Speaker: Nattalie Tamam (University of Michigan)

Title: Closure of orbits of the pure mapping class group in the character variety

Abstract:

The pure mapping class group of an oriented surface acts on the character variety of the surface. For certain surfaces, such orbits are connected to solutions of known problems, such as the Markoff triples and the sixth Painlevé equation. We will discuss these examples, as well as the possible orbits closure in the general case; the algebraic relations preserved under the action, the obstructions to 'big' orbits, and the exceptional cases. This is a joint work with Alireza Salehi-Golsefidy.