Dubrovin-Novikov operators in 2D and bi-Hamiltonian deformationsBA
Andrea Savoldi (Loughborough)
Thursday 12th November, 2015 16:00-17:00 Maths 522
In this talk we discuss some of the recent results obtained in the framework of Poisson structures of hydrodynamic type and their deformations. In particular, the first part of the talk is devoted to the classification of such structures in two dimensions, both non-degenerate and degenerate. Complete lists of such structures are provided for a small number of components, as well as partial results in the multi-component non-degenerate case.
In the second part, we deal with deformations of Poisson structures of hydrodynamic type. Deformation theory of Poisson structures is of great interest in the theory of integrable systems, and plays also a key role in the theory of Frobenius manifolds. In particular, we investigate deformations of non-semisimple bi-Hamiltonian structures associated with Balinskii-Novikov algebras. Complete classification of second-order deformations are presented for two-component structures.