EVENT DETAILS AND ABSTRACT

Title: The remarkable arithmetic of Teichmuller curves and some applications to billiards
Speaker: Ronen Mukamel
Speaker Info: University of Chicago
Brief Description:
Special Note:
Abstract:

A Teichmuller curve is an algebraic curve which is isometrically and algebraically immersed in the moduli space of Riemann surfaces. Many examples of Teichmuller curves emerge from the study of billiards in polygons.

We will present the first explicit algebraic models for Teichmuller curves of genus greater than zero. Our examples emerge from the study of billiards in L-shaped polygons and Hilbert modular surfaces. We will also give evidence that Teichmuller curves are arithmetically interesting by highlighting some remarkable features of our examples. This work is joint with A. Kumar.