Teleman’s reconstruction theorem for semi-simple cohomological field theories

In his paper "The structure of 2D semi-simple field theories", Teleman showed that the Givental group acts transitively on semi-simple CohFTs, so that any semi-simple flat unit CohFT can be reconstructed from its cohomological 0-degree part by means of its associated Frobenius manifold. The goal of my thesis is to understand his proof. In their paper "Semisimple flat F-manifolds in higher genus", Arsie, Buryak, Lorenzoni and Rossi found an adaptation of the Givental group and they showed that it can be used to produce a F-CohFT FΩ' from the cohomological 0-degree part of an original flat unit F-CohFT FΩ by means of the FΩ-associated Flat F-Manifold. Inspired by their work, in the last chapter of my thesis I try to sketch an adaption of Teleman’s proof to show that FΩ and FΩ' actually coincide after taking the restriction to a partial compactification of the moduli space of Riemann Surfaces, namely to the union of those strata whose dual graphs are stable trees, provided that another tecnical hypothesis is added. This may be the starting point for a future work in the direction of actually prove this result.