EVENT DETAILS AND ABSTRACT

Title: Billiards, the square root of eleven and a Teichmuller curve of genus one
Speaker: Ronen Mukamel
Speaker Info: U Chicago
Brief Description:
Special Note: Note special time
Abstract:

A Teichmuller curve is an algebraic and isometric immersion of an algebraic curve into the moduli space of Riemann surfaces. We will present the first explicit algebraic model for an elliptic curve birational to a Teichmuller curve. Our example emerges from the study of billiards in L-shaped polygons and the Hilbert modular surface associated to the square root of eleven.

We will also give algebraic models for other higher genus Teichmuller curves and present evidence, drawn from our examples, that Teichmuller curves are arithmetically interesting. Our models are all obtained by studying certain Hilbert modular forms. This work is joint with A. Kumar.