PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Svetlana Katok, Stephanie Zerby, Anatole Katok, Federico Rodriguez Hertz.

Title:Applications of Hodge theory to Teichmuller dynamics
Seminar:Dynamical systems seminar
Speaker:Simion Filip, University of Chicago
Abstract:
A number of classical dynamical systems, such as IETs or billiards in (rational-angled) polygons are related to to the natural action of SL(2,R) on the space of "flat surfaces". The extra structure, viewing flat surfaces as Riemann surfaces with a holomorphic 1-form, let one use tools from Hodge theory to study the action of SL(2,R). This action enjoys a number of rigidity properties - by results of Eskin, Mirzakhani, and Mohammadi, orbit closures are manifolds and invariant measures are Lebesgue-class. I will explain why orbit closures are in fact algebraic varieties, with unusual arithmetic properties. I will also explain some rigidity results, and a proof that the Lyapunov spectrum associated to the action of the diagonal group has minimal number of zero exponents, provided the constraints from geometry. No background in Hodge theory will be assumed and I will provide the necessary introduction.

Room Reservation Information

Room Number:MB114
Date:02 / 09 / 2015
Time:03:35pm - 04:35pm