# Topology of resolvent problems

 Special Seminar on Hilbert's 13th Problem II Topic: Topology of resolvent problems Speaker: Benson Farb Affiliation: University of Chicago Date: Friday, December 6 Time/Room: 2:00pm - 2:55pm/Simonyi Hall 101 Video Link: https://video.ias.edu/special/2019/1206-BensonFarb

In this talk I will describe a topological approach to some problems about algebraic functions due to Klein and Hilbert. As a sample application of these methods, I will explain the solution to the following problem of Felix Klein: Let $\Phi_{g,n}$ be the algebraic function that assigns to a (principally polarized) abelian variety its $n$-torsion points. What is the minimal $d$ such that, after a rational change of variables, $\Phi_{g,n}$ can be written as an algebraic function of $d$ variables? This is joint work with Mark Kisin and Jesse Wolfson.