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.