## Columbia Mathematics Department Colloquium

# On the geometry of étale gerbes*
*

by

# Hsian-Hua Tseng

## Ohio State University

Abstract:

A G-gerbe over a base B is roughly speaking a fiber
bundle whose fibers are the classifying orbifold BG of the group G.
Gerbes occur naturally in the theory of orbifolds. For example every
orbifold with nontrivial generic stabilizers is a gerbe over another
orbifold. Gerbes are also very important in other subjects, such as the
theory of non-abelian cohomology. It is conjectured by physicists that
for finite groups G the geometry of a G-gerbe is equivalent to the
geometry of a disconnected space with a U(1)-twist. The purpose of this
talk is to explain what this conjecture means, and why one should
believe this conjecture. Much of this is joint work with Xiang Tang of
Washington University in St. Louis.