BPS Lie algebras for totally negative 2-Calabi-Yau categories and nonabelian Hodge theory for stacks
B Davison, L Hennecart, SS Mejia - arXiv preprint arXiv:2212.07668, 2022 - arxiv.org
We define and study a sheaf-theoretic cohomological Hall algebra for suitably geometric
Abelian categories $\mathcal {A} $ of homological dimension at most two, and a sheaf …
Abelian categories $\mathcal {A} $ of homological dimension at most two, and a sheaf …
Perverse filtrations and Fourier transforms
D Maulik, J Shen, Q Yin - arXiv preprint arXiv:2308.13160, 2023 - arxiv.org
We study the interaction between Fourier-Mukai transforms and perverse filtrations for a
certain class of dualizable abelian fibrations. Multiplicativity of the perverse filtration and the" …
certain class of dualizable abelian fibrations. Multiplicativity of the perverse filtration and the" …
Purity and 2-Calabi-Yau categories
B Davison - arXiv preprint arXiv:2106.07692, 2021 - arxiv.org
For various 2-Calabi-Yau categories $\mathscr {C} $ for which the stack of objects
$\mathfrak {M} $ has a good moduli space $ p\colon\mathfrak {M}\rightarrow\mathcal {M} …
$\mathfrak {M} $ has a good moduli space $ p\colon\mathfrak {M}\rightarrow\mathcal {M} …
Hitchin systems: some recent advances
OK Sheinman, B Wang - arXiv preprint arXiv:2402.08385, 2024 - arxiv.org
arXiv:2402.08385v1 [math-ph] 13 Feb 2024 Page 1 arXiv:2402.08385v1 [math-ph] 13 Feb
2024 HITCHIN SYSTEMS: SOME RECENT ADVANCES OKSHEINMAN AND BIN WANG …
2024 HITCHIN SYSTEMS: SOME RECENT ADVANCES OKSHEINMAN AND BIN WANG …
Cohomological -independence for Higgs bundles and Gopakumar–Vafa invariants
T Kinjo, N Koseki - Journal of the European Mathematical Society, 2024 - ems.press
The aim of this paper is two-fold. Firstly, we prove Toda's-independence conjecture for
Gopakumar–Vafa invariants of arbitrary local curves. Secondly, following Davison's work, we …
Gopakumar–Vafa invariants of arbitrary local curves. Secondly, following Davison's work, we …
[HTML][HTML] Nonabelian Hodge theory for stacks and a stacky P= W conjecture
B Davison - Advances in Mathematics, 2023 - Elsevier
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 …
stack of representations of the fundamental group of a genus g Riemann surface with the …
Symplectic -manifolds II: Morse-Bott-Floer Spectral Sequences
AF Ritter, F Živanović - arXiv preprint arXiv:2304.14384, 2023 - arxiv.org
In Part I, we defined a large class of open symplectic manifolds, called symplectic $\mathbb
{C}^* $-manifolds, which are typically non-exact at infinity, and we showed that their …
{C}^* $-manifolds, which are typically non-exact at infinity, and we showed that their …
Cohomology rings of the moduli of one-dimensional sheaves on the projective plane
We initiate a systematic study on the cohomology rings of the moduli stack $\mathfrak {M} _
{d,\chi} $ of semistable one-dimensional sheaves on the projective plane. We introduce a set …
{d,\chi} $ of semistable one-dimensional sheaves on the projective plane. We introduce a set …
[HTML][HTML] Geometric realisations of the unipotent enveloping algebra of a quiver
L Hennecart - Advances in Mathematics, 2024 - Elsevier
We compare and generalise the various geometric constructions (due to Ringel, Lusztig,
Schofield, Bozec, Davison...) of the unipotent generalised Kac–Moody algebra associated …
Schofield, Bozec, Davison...) of the unipotent generalised Kac–Moody algebra associated …
Elliptic surfaces and toroidal superalgebras
S DeHority - arXiv preprint arXiv:2311.00349, 2023 - arxiv.org
The equivariant cohomology of certain moduli spaces of sheaves on isotrivial elliptic
surfaces are shown to admit representations of infinite dimensional Lie (super) algebras …
surfaces are shown to admit representations of infinite dimensional Lie (super) algebras …