Video library: G. Carlet, An infinite-dimensional Frobenius manifold and the extended 2D Toda hierarchy

VIDEO LIBRARY


International conference "Geometrical Methods in Mathematical Physics" December 15, 2011 14:45, Moscow, Lomonosov Moscow State University

An infinite-dimensional Frobenius manifold and the extended 2D Toda hierarchy G. Carlet International School for Advanced Studies (SISSA)
Abstract: We consider the recent advances in the programme of extending the Frobenius manifolds techniques to integrable PDE's with two spatial variables. First, we review the construction of an infinite-dimensional Frobenius manifold structure $M$ on a 2-vector bundle on the space of simple analytic curves in the complex plane. Second, we show that it is possible to explicitly solve the operator-valued singular linear system on the complex plane associated with the deformed flat connection of the Frobenius manifold. This solution defines a principal hierarchy which extends the dispersionless 2D Toda hierarchy. Language: English