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A Symbol Calculus for Recurrence Operators and its Relations to Spectral Dynamics of Random Matrices

Analysis, Dynamics, and Applications Seminar

A Symbol Calculus for Recurrence Operators and its Relations to Spectral Dynamics of Random Matrices
Series: Analysis, Dynamics, and Applications Seminar
Location: Hybrid, Math 402/Online
Presenter: Nick Ercolani, Department of Mathematics, University of Arizona

 

There is a great deal of recent literature that connects the asymptotic analyses of three main areas: (1) graphical enumeration on Riemann surfaces; (2) spectrum of random matrices without independence; and (3) Szego theory for orthogonal polynomials. After providing a brief, elementary description of each of these three areas, this talk will focus on the link between (2) and (3) from the perspective of a type of symbol calculus for associated recurrence operators.  This leads to a number of new insights including some related to Poisson structures of symbol asymptotics, the umbral calculus of Bessel-Appell polynomials, and universality in the enumerative combinatorics of area (1) in terms of conservation laws for spectral dynamics and the algebraic geometry of rational scrolls.

 

Place:   Zoom: https://arizona.zoom.us/j/81150211038         
Password: “arizona” (all lower case)