| Résume | A Landau-Ginzburg (LG) model is a triplet of data (X, W, G) consisting of a regular function W:X → C from a quasi-projective variety X with a group G acting on X leaving W invariant. An enumerative theory developed by Fan, Jarvis, and Ruan inspired by ideas of Witten gives FJRW invariants, the analogue of Gromov-Witten invariants for LG models. These invariants are now called FJRW invariants. We define a new open enumerative theory for certain Landau-Ginzburg models. Roughly speaking, this involves computing specific integrals on certain moduli of disks with boundary and interior marked points. One can then construct a mirror Landau-Ginzburg model to a Landau-Ginzburg model using these invariants. If time permits or as interest of the audience guides, I will explain some key features that this enumerative geometry enjoys (e.g., topological recursion relations and wall-crossing phenomena). This is joint work with Mark Gross and Ran Tessler. |
