Abstracts for MPIM Math-Phys Seminar

For a given dimension, there is a well-known monoidal category of compact manifolds with Riemannian metric and boundary (possibly empty). The defining operation is the disjoint union and the empty set the neutral object. The category is self-adjoint in the sense that boundary components can be moved between source and target. An equally well-known monoidal category is given by the linear maps of real Hilbert spaces, with tensor products as defining operation and the real numbers as neutral object.

Generalized theta functions are the global sections of a determinant bundle over the moduli space of stable vector bundles on a Riemann surface, which generalizes the classical theta function. Motivated by the geometric quantization, we will see that the conformal blocks in CFT are isomorphic to vector spaces of generalized theta functions.