Flat coordinates of algebraic Frobenius manifolds

Johan Wright (University of Glasgow)

Tuesday 4th June 16:00-17:00 110

Abstract

In the 1990s, Dubrovin developed the idea of a Frobenius manifold and showed that one could define two flat metrics on them. Dubrovin constructed polynomial Frobenius manifolds from the orbit spaces of finite Coxeter groups and showed that one set of flat coordinates could be written as a particular set of Coxeter-invariant polynomials, called Saito polynomials, in terms of the other set of flat coordinates. 

We look at algebraic Frobenius manifolds and find relations between the two sets of flat coordinates for most known examples in small dimensions. In this talk, we will present our technique for finding these relations along with some other observations on the dual structure for some algebraic Frobenius manifolds.

This talk is based on joint work done with Misha Feigin and Daniele Valeri.

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