Mathematics

 For any semisimple Frobenius manifold, we construct the so-called Hodge integrable hierarchy, which is a tau-symmetric deformation of the integrable hierarchy of topological type. For the one-dimensional Frobenius manifold, we conjecture that the Hodge hierarchy is a universal object in the class of all tau-symmetric Hamiltonian deformations of the KdV hierarchy. We also explain some recent connections between Hodge integrals and random matrices. The talk is based on a joint work with Boris Dubrovin, Si-Qi Liu and Youjin Zhang.