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Colloquium: Towards perturbative topological field theory on manifolds with boundary

Speaker: Pavel Mnev (Steklov Institute)

2013.03.11 | Jane Jamshidi

Date Tue 12 Mar
Time 10:00 11:00
Location Øv. G3.3 (1532-322)

We will explain a hidden algebraic structure on cochains and cohomology of a simplicial complex arising from certain simplicial topological field theory.
Next we will introduce simplicial one-dimensional Chern-Simons theory, as an Atiyah's TFT on triangulated 1-cobordisms, consistent with simplicial aggregations and satisfying a version of Batalin-Vilkovisky master equation.
Finally, we will explain the program of extending our results to more general TFTs in higher dimension, in particular the extension of Batalin-Vilkovisky symplectic homological formalism to TFTs on manifolds with boundary. As a byproduct of the latter construction, one obtains a homological description for certain class of (derived) algebro-geometric moduli spaces (e.g. moduli space of local systems) and for their geometric quantization.