Flat F-manifolds, F-CohFT and integrable systems

https://hu-berlin.zoom.us/j/61686623112
Contact: Gaetan Borot (gaetan.borot@hu-berlin.de)

Cohomological field theories are families of cohomology classes on the moduli space of stable curves of genus g, with n distinct marked points. The parameters in these families live on the n-fold tensor product of a vector space V. They must satisfy boundary conditions prescribing their behaviour at the boundary divisors of the moduli space, parametrizing stable curves with separating and nonseparating nodes. F-CohFTs differ from cohomological field theories in that one marked point plays a special role (S_{n} equivariance is broken to S_{n-1}-equivariance) and a boundary condition is imposed at separating nodes only (the node is formed by attaching the special point on one component and a normal one on the other). If CohFTs reduce to Dubrovin-Frobenius manifolds when restricted to genus 0, F-CohFTs reduce to flat F-manifolds. In this talk I will explain how the well known-relation between CohFTs and integrable systems can be extended to F-CohFTs, at the cost of losing the Hamiltonian structure. I will also mention that the well known Givental-Teleman reconstruction result of a semisimple CohFT from its Frobenius manifold can be generalized to semisimple F-CohFTs. All this is the fruit of a joint work with A. Arsie, A. Buryak and P. Lorenzoni.