| Résume | I will talk about a joint project with Chenjing Bu, Ben Davison, Andrés Ibáñez-Núñez, and Tasuki Kinjo.
For a large class of stacks, we decompose their cohomology in BPS cohomology, which is a structure originating in enumerative geometry of Calabi-Yau 3-folds, but which is of interest beyond this class of examples.
Such stacks include smooth stacks (such as the moduli of G-bundles on a curve), symplectic stacks (such as the moduli of G-Higgs bundle on a curve), or (-1)-shifted symplectic stacks (such as the moduli of semistable sheaves on a Calabi-Yau threefold).
I plan to explain the proof of the main theorem for the example of rank 2 and degree 0 semistable vector bundles on a curve (which was already treated by Meinhardt and Mozgovoy-Reineke). I will then introduce BPS cohomology and state the theorem for (-1)-shifted and 0-shifted symplectic stacks. I will mention conjectural applications of BPS cohomology in Langlands duality for compact real oriented 3-manifolds (following Ben-Zvi-Gunningham-Jordan-Safronov). Time permitting, I will state a version of topological mirror symmetry for G-Higgs bundles (for general reductive groups G) using BPS cohomology. |
