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|
|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
|Date:||03 / 22 / 2012|
|Time:||04:00pm - 05:00pm|