Originally introduced by Eisenbud in the context of commutative algebra, matrix factorizations have since earned a prominent role in mathematical physics as the "D-branes of type B" in a Landau-Ginzburg model. In this spirit, Orlov proved that a certain category of matrix factorizations over affine space is equivalent to the derived category of a Calabi-Yau hypersurface.

In this talk I will describe preliminary work using matrix factorizations to give a new description of the virtual class in Gromov-Witten theory, FJRW theory, and so-called hybrid theories. We hope that this construction will help clarify the relationship between the virtual classes in these various theories.
Speaker(s): Mark Shoemaker (Colorado State)