## Dynamics, Geometry, & Groups - Alena Erchenko (Stony Brook)

### Thursday, April 1st, 2021

**Time:** 1:30 p.m** Place:**

**Speaker:** Alena Erchenko (Stony Brook University)

**Title:** Riemannian Anosov extension.

**Abstract:** Consider a smooth Riemannian manifold Σ with strictly convex spherical boundary, hyperbolic trapped set (possibly empty) and no conjugate points. We show that Σ can be isometrically embedded into a closed Riemannian manifold with Anosov geodesic flow. We will explain one of the main ingredients which is the analysis of the behavior of Jacobi fields. We also discuss some applications of the main result. This is a joint work with Dong Chen and Andrey Gogolev.