Chenjing Bu: Intrinsic enumerative geometry
I will introduce a new framework for studying the enumerative geometry of general algebraic stacks, which is intrinsic to the stack, and generalizes existing enumerative theories for moduli stacks of objects in abelian categories. A key ingredient of the framework is the component lattice of a stack, which is a globalized version of the cocharacter lattice and the Weyl group of an algebraic group. I will explain applications of the framework in motivic and cohomological Donaldson–Thomas theory. These include the construction of motivic DT invariants and BPS cohomology for general smooth, (−1)- or 0-shifted symplectic Artin stacks, and a general decomposition theorem in the style of Davison–Meinhardt. This talk is based on several joint works with Ben Davison, Daniel Halpern-Leistner, Andrés Ibáñez Núñez, Tasuki Kinjo, and Tudor Pădurariu.
More details can be found on https://www.imperial.ac.uk/geometry/seminars/magic-seminar/