Abstract: Intrinsic Donaldson–Thomas theory is a new framework of enumerative geometry that allow certain constructions of enumerative invariants to be interpreted intrinsically to the geometry of the moduli stack, and consequently, to be extended to much more general stacks than previously possible. Such constructions also allow us to prove interesting general properties of algebraic stacks, such as decomposition theorems for cohomology of stacks and semiorthogonal decompositions for derived categories of coherent sheaves on stacks. We also discuss some potential applications that these results open up, including applications to representation theory and to the geometric Langlands programme.

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