Speaker : Adeel Khan (Academia Sinica, Institute of Mathematics)
Title : Cohomological intersection theory and derived algebraic geometry
Time : 2022-01-19 (Wed) 10:00 - 12:00
Place : Seminar Room 638, Institute of Mathematics (NTU Campus)
Abstract: In these lectures, we will explain a cohomological approach to the intersection theory of schemes and stacks. By working with Voevodsky's theory of motivic cohomology, we will see that this recovers and extends the cycle-theoretic approach of Fulton (and its extension to stacks by Kresch). Moreover, we will use the language of derived algebraic geometry to systematically incorporate non-transversality phenomena, most notably Kontsevich's virtual fundamental classes. We will discuss examples related to curve counting, cohomological Hall algebras, and even Shimura varieties, depending on participants' interests. No prior knowledge of stacks or derived geometry will be assumed.
In this second lecture, we will begin with intersection theory. After giving an introduction to derived algebraic geometry, we will see a derived version of Verdier's deformation to the normal cone and use it to construct the elements of intersection theory in cohomology.