Related papers: Multiplicative dimensional reduction
We construct decompositions of: (1) the cohomology of smooth stacks, (2) the Borel--Moore homology of $0$-shifted symplectic stacks, and (3) the vanishing cycle cohomology of $(-1)$-shifted symplectic stacks, assuming a good moduli space…
This paper studies the Cohomological Donaldson-Thomas theory of loop stacks of $0$-shifted symplectic stacks. In particular, we compare $(-1)$-shifted tangent stacks of these moduli problems, which we view as additive, to loop stacks, which…
For oriented $-1$-shifted symplectic derived Artin stacks, Ben-Bassat-Brav-Bussi-Joyce introduced certain perverse sheaves on them which can be regarded as sheaf theoretic categorifications of the Donaldson-Thomas invariants. In this paper,…
We prove the BPS decomposition theorem (a.k.a. cohomological integrality theorem) decomposing the cohomology of smooth symmetric stacks into the Weyl-invariant part of the cohomological Hall induction of the intersection cohomology of good…
This paper concerns the cohomological aspects of Donaldson-Thomas theory for Jacobi algebras and the associated cohomological Hall algebra, introduced by Kontsevich and Soibelman. We prove the Hodge-theoretic categorification of the…
We give a formula comparing the E-series of the moduli stacks of rank 2 degree 0 semistable Higgs bundles in genus $g \geq 2$ to intersection E-polynomials of its coarse moduli space. A parellel formula holds in various 2-Calabi-Yau…
The present paper is an extension of a previous paper written in collaboration with Markus Reineke dealing with quiver representations. The aim of the paper is to generalize the theory and to provide a comprehensive theory of…
By considering a (partial) topological twisting of supersymmetric Yang-Mills compactified on a 2d space with `t Hooft magnetic flux turned on we obtain a supersymmetric $\sigma$-model in 2 dimensions. For N=2 SYM this maps Donaldson…
We introduce a new class of representations of the cohomological Hall algebras of Kontsevich and Soibelman, which we call cohomological Hall modules, or CoHM for short. These representations are constructed from self-dual representations of…
This review gives an introduction to cohomological Donaldson-Thomas theory: the study of a cohomology theory on moduli spaces of sheaves on Calabi-Yau threefolds, and of complexes in 3-Calabi-Yau categories, categorifying their numerical DT…
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 particular, we provide rigorous proofs of all standard results…
We generalize the notion of expanded degenerations and pairs for a simple degeneration or smooth pair to the case of smooth Deligne-Mumford stacks. We then define stable quotients on the classifying stacks of expanded degenerations and…
In arXiv:0805.2192, we set up a gauge-theoretic equation on symplectic 6-manifolds, which is a version of the Hermitian-Einstein equation perturbed by Higgs fields, and call Donaldson-Thomas equation, to analytically approach the…
In this paper, we establish the sheafified version of the cohomological integrality conjecture for stacks obtained as a quotient of a smooth affine symmetric algebraic variety by a reductive algebraic group equipped with an invariant…
Let $S$ be a projective simply connected complex surface and $\mathcal{L}$ be a line bundle on $S$. We study the moduli space of stable compactly supported 2-dimensional sheaves on the total spaces of $\mathcal{L}$. The moduli space admits…
In this paper we prove a toric localization formula in the cohomological Donaldson-Thomas theory. Consider a (-1)-shifted symplectic algebraic space with a $\mathbb{G}_m$-action leaving the (-1)-shifted symplectic form invariant (typical…
We derive conjectures, called genus 1 Enumerative mirror symmetry for moduli spaces of Higgs bundles, which relate curve-counting invariants of moduli spaces of Higgs $\mathrm{SL}_r$-bundles to curve-counting invariants of moduli spaces of…
We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type $\operatorname{SL}_n$ and $\operatorname{PGL}_n$. More precisely, we establish an equality of stringy Hodge numbers for…
The Donaldson-Fujiki K\"ahler reduction of the space of compatible almost complex structures, leading to the interpretation of the scalar curvature of K\"ahler metrics as a moment map, can be lifted canonically to a hyperk\"ahler reduction.…
We study the BPS spectrum and vacuum moduli spaces in dimensional reductions of Chern-Simons-matter theories with N>=2 supersymmetry to zero dimensions. Our main example is a matrix model version of the ABJM theory which we relate…