PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Yakov Pesin, Svetlana Katok.

Title:Absolute continuity, exponents, and rigidity
Seminar:Department of Mathematics Colloquium
Speaker:Amie Wilkinson, University of Chicago
Abstract:
The geodesics in a compact surface of negative curvature display stability properties originating in the chaotic, hyperbolic nature of the geodesic flow on the associated unit tangent bundle. Considered as a foliation of this bundle, this collection of geodesics persists in a strong way when one perturbs of the Riemannian metric, or the geodesic flow generated by this metric, or even the time-one map of this flow: for any perturbed system there is a corresponding "shadow foliation" with one-dimensional smooth leaves that is homeomorphic to the original geodesic foliation. A counterpart to this foliation stability is a curious rigidity phenomenon that arises when one studies the disintegration of volume along the leaves of this perturbed shadow foliation. I will describe this phenomenon and its underlying causes. This is recent work with Artur Avila and Marcelo Viana.

Room Reservation Information

Room Number:MB114
Date:03 / 22 / 2012
Time:04:00pm - 05:00pm