Interplay between extreme value theory and geometry/dynamics

Abstract

Mathematics is a wonderful synergy between various branches with beautiful connections that link them in an elegant fashion. In this series of three lectures, we will discuss how probability theory (more specifically, extreme value theory) can benefit from ergodic theory and hyperbolic geometry, and vice versa.

The first lecture (on 20th July) would concentrate on extreme value theory for continued fractions and Gauss dynamical system. In this case, we shall use probabilistic tools, which will have ergodic theoretic, number theoretic and geometric consequences.

On the other hand, in the second and third lectures (on 21st and 22nd July, respectively), we will focus on extremes of stationary symmetric stable random fields. In this context, we shall discuss how nonsingular dynamics (especially for boundary actions arising in hyperbolic geometry) can give rise to probabilistic results for stationary stable fields.

These lectures will be based on a series of joint work with Anish Ghosh (TIFR Mumbai), Maxim Kirsebom (Univ of Hamburg), Mahan Mj (TIFR Mumbai), Gennady Samorodnitsky (Cornell Univ) and Sourav Sarkar (Univ of Cambridge) carried out at different points of time. Special care will be taken so that everyone can follow these lectures.