# The 19th Geometry and Physics Seminars

- Date: –16:00
- Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 Å4001
- Lecturer: Arkady Vaintrob and Reimundo Heluani
- Contact person: Rebecca Lodin
- Föreläsning

The 19th geometry and physics seminars will take place on June 4 from 13:30 till 16:00

in Å4001. The seminars aim at increasing the interaction between physics and math.

The speakers are Prof. Reimundo Heluani (IMPA, Rio de Janeiro) and Prof. Arkady Vaintrob (Oregon U). The seminars are jointly organized by the Department of Mathematics and the Department of Physics and Astronomy.

A mirror symmetry correspondence for Landau-Ginzburg models

Speaker: Arkady Vaintrob

Department: Oregon U

Time: 2019-06-04 13:30 - 14:30

Location: Å4001, Ångströmlaboratoriet

Abstract: 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.

Classical Freeness of CFTs

Speaker: Reimundo Heluani

Department: IMPA, Rio de Janeiro

Time: 2019-06-04 15:00 - 16:00

Location: Å4001, Ångströmlaboratoriet

Abstract: To any vertex operator algebra/CFT V one can attach a classical field theory limit P (roughly the Poisson algebra of local observables) and a classical mechanics limit C (roughly the Poisson algebra of zero modes). On the other hand to any classical mechanics system, say a Poisson algebra C with Hamiltonian H, one can attach a classical field theory JC "freely generated by C". When C is the classical mechanics limit of a CFT V, there is a canonical surjection JC --> P. We explore the question of when this is an isomorphism providing the first known examples and counterexamples. This is joint work with J. van Ekeren.