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Monday, April 27, 2015

**Abstract:** Let G be a compact Lie group and let S be an oriented 2-manifold. This talk discusses the obstruction to the existence of a prequantization (also called pre-quantum line bundle, a complex line bundle whose Chern class is the symplectic form) of the moduli space M of flat principal G-bundles over S (possibly with marked points and prescribed holonomies around those marked points). The moduli space M is placed in the framework of quasi-Hamiltonian group actions (with Lie group-valued moment maps), where there exists a compatible notion of prequantization expressed in terms of U(1)-gerbes (instead of line bundles). In this context, the obstruction can be described fully if G is simply connected; however if G is not simply connected, less is known.