Geometry, Topology and Dynamics Seminar
Roman Muchnik
University of Chicago
Boundary $L^2$-representations for negatively curved groups
Abstract: Let $M$ be a compact negatively curved manifold, $G$ be its fundamental group and $X$ its universal
cover. Denote the (geodesic) boundary of $X$ by $B$. $B$ is endowed with Patterson-Sullivan measure $
\nu$. Consider the natural unitary representation of $G$ on $L^2(B,\nu)$.
I will explain how analytical methods help proving that these representation are irreducible. I will describe
a sequence of operators that play a role of mixing on $(B, \nu)$. Using these operators we get some
interesting rigidity results. This is a joint work with Uri Bader.
Monday November 14, 2005 at 3:00 PM in SEO 512