Intrinsic Donaldson–Thomas theory

Intrinsic Donaldson–Thomas theory is a new framework of 
enumerative geometry that allows 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.