北航微分几何讨论班（第13讲）

题目:Geometry of Maurer-Cartan Elements on Complex Manifolds

报告人：陈酌（清华大学）

报告时间：2020年12月10日10:30-11:30

地点：沙河校区E-405

题目：Geometry of Maurer-Cartan Elements on Complex Manifolds

摘要:The semi-classical data attached to stacks of algebroids in the sense of Kashiwara and Kontsevich are Maurer-Cartan elements on complex manifolds, which we call extended Poisson structures as they generalize holomorphic Poisson structures. A canonical Lie algebroid is associated to each Maurer-Cartan element. We study the geometry underlying these Maurer-Cartan elements in the light of Lie algebroid theory. In particular, we extend Lichnerowicz-Poisson cohomology and Koszul-Brylinski homology to the realm of extended Poisson manifolds; we establish a sufficient criterion for these to be finite dimensional; we describe how homology and cohomology are related through the Evens-Lu-Weinstein duality module; and we describe a duality on Koszul-Brylinski homology, which generalizes the Serre duality of Dolbeault cohomology. This is a joint work with Mathieu Stienon and Ping Xu.

报告人简介：陈酌，2004年在北京大学获博士学位，现任清华大学数学科学系副教授，研究领域属于经典微分几何与数学物理的交叉与结合。近年来在非线性李理论，特别是Atiyah示性类, Poisson群胚,李双代数胚和Courant代数胚的课题研究中,取得了一系列重要学术成果，发表在J. Differential Geometry, Comm. Math. Phys.等权威期刊上。

邀请人：沈良明