Friday, April 26, 2019
Time  Items 

All day 

1pm 
04/26/2019  1:15pm 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 oneforms on Riemann surfaces. Special attention will be given to the connection between the nonuniqueergodicity of straight line flow and the divergence of Teichmuller geodesics. The talk will conclude with an example of a minimal nonuniquely ergodic foliation of a flat surface. No background will be assumed for the talk. Location:
DL 431

2pm 
04/26/2019  2:30pm to 3:30pm Ratner, Margulis, Dani and many others, showed that the horocycle flow on homogeneous spaces has strong measure theoretic and topological rigidity properties. EskinMirzakhani and EskinMirzakhaniMohammadi, showed that the action of SL(2,R) and the upper triangular subgroup of SL(2,R) on strata of translation surfaces have similar rigidity properties. We will describe how some of these results fail for the horocycle flow on strata of translation surfaces. In particular, 1) There exist horocycle orbit closures with fractional Hausdorff dimension. 2) There exist points which do not equidistribute under the horocycle flow with respect to any measure. 3) There exist points which equidistribute distribute under the horocycle flow to a measure, but they are not in the topological support of that measure. No familiarity with these objects will be assumed and the talk will begin with motivating the subject of dynamics and ergodic theory. This is joint work with John Smillie and Barak Weiss. Location:
DL 431

4pm 
04/26/2019  4:00pm Public lecture courtesy of the Franke Program in Science and the Humanities. Location:
Whitney Humanities Center
53 Wall street
New Haven 