Speaker:    

吴磊副教授，浙江大学
Inviter:     谢松晏
Title:
    Logarithmic cotangent bundles, Chern classes, and applications
Language:     Chinese
Time & Venue:
    2023.12.06 14:00-15:00 zoom会议：859 4788 3836 密码： 375181
Abstract:
    

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 applylications 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.
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FROM 202.120.11.*