学术报告(吴磊 11.3)

Logarithmic cotangent bundles, Chern classes, and applications

发布人:杨晓静 发布日期:2023-10-26
主题
Logarithmic cotangent bundles, Chern classes, and applications
活动时间
-
活动地址
新数学楼403、405
主讲人
吴磊 副教授 浙江大学
主持人
宋雷

Using MacPherson's Euler obstruction function, one can identify the abelian group of constructible functions with the group of algebraic cycles on a smooth complex algebraic variety. Kashiwara's local index formula gives an alternative approach to this identification by using characteristic cycles for holonomic D-modules (they are Lagrangian cycles in the cotangent bundle). This identification then enables us to define Chern classes of algebraic cycles by using characteristic cycles. In this talk, I will first explain how to obtain Chern classes of the pushforward of Lagrangian cycles under an open embedding with normal crossing complement by using logarithmic cotangent bundles motivated by D-module theory. Then I will discuss applications of such Chern classes in understanding Chern-Mather classes of very affine varieties and in proving the Involution Conjecture of Huh and Sturmfels in likelihood geometry. This work is joint with Maxim, Rodriguez, and Wang.