MS Seminar (Mathematics - String Theory)

Speaker: Arkady Vaintrob (U of Oregon)
Title: Cohomological field theories from matrix factorizations
Date: Tue, May 08, 2018, 13:15 - 14:45
Place: Seminar Room A
Abstract: A Cohomological field theory (CohFT) is an algebraic structure underlying the properties of Gromov-Witten invariants and quantum cohomology. I will describe a CohFT associated with a quasihomogeneous hypersurface singularity together with a finite group G of its symmetries. The state space of this theory is the equivariant Milnor ring of W and the corresponding invariants can be viewed as analogs of Gromov-Witten invariants for the non-commutative space associated with the pair (W,G). The construction is based on categories of (equivariant) matrix factorizations of singularities. The role of the virtual fundamental class from the Gromov-Witten theory played by a "fundamental matrix factorization" over a certain moduli space. I will present the main ingredients of the construction of the CohFT and some recent results and applications. The talk is based on joint work with A.Polishchuk.