报告时间：2024年12月2日 16:00开始
报 告 人：Guido CARLET（法国第戎大学 教授）
报告地点：9-305
报告题目：Cohomology, deformations and structure of local homogeneous Poisson brackets of arbitrary degree
报告摘要：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. Work in progress with M. Casati.
报告人简介：Guido Carlet, 法国第戎大学布尔古涅数学研究所教授，博士生导师。拥有意大利帕多瓦大学理论物理学学位和意大利里雅斯特国际高等研究学院数学物理学博士学位。
