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.
Primary author
Guido Carlet
(Université de Bourgogne)
