Aarhus University Seal / Aarhus Universitets segl

Towards perturbative topological field theory on manifolds with boundary

Pavel Mnev
(Steklov Institute)
Colloquium
Tuesday, 12 March, 2013, at 10:00, in G3.3 (1532-322)
Abstract:
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.
Organised by: QGM
Contact person: Jørgen Ellegaard Andersen