4 papers · 1 filter
Hecke operators on symplectic surfaces and -independence
Ben Davison, Lucien Hennecart, Tasuki Kinjo +2
We prove Toda's chi-independence conjecture for the BPS cohomology of moduli spaces of one-dimensional sheaves on quasi-projective symplectic surfaces, relative to the Chow variety…
BPS cohomology in geometry and representation theory
Ben Davison
We motivate and survey the theory of BPS invariants of categories and BPS cohomology of stacks, indicating applications in enumerative geometry and representation theory, as well a…
Degree two Gopakumar-Vafa invariants of local curves
Ben Davison, Naoki Koseki
We investigate the Gopakumar-Vafa (GV) theory of local curves, namely, the total spaces of rank two vector bundles with canonical determinant on smooth projective curves. Under a c…
Cohomology of symmetric stacks
Chenjing Bu, Ben Davison, Andrés Ibáñez Núñez +2
We construct decompositions of: (1) the cohomology of smooth stacks, (2) the Borel--Moore homology of -shifted symplectic stacks, and (3) the vanishing cycle cohomology of $(-1)…