68 citations · 333 across the 29 of their papers we have counts for
19 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…
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…
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-…
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…
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…
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…
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 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…
The motivic Donaldson-Thomas invariants of (-2) curves
Ben Davison, Sven Meinhardt
In this paper we calculate the motivic Donaldson-Thomas invariants for (-2)-curves arising from 3-fold flopping contractions in the minimal model programme. We translate this geome…
Motivic DT-invariants for the one loop quiver with potential
Ben Davison, Sven Meinhardt
In this paper we compute the motivic Donaldson--Thomas invariants for the quiver with one loop and any potential. As the presence of arbitrary potentials requires the full machiner…
Invariance of orientation data for ind-constructible Calabi-Yau categories under derived equivalence
Ben Davison
We study orientation data, as introduced by Kontsevich and Soibelman in order to define well-behaved integration maps from the motivic Hall algebra of 3-dimensional Calabi-Yau cate…
Consistency conditions for brane tilings
Ben Davison
Given a brane tiling on a torus, we provide a new way to prove and generalise the recent results of Szendroi, Mozgovoy and Reineke regarding the Donaldson-Thomas theory of the modu…