Speaker: Roberto Fringuelli

Title: The Picard group of the universal moduli space of principal bundles on 
Riemann surfaces.

Abstract: The Wess-Zumino-Witten model is a type of two dimensional conformal 
field theory, which associates to a Riemann surface with marked points and 
irreducible representations of a Lie algebra attached to the points, a finite 
dimensional vector space satisfying certain axioms. Deforming the pointed 
surface in a family, we get the sheaf of conformal blocks. This sheaf have a 
geometric interpretation as the sheaf of generalized theta functions, which is 
the push-forward of a line bundle over the universal moduli space of principal 
bundles on Riemann surfaces. In this talk, we present a complete description of 
the group of line bundles (Picard group) over the universal moduli space of 
principal bundles on Riemann surfaces. It is a joint work with Filippo Viviani.