题目：Structure, cohomology and deformations  of local homogeneous Poisson brackets of arbitrary degree

报告人：Professor Guido Carlet ,  Institut de Mathématiques de Bourgogne, France

时间：2025年4月15日（周二）下午 3:20--4:20

地点：东区管理科研楼1418教室

摘要：Dubrovin and Novikov initiated the study of local homogeneous differential-geometric Poisson brackets of arbitrary degree k in their seminal 1984 paper. Despite many efforts, and several results in low degree, very little is known about their structure for arbitrary k. After an introduction to the topic, we first report on our recent results on the structure of DN brackets of degree k. By applying homological algebra methods to the computation of their Poisson cohomology (or rather of an associated differential complex) we show that certain linear combinations of the coefficients of a degree k DN bracket define k flat connections. Moreover the Poisson cohomology of such brackets is related with the Chevalley-Eilenberg cohomology of an associate finite-dimensional Lie algebra. In collaboration with M. Casati.