### Julia Slipantschuk

University of Warwick

Thursday 23 November 2023, 4.00pm – 5.00pm

Lecture Theatre D (Mathematical Institute)

** Resonances for Anosov diffeomorphisms on the torus **

I will give a short introduction to the spectral theory of transfer operators associated to hyperbolic dynamical systems. I will explain how their eigenvalues, known as Pollicott-Ruelle resonances,
provide insight into the long-term behaviour of the underlying dynamical system, in particular determining its exponential mixing rates. I will then present a complete description of Pollicott-Ruelle
resonances for a large class of rational Anosov diffeomorphisms of the two-torus, notably exhausting all homotopy classes of toral Anosov maps.

series: Pure Mathematics Colloquium

organiser: Scott Harper