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On the Calculus underlying Donaldson-Thomas theory

Thursday 27th January 2011 - 15:30 to 16:30
INI Seminar Room 1
On a manifold there is the graded algebra of polyvector fields with its Lie-Schouten bracket, and the module of de Rham differentials with exteriour differentiation. This package is called a "calculus". The moduli space of sheaves (or derived category objects) on a Calabi-Yau threefold has a kind of "virtual calculus" on it. In particular, this moduli space has virtual de Rham cohomology groups, which categorify Donaldson-Thomas invariants, at least conjecturally. We describe some attempts at constructing such a virtual calculus. This is work in progress.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons