Mirror pairs XY are related by a geometric duality. Does this Geometry (G) produce Enumerative Mirror Symmetry (EMS), namely the prediction that the genus 0 Gromov-Witten invariants of X are computed by period integrals on Y? I will give a positive answer in a few examples, where we take XY to be intrinsic mirror pairs (Gross--Siebert). Based on joint work…

Abstract: Landau--Ginzburg (LG) models are the natural mirror candidates to Fano manifolds and have an enumerative theory analogous to quantum cohomology, known as FJRW theory. In this talk, I will begin by giving an overview of these ideas, keeping a running comparison to quantum cohomology in order to explain some of the similarities and subtleties. I will then briefly…

Manifolds with generalized corners (g-corners), introduced by Joyce, are spaces that locally look like rational polyhedral cones. We describe the notion of b-complex manifolds with g-corners and establish an analogue of the (formal) Newlander–Nirenberg theorem ensuring the existence of local complex coordinates on such manifolds. We also show that Kato–Nakayama spaces associated to log smooth complex analytic…

We study boomerangs in the derived category of an elliptic curve C. These are filtrations of the zero object whose factors are polystable objects with strictly increasing phase. The numerical invariants of a boomerang are given by the Chern characters of the direct summands of these factors, which together determine a lattice polygon. When this polygon is a T-polygon,…