The Barannikov-Kontsevich theorem from a derived algebraic geometry point of view

Márton Hablicsek (U. Penn)

In this talk I consider a generalization of the de Rham theorem that is of interest in the study of singularity theory and in the theory of matrix factorizations. Let X be a quasi-projective scheme equipped with a regular function f such that its critical locus is proper. This data gives rise to two complexes: the algebraic de Rham complex with twisted differential d-df and the algebraic de Rham complex with differential df. A famous claim of Barannikov-Kontsevich asserts that the hypercohomology spaces of the two complexes are of the same finite dimensions. In the talk I give a description of the two complexes from a derived algebraic geometry point of view. In the end of the talk I deduce the Barannikov-Kontsevich theorem using the theory of derived intersections. The work is joint with Dima Arinkin and Andrei Caldararu.

Tuesday, November 11th, at 4:00pm in HBH 227

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