Geometry, Topology and Dynamics Seminar
Natalie McGathey
UIC
Invariant Measures and Homeomorphisms of Boundaries
Abstract: An important question in ergodic theory is: given an action of a
group $G$ on a space $X$, classify all (ergodic) invariant probability measures for this action.
We will give such a classification for the case $G = \mathrm{PSL}_2(\mathbf{R})$,
$\mathrm{Isom}_+\mathbb{H}_K^n$, where $K$ denotes $\mathbf{R}$,
$\mathbf{C}$, $\mathbf{H}$, or $\mathbf{O}$ with $n=2$, and $X$ is $L/G$ for
some large group $L$. In this talk, we will briefly describe how this
particular setting is motivated by trying to understand embeddings of
Teichmüller Space; we will then state the classification results and
give a flavor of the proofs.
Monday April 18, 2011 at 3:00 PM in SEO 636