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
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.