Joint IAS/PU Groups and Dynamics Seminar

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 and related billiard flows. Furthermore, we construct explicit eigenfunctions for translation flows in pseudo-Anosov directions with Pisot expansion factors, and use this construction to build explicit examples of non-ergodic prism flows, and non-ergodic billiard flows in a right prism over a regular n-gon for $n = 7, 9, 14, 16, 18, 20, 24, 30$. This is joint work with Nicolas Bedaride, Pat Hooper, and Pascal Hubert.