Categorical and K-theoretic Hall algebras for quivers with potential
T Pădurariu - Journal of the Institute of Mathematics of Jussieu, 2023 - cambridge.org
Given a quiver with potential $(Q, W) $, Kontsevich–Soibelman constructed a cohomological
Hall algebra (CoHA) on the critical cohomology of the stack of representations of $(Q, W) …
Hall algebra (CoHA) on the critical cohomology of the stack of representations of $(Q, W) …
Equivariant Hodge theory and noncommutative geometry
D Halpern-Leistner, D Pomerleano - Geometry & Topology, 2020 - msp.org
We develop a version of Hodge theory for a large class of smooth formally proper quotient
stacks X∕ G analogous to Hodge theory for smooth projective schemes. We show that the …
stacks X∕ G analogous to Hodge theory for smooth projective schemes. We show that the …
Categorical Donaldson-Thomas theory for local surfaces
Y Toda - arXiv preprint arXiv:1907.09076, 2019 - arxiv.org
We develope $\mathbb {C}^{\ast} $-equivariant categorical Donaldson-Thomas theory for
local surfaces, ie the total spaces of canonical line bundles on smooth projective surfaces …
local surfaces, ie the total spaces of canonical line bundles on smooth projective surfaces …
Categorical and K-theoretic Donaldson–Thomas theory of (part II)
T Pădurariu, Y Toda - Forum of Mathematics, Sigma, 2023 - cambridge.org
Quasi-BPS categories appear as summands in semiorthogonal decompositions of DT
categories for Hilbert schemes of points in the three-dimensional affine space and in the …
categories for Hilbert schemes of points in the three-dimensional affine space and in the …
Motivic realizations of singularity categories and vanishing cycles
Dans cet article, on démontre un théorème de comparaison entre la théorie des cycles
évanescents à la SGA7 et la catégorie des singularités d'un modèle de Landau-Ginzburg …
évanescents à la SGA7 et la catégorie des singularités d'un modèle de Landau-Ginzburg …
Semiorthogonal decompositions of stable pair moduli spaces via d-critical flips
Y Toda - Journal of the European Mathematical Society, 2021 - ems.press
We show the existence of semiorthogonal decompositions (SOD) of Pandharipande–
Thomas (PT) stable pair moduli spaces on Calabi–Yau 3-folds with irreducible curve …
Thomas (PT) stable pair moduli spaces on Calabi–Yau 3-folds with irreducible curve …
K-theoretic Hall algebras for quivers with potential
T Pădurariu - arXiv preprint arXiv:1911.05526, 2019 - arxiv.org
Given a quiver with potential $(Q, W) $, Kontsevich-Soibelman constructed a Hall algebra on
the cohomology of the stack of representations of $(Q, W) $. As shown by Davison …
the cohomology of the stack of representations of $(Q, W) $. As shown by Davison …
A chain-level HKR-type map and a Chern character formula
K Chung, B Kim, T Kim - arXiv preprint arXiv:2109.14372, 2021 - arxiv.org
We construct a Hochschild-Kostant-Rosenberg-type quasi-isomorphism for the negative
cyclic homology of the category of global matrix factorizations on a smooth separated …
cyclic homology of the category of global matrix factorizations on a smooth separated …
Quantum cluster variables via vanishing cycles
AI Efimov - arXiv preprint arXiv:1112.3601, 2011 - arxiv.org
In this paper, we provide a Hodge-theoretic interpretation of Laurent phenomenon for
general skew-symmetric quantum cluster algebras, using Donaldson-Thomas theory for a …
general skew-symmetric quantum cluster algebras, using Donaldson-Thomas theory for a …
Categorical wall-crossing formula for Donaldson-Thomas theory on the resolved conifold
Y Toda - arXiv preprint arXiv:2109.07064, 2021 - arxiv.org
We prove wall-crossing formula for categorical Donaldson-Thomas invariants on the
resolved conifold, which categorifies Nagao-Nakajima wall-crossing formula for numerical …
resolved conifold, which categorifies Nagao-Nakajima wall-crossing formula for numerical …