## Department Colloquium

### Friday, October 16th, 2020

**Time:** 2:30 p.m. **Place:** Online (via Zoom)

**Speaker:** Rafael Potrie (Universidad de la Republica-Uruguay)

**Title:** Anosov flows and the fundamental group.

**Abstract: ** The hairy ball theorem says that a vector field in the sphere must have some singularity. How does the dynamics interact with the topology of the underlying manifold in higher dimensions? We will discuss some instances of this question for dynamics in 3-manifolds, featuring a beautiful result due to Margulis and Plante-Thurston. Time permitting, we will touch upon more recent developments on the interactions between the topology and dynamics in 3 dimensions.

**Rafael Potrie** is an Associate Professor at the Universidad de la Republica-Uruguay. He obtained his Ph.D. in Mathematics from Universite Paris 13/Universidad de la Republica-Uruguay in 2012. He was an invited speaker of the Dynamical Systems session at the International Congress of Mathematicians (ICM) in 2018. His research mainly concerns the topological classification of partially hyperbolic systems in three-dimensional manifolds and its dynamical consequences. Other interests include smooth dynamics, ergodic theory, discrete subgroups of Lie groups, and the geometry of foliations and laminations.