I will explain a new intrinsic framework for enumerative geometry, with the aim of generalizing existing theories, such as Donaldson–Thomas theory, from moduli stacks of objects in abelian categories to general stacks. I will focus on a key ingredient of the framework, the component lattice of a stack, which globalizes the cocharacter lattice and the Weyl group of an algebraic group. I will briefly describe applications of the framework in motivic and cohomological DT theory.

This talk is based on joint works with Ben Davison, Daniel Halpern-Leistner, Andrés Ibáñez Núñez, Tasuki Kinjo, and Tudor Pădurariu.