06.06.2023, 15 Uhr
Phenomena in High Dimensions
Pierre Youssef (New York University, Abu Dhabi)
Nguyen Viet Dang (University Claude Bernard, Lyon 1) und Colin Guillarmou (University Paris XI)
14:00 Nguyen Viet Dang (University Claude Bernard, Lyon 1): Dynamical systems: spectral and topological features
15:30 Colin Guillarmou (University Paris XI): Rigidity results from geodesic flow
Nguyen Viet Dang (University Claude Bernard, Lyon 1): Dynamical systems: spectral and topological features
The aim of this talk is to relate topological and spectral features arising in dynamical systems. I will first explain the concept of hyperbolicity in dynamics, illustrating it with various examples. Then I will show how to define some kind of spectrum for some hyperbolic dynamical systems called "Pollicott-Ruelle" resonances. These resonances will play a crucial role in the present discussion. I hope to explain how, together with Gabriel Rivière, we interpret some topological properties of the underlying space carrying the dynamics in terms of these dynamical spectra.
From dynamics to rigidity via spectra
Colin Guillarmou (University Paris XI): Rigidity results from geodesic flow
We will review recent results on a rigidity problem for a class of Riemannian manifolds whose metric admits an Anosov geodesic flow, such as negatively curved compact manifolds. For manifolds with Anosov geodesic flows and non-positive curvature, we prove that the marked length spectrum locally determines the metric in the sense that two close enough metrics with the same marked length spectrum are isometric.