Speaker: Guido Carlet (SISSA, Italia)

Title: "An infinite-dimensional Frobenius manifold associated to a 2+1 integrable hierarchy."

Abstract:
Abstract:  The notion of Frobenius manifold originated from topological field 
theory and proved important in the study of integrable hierarchies of PDEs with
 one spatial dimension. In this talk we introduce a structure of infinite-dimensional
 Frobenius manifold on a subspace in the space of pairs of functions analytic 
in the inner/outer regions of the unit circle in the complex plane with simple
 poles at 0/infinity respectively.We argue that the equations of the dispersionless
 2D Toda hierarchy are contained in a much larger integrable hierarchy associated
 with this Frobenius manifold. In the first part of the talk we will review the
 construction of the bi-Hamiltonian formulation of the (dispersive) 2D Toda
 hierarchy through R-matrix theory and some basic facts of the theory of 
Frobenius manifolds.
http://arxiv.org/abs/0902.1245v1