Bi-Flat F-manifolds, complex reflection groups and integrable systems of conservation laws

Paolo Lorenzoni, University of Milano-Bicocca

We show that bi-flat F-manifolds can be interpreted as natural geometrical structures encoding the almost duality for Frobenius manifolds without metric. Using this framework, we extend Dubrovin's duality between orbit spaces of Coxeter groups and Veselov's v-systems,  to the orbit spaces of exceptional well-generated complex reflection groups of rank 2 and 3.

We finally discuss some applications to integrable systems of conservation laws. The talk is based on joint works with A. Arsie.