清华主页 EN
导航菜单

Indices of vector fields and Chern classes for singular varieties

来源: 04-19

时间:Wed., 9:50-11:25 am; Fri., 1:30-3:05 pm; Apr. 19-May 12, 2023

地点:Room A-404, Science Building, Department of Mathematical Sciences, Tsinghua Univerisity

主讲人:José Antonio Seade Kuri National University of Mexico

Speaker

José Seade obtained his BSc in mathematics from the National University of Mexico (UNAM) in 1976 and his Masters and PhD from the University of Oxford in 1977 and 1980, respectively. Since then, he has worked at the Institute of Mathematics, UNAM, where he has been director since April of 2014.

His present research interests are on singularities theory and complex geometry and he has authored several publications in algebraic topology, algebraic and differential geometry and geometric analysis. He has been awarded the Ferran Sunyer i Balaguer Prize twice (2005 and 2012), was President of the Mexican Mathematical Society (1986-87) and founded the Mexican Mathematics Olympiades. He also founded the Solomon Lefschetz International Laboratory of Mathematics, in Cuernavaca, Mexico, which is associated with the CNRS of France, and is the current Scientific Coordinator of that laboratory. He was a member of the Scientific Council of UMALCA, the Latin American and Caribbean Union of Mathematicians (2001-2009) and since then has been a member of the Executive Committee of UMALCA.


Course Description:

The Poincare- Hopf local index of a vector field at an isolated singularity on a smooth manifold is a classical invariant that has given rise to a vast literature. The Poincare-Hopf theorem stating that the total index of a vector field on a closed smooth manifold equals the Euler characteristic is a cornerstone in several areas of mathematics. These are much related with the theory of Chern classes on smooth manifolds, which play a fundamental role in geometry and topology. In this course we shall discuss generalizations to the case of complex analytic singular varieties. In this setting there is not a unique concept of index of a vector field, nor a unique notion of Chern classes, but several different ones, each with its own properties and interest. On a singular variety one does not have a tangent bundle over the singular set, and the various notions of index and Chern classes somehow correspond to different ways of extending the tangent bundle over the singular part.

In this course we will start by reviewing the classical theory. Then we shall move toward singular varieties, starting with examples, the basic definitions and properties, stratifications, the local conical structure of analytic sets and Milnor’s fibration theorem.

返回顶部
相关文章
  • Valuative stability of polarized varieties and applications

    AbstractRecently, Dervan-Legendre considered the valuative criterion of polarized varieties. We will study the valuative stability and show that it is an open condition. We would like to study the valuative criterion for the Donaldson's J-equation. Motivated by the beta-invariant of Dervan-Legendre, we introduce a notion, the so-called valuative J-stability and prove that J-stability implies va...

  • Fibre bundles, characteristic classes, and index theorems

    AbstractThis course will cover fiber bundles, characteristic classes, and index theorems, emphasizing their applications in physics.Lecturer Intro.本科和博士毕业于中国科学技术大学,之前是清华大学丘成桐数学科学中心博士后,现在是北京雁栖湖应用数学研究院助理研究员,研究兴趣是用拓扑方法(cobordism)研究理论物理(anomaly)