Gauss-Bonnet-Chern theorem for singular spaces and Donaldson-Thomas theory

发布时间：2018-06-21 来源：赢咖3 浏览次数：

Speaker:	蒋云峰教授	DateTime:	2018年6月25日（周一）上午10:00-11:00
Brief Introduction to Speaker: 蒋云峰教授，美国堪萨斯大学。		Place:	六号楼二楼报告厅
Abstract:The Gauss-Bonnet-Chern theorem states that for a smooth compact complex manifold,the integration of the top Chern class is the topological Euler characteristic of the manifold.In order to study Chern class for singular spaces,R. MacPherson introduced the notion of local Euler obstruction.A characteristic class for a local Euler obstruction was defined by using Nash blow-ups, and is called the Chern-Mather class or Chern-Schwartz-MacPherson class. The Gauss-Bonnet-Chern theorem is generalized to singular spaces by the top Chern-Schwartz-MacPherson classes. Inspired by gauge theory in higher dimension and string theory, the curve counting theory via stable coherent sheaves was constructed by Donaldson-Thomas on projective 3-folds, which is now called the Donaldson-Thomas theory.