Daniel Perales Anaya, Department of Pure Mathematics, University of Waterloo
"Free Probability and Non-crossing Partitions"
Free probability is a non-commutative analogue of Probability where the concept of independence is replaced by the concept of freeness. If you know the distribution of 2 random variables X and Y, then computing the distribution of X+Y is impossible, unless you assume some relation between X and Y. Usually in probability you just assume they are not related at all (independent), and this translates into a universal rule to compute X+Y. Freeness is just another universal rule to compute X+Y, specially manufactured to handle non-commutative case (XY not equal to YX). Thus, the distribution of X+Y depends on whether you assume X,Y are independent or free. The combinatorial descriptions of these rules are very similar and use set partitions and non-crossing partitions. In this talk we will give a introduction to Free Probability as an analogue to Probability. Then we will focus on non-crossing partitions, study their important properties and how they relate to free probability.
We will be using Microsoft Teams for the talk and the link for which will be shared in a separate email.