Random Matrices and Random Partitions at Varying Temperatures

The Department of Mathematics in the College of Arts and Sciences is honored to welcome Dr. Cesar Cuenca to deliver the weekly colloquium. Dr. Cuenca is a Benjamin Peirce Fellow in the Mathematics Department, Harvard University, where he works in Random matrix theory, asymptotic representation theory, and algebraic combinatorics.

Abstract: Cuenca will discuss the global-scale behavior of ensembles of random matrix eigenvalues and random partitions which depend on the “inverse temperature” parameter beta. The goal is to convince the audience of the effectiveness of the moment method via Fourier-like transforms in characterizing the Law of Large Numbers and Central Limit Theorems in various settings. The talk will focus on the regimes of high and low temperatures, that is, when the parameter beta converges to zero and infinity, respectively. Part of this talk is based on joint projects with F. Benaych-Georges — V. Gorin, and M. Dolega — A. Moll.