# Proper moment maps, K-homology and geometric quantization

## GAP Seminar

## Meeting Details

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

**Speaker:** Yanli Song, Penn State University

**Abstract:** 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:** 106 McAllister

**Date:** 04/03/2012

**Time:** 2:30pm - 3:30pm