Sep 14 – 16, 2020
SISSA
Europe/Rome timezone

Correlators of classical invariant unitary ensemble and enumerative problems

Sep 15, 2020, 4:00 PM
30m
Chairman: Mattia Cafasso

Chairman: Mattia Cafasso

Scientific Programme

Speaker

Massimo Gisonni (SISSA)

Description

In the early eighties, Bessis, Itzykson and Zuber showed how correlators of the Gaussian Unitary Ensemble (GUE) are related to the counting problem of ribbon graphs. However, their explicit computation was given only thirty years later by Dubrovin and Yang. More recently, it was proven that correlators of the Laguerre Unitary Ensemble (LUE) are likewise related to the counting problem of double weighted monotone Hurwitz numbers.
In this seminar we will show how a generating function for these objects can be obtained starting from the RHP of the associated orthogonal polynomials. We will also discuss how the Laguerre Partition function serves as a generating function for Cubic Hodge Integrals, and further directions of research. This talk is based on joint work with T.Grava and G.Ruzza (https://arxiv.org/abs/1912.00525).

Primary author

Massimo Gisonni (SISSA)

Presentation materials