Seminar

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As Nick explained in his talk the moduli space of suitable sheaves on a Calabi-Yau 3-fold has a (-1)-shifted symplectic structure, and by a derived Darboux theorem it can locally be written as the derived critical locus of a potential on a smooth variety.

On such a local model one can define certain categorifications of DT invariants via vanishing cycles or matrix factorizations. It is then a highly non-trivial question how to glue together these local models.

I will describe a framework that allows us to do this. In particular we recover Brav-Bussi-Dupont-Joyce-Szendroi's perverse sheaf categorifying DT-invariants, and see how to categorify again and glue (nc motives of) matrix factorizations, subject to certain orientation data.

This is joint work in progress with B. Hennion and M. Robal