VIRTUAL SEMINAR SERIES -- INTEGRABLE SYSTEMS: Geometry and integrability from affine Weyl groups

Andrea Brini (University of Sheffield)

Wednesday 27th January 13:30-14:30 Zoom seminar hosted by ICMS

Abstract

Frobenius manifolds were introduced by Boris Dubrovin in the early nineties as an axiomatic framework to encode the properties of chiral rings of 2D topological field theories, and at the same time provide a natural stepping stone for the classification of KdV-type, local bihamiltonian integrable hierarchies in one space dimension. While traditional constructions of Frobenius manifolds are given in the quantum co-homology of symplectic manifolds and in singularity theory, a somewhat lesser studied source of Frobenius manifolds and its associated integrable hierarchies arise in Lie theory: in a seminal 1995 paper, Dubrovin and Zhang propose a construction of Frobenius manifolds on the orbits of certain extensions of affine Weyl groups, and propose a Landau--Ginzburg formulation in type A. In this talk I will give a unified picture Landau--Ginzburg description for all Dynkin types. I will also explain how this unlocks simultaneous applications to Frobenius manifolds, topology, integrable systems, Gromov--Witten theory, and five-dimensional gauge theory. This is joint work with K. van Gemst (Sheffield).

 

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