Integrable Systems: Geometrical and Analytical Approaches

On Dubrovin-Novikov brackets

Jun 3, 2024, 9:30 AM

50m

128 (SISSA)

Lecture

Speaker

Guido Carlet (Université de Bourgogne)

Description

Dubrovin and Novikov initiated the study of local homogeneous differential-geometric Poisson brackets of arbitrary degree $k$ in their seminal 1984 paper. Despite several results in low degree, very little is known about their structure for arbitrary $k$. After an introduction to the topic we report on our recent results on the structure of DN brackets of degree $k$. We show that certain linear combinations of the coefficients of a DN bracket define $k$ connections which are all flat and that the Poisson cohomology of a DN bracket is related with the Chevalley-Eilenberg cohomology of a Lie algebra which is naturally associated with the bracket. Joint work with M. Casati.