Pure Maths Colloquium: Wael Bahsoun

Smooth ergodic theory aims to analyse the long-term statistics of chaotic dynamical systems. There are several analytic and probabilistic tools that are used to answer such questions. Each of these approaches has its advantages and its shortcomings, depending on the system under consideration. In this talk, I will focus on transfer operator techniques and spectral methods. In the first half of this talk, I will explain ideas behind this approach through simple, yet important examples. In the second half of the talk, I will discuss a recent joint work with C. Liverani, whose long-term goal is to provide a good spectral picture for pricewise hyperbolic systems with singularities (e.g. billiard maps) in any dimension.