Lecture: A mirror symmetry correspondence for Landau-Ginzburg models
- Date: –14:30
- Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 Å4001
- Lecturer: Arkady Vaintrob, Oregon U
- Contact person: Tobias Ekholm and Maxim Zabzine
Here are several known constructions (generally called Landau-Ginzburg models) of quantum invariants associated to a quasi-homogeneous polynomial W with an isolated singularity at the origin. These invariants play a prominent role in various mirror symmetry correspondences connecting LG models with other kinds of quantum invariants. If the polynomial W is invertible (i.e. when the number of monomials in W is equal to the number of variables), then the dual polynomial W' with the transposed matrix of exponents also has an isolated singularity and we can talk about relations between LG models for W and W'. Correspondences of this type were first considered by Berglund and Huebsch in the early 1990s, but their mathematical understanding was developed only relatively recently. I will present a mirror symmetry theorem connecting a LG B-model of W and a LG A-model of W' based respectively on Saito's theory of primitive forms and a cohomological field theory for W' constructed in my earlier work with Polishchuk using categories of matrix factorizations.