Title: Finiteness of Teichmüller curve in genus three
Speaker: Matthew Bainbridge
Speaker Info: Indiana University
There are many closed geodesics in the moduli space M_g of genus g Riemann surfaces, and each of these geodesics can be extended to an isometrically immersed hyperbolic plane in M_g. Usually, these hyperbolic planes are dense in M_g, but very rarely one may cover an algebraic curve. Such isometrically immersed algebraic curves in M_g are called Teichmüller curves. There are infinitely many "primitive" Teichmüller curves in M_2, discovered by McMullen and Calta. In further work, McMullen classified Teichmüller curves in M_2, but the situation in higher genus remained mysterious.Date: Tuesday, May 26, 2015
In this talk, I'll discuss recent work with Martin Moller and Philipp Habegger showing that there are only finitely many "algebraicallly primitive" Teichmüller curves in M_3. The proof uses ideas from algebraic geometry, number theory, and conformal geometry.