Integral points and curves on moduli of local systems

Special Seminar
Topic:Integral points and curves on moduli of local systems
Speaker:Junho Peter Whang
Affiliation:Princeton University
Date:Friday, December 8
Time/Room:5:05pm - 5:50pm/S-101
Video Link:https://video.ias.edu/special/2017/1208-JunhoPeterWhang

The classical affine cubic surface of Markoff has a well-known interpretation as a moduli space for local systems on the once-punctured torus. We show that the analogous moduli spaces for general topological surfaces form a rich family of log Calabi-Yau varieties, where a structure theorem for their integral points can be established using mapping class group descent. Related analysis also yields new results on the arithmetic of algebraic curves in these moduli spaces, including finiteness of imaginary quadratic integral points for non-special curves.