### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Matthew Russell**, Rutgers University, russell2 {at} math [dot] rutgers [dot] edu)
** Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Fourier Analysis of Word Maps

Speaker: **Ori Parzanchevski**, Institute for Advanced Study

Date: Thursday, February 6, 2014 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

Let G be a finite group. How many times is an element g obtained as a commutator in G? Namely, how many solutions are there to the equation x*y*x^-1*y^-1=g ? In 1886 Frobenius gave a striking answer to this question in terms of the character theory of the G. But for a general word w replacing the commutator word x*y*x^-1*y^-1, surprisingly little is known. I will show some examples and survey old and recent results, including recent joint works with Doron Puder and Gili Schul.

See: http://www.math.rutgers.edu/~russell2/expmath/