Masoud Khalkhali (University of Western Ontario)

Math & Stats Department Colloquium

Thursday, November 4th, 2021

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Masoud Khalkhali (University of Western Ontario)

Title: Bootstrapping Dirac ensembles

Abstract: In this talk, I shall explain certain techniques we have employed so far in the study of spectral statistics of certain classes of random matrices suggested by noncommutative geometry. In some cases, one can apply the Coulomb gas method to find the empirical spectral distribution and rigorously prove existence of phase transition. More recently, we applied the newly developed bootstrap technique to find the moments of certain multi-trace and multi-matrix random matrix models. Using bootstrapping, we are able to find the relationships between the coupling constants of these models and their second moments. Using the Schwinger-Dyson equations, all other moments can be expressed in terms of the coupling constant and the second moment. Explicit relations for higher moments are obtained. The talk will be mostly an overview of techniques we have used so far. (Based on joint works with H. Hessam and N. Pagliaroli).

Masoud Khalkhali is a Professor in the Department of Mathematics at the University of Western Ontario. His research interests include noncommutative geometry, cyclic cohomology, operator algebras, quantum groups, and Hopf algebras.