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学术报告四十五:Gauss-Bonnet-Chern theorem for singular manifolds and Donaldson-Thomas theory

来源:数学与统计学院     作者:     时间:2018/6/11 15:55:44  0次

数学与统计学院学术报告[2018] 045

(高水平大学建设系列报告164)

讲座题目:  Gauss-Bonnet-Chern theorem for singular manifolds and Donaldson-Thomas theory

讲座人: 蒋云峰  副教授  美国堪萨斯   大学

讲座时间:6.12(周二)14:30-15:30

讲座地点: 科技楼514

邀请人:   汤建良  教授

报告内容:

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. In the case of the Calabi-Yau threefolds, the Donaldson-Thomas invariants are proved by Behrend to be "weighted Euler characteristic" of the moduli space, where the weights come from the local Euler obstruction of the moduli space. In this talk I will survey some results of the Donaldson-Thomas invariants along this line, and talk about one case that how the Behrend weighted Euler characteristic is related the Y. Kiem and J. Lis cosection localization invariants.  

报告人简历:蒋云峰, 美国堪萨斯大学, 数学系副教授。  研究方向: 代数几何,枚举几何,数学物理。 代表性论文发表在: Advances in Mathematics》,《Journal of Differential Geometry》, Journal of Algebraic Geometry》,《C re l le s Journal》等著名数学杂志上。

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