EVENT DETAILS AND ABSTRACT

Title: Diophantine analysis on moduli of local systems
Speaker: Junho Peter Whang
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

We consider the Diophantine geometry of moduli spaces for special linear rank two local systems (with fixed boundary traces) on surfaces. After motivating their Diophantine study, we use mapping class group dynamics and differential geometric tools to prove a type of finite generation theorem for the integral points of these varieties, generalizing work of Markoff (1880). We also give an effective Diophantine analysis of integral points for nondegenerate algebraic curves on the moduli spaces, and discuss more recent works around the arithmetic and dynamics on these moduli spaces.