UWashington-PIMS Mathematics Colloquium: Semyon Dyatlov

Anosov flows are a standard model for strongly chaotic behavior in dynamical systems. A classical example is the geodesic flow on a compact negatively curved Riemannian manifold. The chaotic behavior of an Anosov flow manifests in decay of correlations and in the exponential growth of the number of closed trajectories.

This talk is about Pollicott-Ruelle resonances, which are the complex characteristic frequencies featured in long time asymptotic behavior of correlations. They also appear as singularities of dynamical zeta functions, defined as Euler products over the lengths of closed trajectories. This subject has a long history going back to the 1960s but in the past 15 years many new results have been proved using an approach based on microlocal analysis and scattering theory. Among these results I will discuss in particular meromorphic continuation of zeta functions and their connections to topology.