Geometry, Topology and Dynamics Seminar
Jayadev Athreya
UIUC
Cusp excursions on parameter spaces
Abstract: We describe an axiomatic approach to studying cusp excursions for diagonal and horoshperical actions on non-compact parameter spaces of geometric objects. In particular, we give a unified treatment of the space of unimodular Euclidean lattices and the space of holomorphic quadratic differentials on Riemann surfaces. We also have applications to hyperbolic manifolds. The idea is to associate (in an equivariant manner) a discrete set in a Euclidean space to each point in the parameter space, in such a way that a subset of the parameter space is pre-compact only if the lengths of vectors in the associated discrete set are bounded below.
Monday April 4, 2011 at 3:00 PM in SEO 636