Integral points on character varieties - Junho Peter Whang

Character Varieties, Dynamics and Arithmetic

Topic: Integral points on character varieties
Speaker: Junho Peter Whang
Affiliation: Seoul National University
Date: December 01, 2021

In this talk, we discuss the Diophantine study of relative SL2-character varieties of surfaces. In particular, we prove that the integral points on these varieties are effectively finitely generated in a precise sense, and in particular their existence is decidable. The proof combines mapping class group descent (using geometric tools) and classical finite generation results for integral points on affine homogeneous varieties under arithmetic groups.