Oberseminar Algebra und Geometrie

Talk by Tyler Kelly (Birmingham)

An Open Enumerative Theory for Landau-Ginzburg models.

Abstract: Landau-Ginzburg models consist of a pair (W, G) where W is a potential (that is, a complex valued regular function from a quasi-affine variety X) and G is a group acting on X so that W is invariant. In the context of mirror symmetry, oftentimes they can be viewed as a noncommutative symplectic deformation of a symplectic manifold. Over the past couple of decades there has been work in establishing an enumerative theory for a Landau-Ginzburg model, akin to Gromov-Witten theory. Recently, a few of us have aimed to create an open enumerative theory for Landau-Ginzburg models. In the end, we can construct the mirror Landau-Ginzburg model’s potential function as a generating function of open enumerative invariants. This provides the Landau-Ginzburg analogue to Maslov index two discs / tropical discs for a symplectic manifold. This is joint work with Mark Gross and Ran Tessler.