7 papers
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…
BPS algebras and generalised Kac-Moody algebras from 2-Calabi-Yau categories
Ben Davison, Lucien Hennecart, Sebastian Schlegel Mejia
We determine the structure of the BPS algebra of 2-Calabi-Yau Abelian categories for which the stack of objects admits a good moduli space. We prove that this algebra is isomorphic…
BPS Lie algebras for totally negative 2-Calabi-Yau categories and nonabelian Hodge theory for stacks
Ben Davison, Lucien Hennecart, Sebastian Schlegel Mejia
We define and study a sheaf-theoretic cohomological Hall algebra for suitably geometric Abelian categories of homological dimension at most two, and a sheaf-theoretic…
Affine BPS algebras, W algebras, and the cohomological Hall algebra of
Ben Davison
We introduce affinizations and deformations of the BPS Lie algebra associated to a tripled quiver with potential, and use them to precisely determine the -equivariant cohomologi…