Lecture 1: The pro-Chern-Schwarz-MacPherson class in Borel-Moore motivic homology

Speaker: Fangzhou Jin, Tongji University

Time: 20:00-21:00 pm, September 22, 2022, GMT+8 (15:00-16:00 pm St Petersburg time)

Venue: Zoom Meeting ID: 813 3853 9299 Password: 654321

Abstract:

We show that the zero-dimensional part of the pro-Chern-Schwarz-MacPherson class defined by Aluffi is equal to the pro-characteristic class in limit Borel-Moore motivic homology. A similar construction also produces a quadratic refinement of this class in the limit Borel-Moore Milnor-Witt homology. This is a joint work with Peng Sun and Enlin Yang.

Biography:

Fangzhou Jin is an assistant professor at Tongji University. He obtained his PhD at Ecole Normale Supérieure de Lyon in 2016 under the supervision of Frédéric Déglise. His work is related to foundational aspects of motivic homotopy theory, a theory introduced by Morel and Voevodsky which studies cohomology theories on algebraic varieties using geometric as well as categorical tools by importing ideas from algebraic topology.

Lecture 2: Triangulated categories, weight structures, and weight complexes

Speaker: Mikhail Bondarko, St. Petersburg State University

Time: 21:00-22:00 pm, September 22, 2022, GMT+8 (16:00-17:00 pm St Petersburg time)

Venue: Zoom Meeting ID: 813 3853 9299 Password: 654321

Abstract:

(Co)homology functors usually yield certain functors into triangulated categories. I will justify this claim and recall some basics on homotopy categories of complexes and other triangulated categories. Next, I define weight structures on triangulated categories; these were independently introduced by B. and D. Pauksztello. Weight structures give certain filtrations of triangulated categories; the definition is a certain cousin of that of t-structures. I will mention some methods of constructing weight structures as well as interesting "topological" and motivic examples. Weight structures give certain weight complex functors that are "usually" exact; they are also conservative up to "objects of infinitely large and infinitely small weights" (that is, weight complexes only kill extensions of objects of these two sorts). In particular, one has an exact conservative functor from geometric Voevodsky motives into complexes of Chow motives, whereas the corresponding weight spectral sequences vastly generalize Deligne’s ones. Weight complexes also enable one to calculate the corresponding pure functors; some of the latter are quite new and interesting.

The talk can be interesting to anyone who had some experience with (co)homology and categories.

Biography:

Mikhail Bondarko is an associate professor at the St. Petersburg State University and also a professor of the Russian Academy of Sciences. He obtained his PhD in 2000 and got his Doctor Degree (habilitation) in 2007. He has some prestigious awards; this includes first prize in the Chinese Mathematical Olympiad in 1994. Currently, Bondarko studies triangulated categories (including motivic ones), weight structures, and t-structures on them. He also has several papers on formal groups, finite flat group schemes, and additive Galois modules.

Source: SRMC