Peter Sarnak “Reflection groups and monodromy“ | The Vinberg Lecture

The Vinberg Lecture Series: Lecture 4 (Nov 30, 2021) -------- Peter Sarnak (IAS Princeton) Title: Reflection groups and monodromy Abstract: Vinberg’s theory of reflection groups has wide applications. We discuss some of these, to monodromy groups of hypergeometric and Painlevé equations. The nonlinear case is intimately connected to affine Markoff surfaces and it is a central ingredient in the Diophantine analysis of these surfaces.