I: An Introduction to Characteristic Classes on Singular Varieties II: The Characteristic Classes of Restricted Constructible Functions on Free Divisor Complement

：Xiping Zhang (TongJi University)
： 2024-11-19 09:30
：Conference Room S204 at Experiment Building at Haiyun Campus

Speaker：Xiping Zhang (TongJi University)

Time：2024-11-19, 9:30

Location：Conference Room S204 at Experiment Building at Haiyun Campus

Abstract:

I: Characteristic classes generalize classical topological invariants by extending them from numbers to cohomology classes. These classes capture important topological features of the base space, particularly the appearance of singularities. In recent work by June Huh, Bernd Sturmfels and others, these numerical invariants have been connected to other areas of mathematics such as algebraic combinatorics and algebraic statics. In this talk, we will introduce the theory of characteristic classes in the context of singular projective varieties, exploring their role in understanding the topology of such spaces.

II: Let U be the complement of a divisor D. For any other hypersurface V of M, the intersection of V with D is affected by both the intersection behavior and their singularities. This intersection is traditionally studied using a log resolution and logarithmic methods. In this talk we will focus on the Chern class of the complement V∩U. We will discuss how to understand such Chern class when V is Logarithmic transverse to D.