GATSBY Pre-talk - Flat Surfaces, Foliations, and Dynamics

Event time: 
Friday, April 26, 2019 - 1:15pm
DL 431
Paul Apisa
Speaker affiliation: 
Event description: 

This talk is intended as a prologue to the subsequent GATSBY lecture, which will be delivered by Jon Chaika. 

I will begin by describing how playing billiards in a polygon with all angles rational multiples of pi, naturally leads to two distinct, but related, dynamical systems - the dynamics of straight line flow on a flat surface and the dynamics of Teichmuller geodesic flow on the moduli space of holomorphic one-forms on Riemann surfaces. 

Special attention will be given to the connection between the non-unique-ergodicity of straight line flow and the divergence of Teichmuller geodesics. The talk will conclude with an example of a minimal non-uniquely ergodic foliation of a flat surface. 

No background will be assumed for the talk. 

Research Area(s):