Open enumerative geometry for Landau-Ginzburg models and Mirror Symmetry

A Landau-Ginzburg (LG) model is a triplet of data $(X,W,G)$ consisting of a regular complex-valued function W from a quasi-projective variety X with a group G acting on X so that W is invariant. An enumerative theory developed by Fan, Jarvis and Ruan gives FJRW invariants, an analogue of Gromov-Witten invariants, for LG models. We define an open enumerative theory for certain LG models, building on the FJRW point of view. Roughly speaking, our theory involves computing specific integrals on certain moduli of discs with boundary and interior marked points. One can then construct a mirror LG model to the original one using these invariants. This allows us to prove a mirror symmetry result analogous to that established by Cho-Oh, Fukaya-Oh-Ohta-Ono and Gross in the context of mirror symmetry for toric Fano manifolds. If time permits, I will explain some key features that this enumerative geometry enjoys (e.g., open topological recursion relations and wall-crossing). This is joint work with Mark Gross and Ran Tessler.

https://hu-berlin.zoom.us/j/61686623112 
Contact: Gaetan Borot (HU Berlin, gaetan.borot@hu-berlin.de)

Even when the speakers are not from Bonn, the seminar is videostreamed from the Lecture Hall.