报告题目：Poisson cohomology and linearization

报 告 人：Florian Michael Zeiser

所在单位：Institute for Basic Science

报告时间：9:00-11:00， May 12, 2026, May 13, 2026, May 14, 2026

报告地点：伍卓群楼3楼多功能厅2

报告摘要:  

The (non-)existence of a local form is an important question for any geometric structure. The non existence of a local normal form in Riemannian geometry implies the existence of local invariants, e.g. curvature, while the existence of a local normal form for a symplectic structure implies that we can not distinguish such manifolds locally. In this minicourse we investigate this question for Poisson structures.

In the first lecture we introduce the basics of Poisson geometry. Starting from a Poisson bracket, we give a reinterpretation in terms of bivector fields and take a first step towards a local normal form theorem with Weinstein's splitting theorem. Moreover, we will see that any Poisson structure induces a symplectic foliation and provide various examples.

Any Poisson structure induce a cohomology, Poisson cohomology. In the second part, we discuss its importance in Poisson geometry and different methods which allow us to compute Poisson cohomology in some cases. Finally, in the third part of this minicourse we discuss the (non)existence of normal forms, i.e. the question of linearization in Poisson geometry, and the role of Poisson cohomology to answer it.

报告人简介：Florian Michael Zeiser is a Research Fellow at the Institute for Basic Science in the Center for Geometry and Physics in Pohang. He is interested in the study of geometric structures such as folitations, symplectic geometry and Poisson geometry. He has published papers in Memoirs of the AMS, Journal of Symplectic Geometry, Journal of Algebra and other journals.