HUJI Combinatorics Seminar 

When: Monday March 28th, 2022, at 11AM (Israel time)
Where: Sprinzak 202
Link to live session:

Speaker: Doron Puder (TAU)

Title: Measures induced by words on GLn(Fq)

Abstract:


Fix a finite field F_q and a formal free word w in a free group. A w-random element in GLn(Fq) is obtained by substituting the letters of w by uniformly random elements of GLn(Fq). For example, if w=abab^{-2}, a w-random element is ghgh^{-2} with g,h independent and uniformly random in the group.

The study of w-random elements reveals a surprising structure with connections to algebraic concepts, and interesting analogies with w-random permutations. I will describe what we know about this structure, and how it fits in the larger picture of word measures on groups.
This is joint work with Danielle Ernst-West and Matan Seidel.