报告题目：DG manifolds and Atiyah classes

报告人：陈酌副教授  清华大学

报告时间：2018年1月16日上午10:30-12:00

报告地点：mk体育官网一楼报告厅

欢迎光临！

摘要: The notion of DG (differential graded) manifold, also known as NQ supermanifold, is a generalizationof the notion of smooth manifold from ordinary geometry to higher geometry, specifically to DG geometry.A DG vector bundle is a vector bundle in the category of DG manifolds. In this talk, we review the originalAtiyah class (and Todd class) of holomorphic vector bundles, that of DG vector bundles and that of DGmanifolds introduced by Mehta, Stienon and Xu. We show some emerging connections between derivedgeometry and classical areas of mathematics such as complex geometry, foliation theory, Poisson geometryand Lie theory. We study, in particular, the Atiyah class and Todd class of the DG manifold (F[1], dF )coming from an integrable distribution F _ TKM = TM R K, where K = R or C. It develops aframework that encompasses both the original Atiyah class of holomorphic vector bundles and Molino classof real vector bundles foliated over a foliation as special cases. This is a joint work with M. Xiang and P. Xu.

报告人简介：陈酌，清华大学数学科学系副教授。研究领域是辛几何, Poisson几何与非线性李理论。近年来在Poisson群胚, 李双代数胚和Courant代数胚的课题研究中,取得了一系列学术成就。在J. Diff. Geom和Commu. Math. Phys等国际著名期刊发表数十篇论文。