"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.
," coorganized by the PI, which took place at the Erwin Schrödinger Institute (ESI) for Mathematical Physics in July 2011. Over the two weeks of the workshop, there were approximately 67 participants. The award was used to support the participation of 6 people in the workshop, including the PI, all of whom were based at US institutions. One of these was a graduate student, three more were within 6 years of their PhD; two were women, and two were Latino. The workshop introduced different research groups in differential geometry and dynamics of group actions to each other and provided an introduction to Cartan geometries, for those previously unfamiliar. A major goal of the workshop was to foster collaboration across these subfields. A web page for the worskhop is maintained at www.mat.univie.ac.at/~cap/files/esiprog11.html It includes some links to slides from talks given at the conference. Many participants have submitted papers related to the workshop to the ESI preprint series. A special issue of the Central European Journal of Mathematics, partly dedicated to the the workshop, appeared in the summer of 2012. This issue was guest-edited by the PI, co-organizer Andreas Cap, participant Vladimir Matveev, and Galliano Valent. A secondary use of the grant has been for fa ollow-up visit between the PI and co-organizer Andreas Cap, to work on a project related to the topics of the conference. This project has resulted in two papers, both to appear.
