# University of Toronto's Symplectic Geometry Seminar

May 28, 2007, 3:10pm

BA 6183

## Chenchang Zhu

### Institut Fourier Grenoble

## A gerbe of Gamma functions---with fantasy towards toric varieties?

**Abstract: **
As we know that theta function provides a section of a
non-trivial line bundle (theta bundle) on an elliptic curve, in this
talk, we will give a geometric realization of elliptic Gamma
functions whose highly non-trivial identities are developed by Felder
and Varchenko. Elliptic gamma function can also be regarded as the
difference of theta
functions. It turns out these identities can be geometrically
interpreted as the fact that Gamma functions give a meremorphic
section of a holomorphic gerbe over
the stack [CP^2-RP^2/SL(3,Z)\times Z^3]. In the construction, a choice
of frames of an integer
lattice is involved. Therefore that leads some fantasy towards toric
varieties...