# Genus one correction to free energy of Hermitian matrix models,

G-function of Hurwitz Frobenius manifolds and isomonodromic tau-function

## Dmitri Korotkin

**Abstract: **

The theory of Frobenius manifolds and the theory of Hermitian matrix models
are two different approaches to quantization of 2D topological field theories.
Therefore, it is not very surprising that these theories turn out to be
parallel in several aspects. In particular, in this talk we discuss
similarities between the large N expansion in Hermitian two-matrix models and
the genus expansion of the free energy of a class of Frobenius manifolds
associated to Hurwitz spaces (spaces of meromorphic functions on Riemann
surfaces). In both cases the computation of the higher order corrections to
free energy is based on loop equations; in the subleading order the solution of
the loop equations turns out to be very similar for the two models, and can
be expressed via an appropriate isomonodromic tau function.

(Based on joint work with B.Eynard and A.Kokotov)