Random matrices, random partitions and the combinatorics of set partitions.

Dates and time: Martes 19 dic y jueves 21 dic 2023. 17:00-18:00.

Abstract: In this minicourse, we will discuss some interactions between probability theory and the combinatorics of set partitions that arise in the proofs of limit theorems through the method of moments. We focus on random matrix models, especially on the Gaussian Unitary Ensemble, for which we review the proof of the limit shape phenomenon to the semicircle distribution. We will also survey some modern results, from my own research, on the theory of random matrices and random partitions.

Requirements and language: The attendants should know analysis on R^d and linear algebra. It would also be helpful to have seen some basic concepts from probability. The writing and slides will be in English, but most of the spoken presentation will be in Spanish (except for some of the mathematical terms).

Speaker webpage: https://u.osu.edu/cuenca/