uk/Mediasite/Play/50a1f09b1ac14b2287d230ce54c40c601d

*Organiser*: Thomas Bothner

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