Frobenius manifolds, mirror symmetry and integrable systems

Abstract: Frobenius manifolds were introduced by Boris Dubrovin in the early 90’s as a means to describe 2-dimensional topological field theories in a coordinate-free way. Now, however, they arise in seemingly very distant mathematical areas and provide a bridge between them. Examples of such topics are enumerative geometry, singularity theory and integrable systems. In fact, mirror symmetry can be phrased as an isomorphism of Frobenius manifolds.

In this talk I will give a brief overview of what a Frobenius manifold is and how they are useful in the context of mirror symmetry. I will then present recent results obtained together with Andrea Brini. Lastly, I will highlight the connection between Frobenius manifolds and integrable systems, and an application of our mirror theorem in this context.

arxiv.org/abs/2103.12673

mathematical physicsalgebraic geometrydifferential geometrydynamical systemssymplectic geometry

Audience: researchers in the topic

( paper )

Junior Global Poisson Workshop II