# Meeting Details

For more information about this meeting, contact Nigel Higson, Mathieu Stienon, Ping Xu.

Title: Proper moment maps, K-homology and geometric quantization GAP Seminar Yanli Song, Penn State University This talk is devoted to the study of conjecture of Guillemin and Sternberg in the non-compact setting which was proved by Ma-Zhang, Paradan in 2009. Suppose that a compact Lie group G acts on a symplectic manifold(non-compact) with pre-quantuam line bundle, we can "quantize" them to obtain a formal representation of G under the assumption that moment is proper. In fact, we can consider more general objects : weakly complex G-manifold, vector bundle and an equivariant map from M to Lie algebra. Adopting some ideas from geometric K-homology, we can construct an abelian group by means of bordism, bundle modification, etc. The main goal is to show the abelian group is isomorphic to the formal representation of G and the isomorphism gives sorts of "quantization". Moreover, this "quantization" has some nice properties such that multiplicative, commuting with reduction, etc. I shall outline the proof in the talk.

### Room Reservation Information

Room Number: MB106 04 / 03 / 2012 02:30pm - 03:30pm