Department of Mathematics
Hebrew University of Jerusalem
Finite simple groups, random walks, Fuchsian groups and Witten's zeta function
We use character
theory and probabilistic methods to solve several seemingly unrelated
problems of combinatorial and geometric flavor involving finite and
infinite groups.
These include counting branched coverings of Riemann surfaces, determining the mixing time of certain random walks on symmetric groups and finite simple groups, finding the subgroup growth of Fuchsian groups, and giving a probabilistic proof to a conjecture of Higman on their finite quotients.
If time allows I will also discuss further applications, regarding representation varieties of surface groups.
A main tool in the proofs is the study of the so called Witten's zeta function encoding the character degrees of certain groups.
These include counting branched coverings of Riemann surfaces, determining the mixing time of certain random walks on symmetric groups and finite simple groups, finding the subgroup growth of Fuchsian groups, and giving a probabilistic proof to a conjecture of Higman on their finite quotients.
If time allows I will also discuss further applications, regarding representation varieties of surface groups.
A main tool in the proofs is the study of the so called Witten's zeta function encoding the character degrees of certain groups.