## Department Colloquium

### Friday, November 27th, 2020

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

**Speaker:** Ian Frankel (Queen's University)

**Title:** Invariant measures for straight line flows.

**Abstract: ** We discuss the question of equidistribution of billiard trajectories in polygons. As it turns out, for polygons whose angles are rational, this is related to the geometry of a 1-parameter family of surfaces in a moduli space. We will describe how the possible measures with respect to which a billiard trajectory may equidistribute are constrained by this 1-parameter family of surfaces.

**Ian Frankel** is a Coleman Research Fellow within the Department of Mathematics and Statistics at Queen’s University. He obtained his Ph.D. in Mathematics from the University of Chicago in 2018. He was a Research Fellow at the Higher School of Economics and a Fields Postdoctoral Fellow at The Fields Institute for Research in Mathematical Sciences. He is mainly interested in geometry and topology and dynamical systems.