### Student Geometry and Topology Archives for Academic Year 2012

#### Discrete groups of isometries: dynamical invariants

When: Tue, September 18, 2012 - 3:30pm

Where: Math 1313

Speaker: Andrew Sanders (UMD) -

#### Introduction to Parabolic Geometries

When: Tue, October 2, 2012 - 3:30pm

Where: Math 1313

Speaker: Katharina Neusser (Australian National University) - http://maths.anu.edu.au/~neusser/

For a Lie group G and a closed subgroup H a Cartan geometry of type (G,H) can be viewed (in a sense) as a curved analog of the homogeneous space G/H.

Parabolic geometries are Cartan geometries, whose homogeneous model is a homogeneous space of a semisimple Lie group by a parabolic subgroup.

It turns out that many interesting geometric structures can be described as parabolic geometries and so parabolic geometries offer a uniform approach to a broad variety of geometric structures. Among these structures we have conformal structures, projective structures, partially integrable almost CR structures of hypersurface type and certain types of generic distributions. In my talk I will give an introduction to parabolic geometries and an overview of some of the tools that were developed in the last decades to study them.

#### Patterson-Sullivan measures for convex, cocompact Kleinian groups

When: Tue, November 6, 2012 - 3:30am

Where: Math 1313

Speaker: Andrew Sanders (UMCP) - www.math.umd.edu/~andysan

Abstract: Continuing with our series of talks about Patterson-Sullivan theory, we will study special properties of Patterson-Sullivan measures in the case that the group is convex co-compact. In particular, we will show that the Patterson-Sullivan measure is a multiple of the Hausdorff measure in dimension equal to the critical exponent of the group. If time permits, we will also discuss the ergodicity properties of this measure.