Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Trace formulae and dynamical determinants for Anosov flows (e-seminar)

Talk by Malo Jézéquel

**Date:** 19.10.20 **Time:** 15.00 - 16.15 **Room:** Y27H28

In order to study fine statistical properties of an Anosov flow, one may introduce the notion of Ruelle resonances. These resonances are complex numbers, with spectral theoretic interpretation, that are in principle hard to compute. However, these resonances are known to be the zeros of a dynamical determinant (an entire function defined from the periodic data of the flow). We will discuss the validity of a morally stronger relationship between Ruelle resonances and periodic orbits (a trace formula conjectured by Dyatlov and Zworski), and explain how it is related to complex analytic properties of the dynamical determinant.