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