Summations over generalized ribbon Feynman diagrams and all genus Gromov-Witten invariants

The construction of cohomology classes of compactified moduli spaces of curves from asymptotic expansions of EA matrix integrals, described in the works of speaker, is presented. The construction defines a cohomological field theory, which conjecturally coincides with the all genus Gromov-Witten invariants of the mirror manifold. The construction is based on the speaker’s theorem identifying the cell complex of the compactified moduli space of curves with the Feynman transform of the operad of permutation group algebras. As a simple application a new formula for generating function for products of psi classes in the total cohomology of the compactified moduli spaces of curves is described. Relevant papers: arxiv:1803.11549 / HAL-00429963 (2009), arxiv:0912.5484 / hal-00102085(2006)