Departmental Colloquium
Simion Filip
University of Chicago
Measure Rigidity beyond Homogeneous Dynamics
Abstract: For a general dynamical system, it is impossible to analyze
the behavior of all points and instead one has a description of orbits
that are typical with respect to some invariant measure; the description
of all invariant measures is equally unwieldy. For certain flows on
homogeneous spaces associated to Lie groups, the measure and topological
rigidity results initiated by Margulis and Ratner showed that it is
possible to give a useful description for the orbit of every point,
and describe all invariant measures. I will discuss some results which,
under appropriate conditions, give similar measure and topological
rigidity properties for smooth dynamical systems on general manifolds.
Joint work with Aaron Brown, Alex Eskin, and Federico Rodriguez--Hertz,
as well as David Fisher and Ben Lowe.
Friday February 7, 2025 at 3:00 PM in 636 SEO