## International Conference on $p$-ADIC MATHEMATICAL PHYSICS AND ITS APPLICATIONS $p$-ADICS.2015, 07-12.09.2015, Belgrade, Serbia

Alexander, Belavin

### Frobenius manifolds, Integrable structures and Minimal string theory

Abstract

This talk is about of the computations of the correlation numbers in Minimal Liouville gravity . We use the conjecture that the Douglas equation is applicable to the Minimal Liouville Gravity as well as to the Matrix Models of 2d gravity. We found how to choose the desired solution of the Douglas equation and an appropriate form of the resonance transformation from the KdV times to the Liouville coupling constants to satisfy the needed constraints of MLG. For this aim we use the connection of the String equation with the corresponding Frobenius manifold structure and Integrable Kdv structures. We find the necessary solution of this equation. The solution of the Douglas equation has a very simple form in the flat coordinates on the Frobenious manifold . Using this solution and the suitable choosen resonance transformation lead to the results which are consistent with the selection rules of the models of MLG.