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.

# Special Seminar on Hilbert's 13th Problem II

## Topology of resolvent problems

### Featuring

Benson Farb

### Speaker Affiliation

University of Chicago

### Affiliation

Mathematics

### Event Series

### Video

https://video.ias.edu/special/2019/1206-BensonFarbDate & Time

December 06, 2019 | 2:00 – 2:55pm

### Location

Simonyi Hall 101