Speaker: Aliaa Barakat
Title: Integrable hierarchies on Frobenius manifolds

Abstract: Frobenius manifolds carry rich, and compatible,geometric and algebraic structures on their tangent bundle. They were defined by B. Dubrovin in his work on topological field theory, but turned out to also arise in the study of moduli problems in other areas of mathematics.

We will begin this talk with the definition of a Frobenius manifold, and give examples from quantum cohomology and singularity theory. We will then discuss their relation to the moduli space of certain integrable hierarchies, and present recent results on the classification of these hierarchies. Time permitting, we will also discuss some conjectures on the Poisson algebras underlying them.