Speaker：Youjin Zhang（Tsinghua University）

Time：2022-12-13, 15:00

Location：Tencent Meeting ID：466-005-8776（No Password）

Abstract:

The notion of Frobenius manifold was introduced by Dubrovin in the beginning of the 90's of the last century, it is a geometric description of the Witten-Dijkgraaf-Verlinde-Verlinde equations. Associated to any Frobenius manifold there is an integrable hierarchy of hydrodynamic type, which is called the Principal Hierarchy of the Frobenius manifold. For a semisimple Frobenius manifold, Dubrovin and Zhang constructed the topological deformation of the Principal Hierarchy in 2001, the tau function of a particular solution of this deformed integrable hierarchy corresponds to partition functions of 2d topological field theories. By using this construction, one can establish relations of some integrable hiearchies that are well-known in the theory of nonlinear integrable systems with Frobenius manifolds, such as the KdV hierarchy and the Toda hierarchy. In this talk, we are to expalin how to generalize the Dubrovin-Zhang construction to a class of generalized Frobenius manifolds with non-flat unit vector fields, and to establish relations of the Volterra hierarchy and the Ablowitz-Ladik hierarchy with such a class of generalized Frobenius manifolds.