68 citations · 333 across the 29 of their papers we have counts for
29 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…
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)…
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…
Nonabelian Hodge theory for stacks and a stacky P=W conjecture
Ben Davison
We introduce a version of the P=W conjecture relating the Borel-Moore homology of the stack of representations of the fundamental group of a genus g Riemann surface with the Borel-…
A boson-fermion correspondence in cohomological Donaldson-Thomas theory
Ben Davison
We introduce and study a fermionization procedure for the cohomological Hall algebra of representations of a preprojective algebra, that selectively switches th…
Purity and 2-Calabi-Yau categories
Ben Davison
For various 2-Calabi-Yau categories for which the stack of objects has a good moduli space , we establish p…
BPS Lie algebras and the less perverse filtration on the preprojective CoHA
Ben Davison
The affinization morphism for the stack of representations of a preprojective algebra is a local model for the morphism from the stack of objects in a gen…
Deformed dimensional reduction
Ben Davison, Tudor Pădurariu
Since its first use by Behrend, Bryan, and Szendrői in the computation of motivic Donaldson-Thomas (DT) invariants of , dimensional reduction has proved…
Strong positivity for quantum theta bases of quantum cluster algebras
Ben Davison, Travis Mandel
We construct "quantum theta bases," extending the set of quantum cluster monomials, for various versions of skew-symmetric quantum cluster algebras. These bases consist precisely o…
The local motivic DT/PT correspondence
Ben Davison, Andrea T. Ricolfi
We show that the Quot scheme parameterising length quotients of the ideal sheaf of a line in is a global cr…
Refined invariants of finite-dimensional Jacobi algebras
Ben Davison
We define and study refined Gopakumar-Vafa invariants of contractible curves in complex algebraic 3-folds, alongside the cohomological Donaldson--Thomas theory of finite-dimensiona…
Enumerating coloured partitions in 2 and 3 dimensions
Ben Davison, Jared Ongaro, Balazs Szendroi
We study generating functions of ordinary and plane partitions coloured by the action of a finite subgroup of the corresponding special linear group. After reviewing known results…
The integrality conjecture and the cohomology of preprojective stacks
Ben Davison
We study the Borel-Moore homology of stacks of representations of preprojective algebras , via the study of the DT theory of the undeformed 3-Calabi-Yau completion . V…
Positivity for quantum cluster algebras
Ben Davison
Building on work by Kontsevich, Soibelman, Nagao and Efimov, we prove the positivity of quantum cluster coefficients for all skew-symmetric quantum cluster algebras, via a proof of…
Cohomological Donaldson-Thomas theory of a quiver with potential and quantum enveloping algebras
Ben Davison, Sven Meinhardt
This paper concerns the cohomological aspects of Donaldson-Thomas theory for Jacobi algebras and the associated cohomological Hall algebra, introduced by Kontsevich and Soibelman.…
Donaldson-Thomas theory for categories of homological dimension one with potential
Ben Davison, Sven Meinhardt
The aim of the paper is twofold. Firstly, we give an axiomatic presentation of Donaldson-Thomas theory for categories of homological dimension at most one with potential. In partic…
Cohomological Hall algebras and character varieties
Ben Davison
In this paper we investigate the relationship between twisted and untwisted character varieties via a specific instance of the Cohomological Hall algebra for moduli of objects in 3…
The critical CoHA of a quiver with potential
Ben Davison
Pursuing the similarity between the Kontsevich--Soibelman construction of the cohomological Hall algebra of BPS states and Lusztig's construction of canonical bases for quantum env…
Purity of critical cohomology and Kac's conjecture
Ben Davison
We provide a new proof of the Kac positivity conjecture for an arbitrary quiver . The ingredients are the cohomological integrality theorem in Donaldson-Thomas theory, dimension…
Purity for graded potentials and quantum cluster positivity
Ben Davison, Davesh Maulik, Joerg Schuermann +1
Consider a smooth quasiprojective variety X equipped with a C*-action, and a regular function f: X -> C which is C*-equivariant with respect to a positive weight action on the base…