Geometry and Topology Seminar: Application of convex surfaces theory to Anosov flows

Abstract: Anosov flows are an important class of dynamical systems due to their ergodic and geometric properties. Even though they represent examples of chaotic dynamics, they enjoy the remarkable property of being stable under small perturbations. In this talk, I will explain how, perhaps surprisingly, Anosov flows are related to both integrable plane fields (foliations) and totally non-integrable plane fields (contact structures). The latter represents a less-studied approach that has the potential to make new connections to other branches of mathematics, such as symplectic geometry and Hamiltonian dynamics.
As main application, I will show how convex surface theory introduced by Giroux in the 90s in the context of contact structures, gives a general framework for cut-and-paste techniques on Anosov flows.

Host: Steven Frankel