Cartan connections, geometry of homogeneous spaces, and dynamics

University Of Maryland, College Park, College Park MD

Investigators

Abstract

"Workshop on Cartan Connections, Geometry of Homogeneous Spaces, and Dynamics" to be held at the Erwin Schroedinger Institute, July 11-22, 2011. The two-week workshop is devoted to two major themes, conformal geometry and its generalizations, and group actions on manifolds, and the discussion will be organized around techniques from Cartan geometries in these areas. Cartan geometries are a framework for study of a wide range of geometric structures, in which each such structure has an infinitesimal model that is a homogeneous space. The symmetry of this model leads to useful algebraic expressions for the geometric invariants of a given geometric manifold. A thorough understanding of existence and basic properties of Cartan geometries in most important contexts has recently been obtained, and the focus has shifted towards using the Cartan connection to study the geometries in question. Primary intellectual goals of the workshop are (1) to gather the diverse group of researchers currently working with Cartan geometries on a range of problems in geometry and analysis, and (2) introduce researchers working on the same problems to the techniques of Cartan geometries that have yielded valuable results. The themes of the workshop have important connections to physics, including general relativity and the AdS/CFT correspondence. The time period overlaps with a semester program on "Dynamics of General Relativity," and the organizers anticipate fruitful interaction among participants in the two events. A particular effort is being made to invite early-career researchers and mathematicians from underrepresented groups or working in developing countries.