## Combinatorics Seminar - Spring '22

When: Sunday, March 6,
10am

Where: Schreiber 309

Speaker: Danielle West,
Tel Aviv University

Title:
Measures Induced by Words on $GL_n(q)$ and Free Group Algebras

## Abstract:

Fix a finite field $K$ and a word $w$ in a free group $F$. A $w$-random
element in $GL_n(K)$ is obtained by substituting the letters of $w$ with
uniform random elements of $GL_n(K)$. For example, if $w=abab^{-2}$, a
$w$-random element is $ghgh^{-2}$ with $g,h$
independent and uniformly random in $GL_n(K)$. The moments of $w$-random
elements
reveal a surprising structure which relates to the free group algebra
$K[F]$.
In this talk I will describe what we know about this structure and draw
some analogies to $w$-random permutations.
This is joint work with Doron Puder and Matan Seidel.

This is joint work with Doron Puder and Matan Seidel.