Professor Doron Puder(Tel Aviv University)

Abstract

Let w be a word in a free group and let G be a finite group (or more generally, a compact group). A w-random element of G is obtained by substituting the letters of w with uniform random elements from G. For example, if w=xyxy^{-2}, the random element is ghg^{-2}, with g and h independent random elements of G. In a series of works with various coauthors, we discovered that in nice families of groups, such as the symmetric groups or the unitary groups, some very interesting invariants of the word w can be extracted from w-random elements.

Note: This story involves probability, topology, algebra, combinatorics and representation theory. In the talk, which is aimed at graduate students, I will try to give a flavor of these interesting phenomena.