Colloquium talk
Title : Billiards in Rational Prisms
Speaker : Jayadev Athreya, University of Washington
Time, Date and day : 7th August (Wed) at 4:00 pm
Venue : Ramanujan Hall
Host: Ravi Raghunathan
Abstract : This talk describes joint work-in-progress with Bedaride, Hooper,
and Hubert. Motivated by the study of billiards in polyhedra, we study
linear flows in a family of singular flat 3-manifolds which we call
translation prisms. Using ideas of Furstenberg and Veech, we connect
results about weak mixing properties of flows on translation surfaces to
ergodic properties of linear flows on translation prisms, and use this to
obtain several results about unique ergodicity of these prism flows.
Furthermore, we construct explicit eigenfunctions for translation flows in
psuedo-Anosov directions with Pisot expansion factors, and use this
construction to build explicit examples of non-ergodic prism flows, and
for
non-ergodic billiard flows in a right prism over a regular 7-gon.