Speaker:	Constantin Teleman (UC Berkeley)
Title:	Gauge Theory in 2 and 3 dimensions and categorical representations
Date (JST):	Mon, Dec 14, 2015, 13:15 - 14:45
Place:	Seminar Room A
Abstract:	I will introduce the notion of a categorified (topological) representation of a compact Lie group G, which is the mathematical counter-part to a topological boundary condition for (pure) 3-dimensional gauge theory. The main examples come from the Gromov-Witten theories of compact symplectic manifolds with Hamiltonian group action. The character theory of these representations is captured, in the spirit of quantum mechanics, by the holomorphic symplectic geometry of a certain manifold, now recognised as the `Coulomb branch' of the pure 3D gauge theory. Twisted versions of Gromov-Witten theory relate to gauge theory with `matter'. The theory gives a clean account of some aspects of the gauged (non-linear!) Sigma-model and the appearance of the Toda integrable system.

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