Equivariant gerbes  over compact simple Lie groups
 
Ping Xu, Penn State University
 
Recently, there is an increasing interest in
gerbes due to their close connection with
string theory. In a certain sense, gerbes are
geometrical objects describing (equivalent classes) of
 higher integer cohomology groups.  In this talk, I
will  give an elementary introduction to
the theory of $S^1$-gerbes over differential stacks using the theory of
Lie groupoids. In particular,
using groupoid $S^1$-central extensions, I will present,
for a compact simple  Lie group $G$,
 an infinite dimensional model of $S^1$-gerbe
over the differential stack $G/G$ whose Dixmier-Douady
class corresponds to the canonical generator of the equivariant
 cohomology $H_G ^3 (G, Z)$.