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Three-dimensional topological field theory anda categorification of the derived category of coherent sheaves

Date: 
Saturday 18th April 2009 - 12:00 to 13:00
Abstract: 
The Rozansky-Witten model is a 3d topological sigma-model whose target space X is a complex symplectic manifold. I will describe the 2-category structure on the set of its boundary conditions and show that it is a categorification of the derived category of coherent sheaves on X. In the special case when X is a cotangent bundle to a complex manifold Y, this 2-category is closely related to the 2-category of derived categorical sheaves over Y introduced by Toen and Vezzosi. I will also explain a surprising connection between a categorification of deformation quantization and complex symplectic geometry.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons