Sergey Mozgovoy
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
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Sergey Mozgovoy has a total of 7 co-authors. Here are the top co-authors by number of shared publications:
- Olivier Schiffmann
Canto XXXIV
3 shared publications - Vladimir Dotsenko
Institut de Recherche Mathématique Avancée, Université de Strasbourg, 7 rue René Descartes, 67084 Strasbourg, France
3 shared publications - Jan Manschot
School of Mathematics, Trinity College, Dublin, Ireland
2 shared publications - Markus Reineke
Ruhr University Bochum
2 shared publications - Boris Pioline
Laboratory of Theoretical and High Energy Physics
1 shared publication Ronan O'Gorman
1 shared publication
Latest Publications
- Open Access
- 11 May 2026
- Published by MathDoc/Centre Mersenne in Annals of Representation Theory
- Vol. 3 (1) , 141-163
Global Weyl modules for thin Lie algebras are finite-dimensional
The notion of Weyl modules, both local and global, goes back to Chari and Pressley in the case of affine Lie algebras, and has been extensively studied for various Lie algebras graded by root systems. We extend that definition to a certain class of Lie algebras graded by weight lattices and prove that if such a Lie algebra satisfies a natural “thinness” condition, then already the global Weyl modules are finite-dimensional. Our motivating example of a thin Lie algebra is the Lie algebra of polynomial Hamiltonian vector fields on the plane vanishing at the origin. We also introduce stratifications of categories of modules over such Lie algebras and identify the corresponding strata categories.
- 11 May 2026
- Published by MathDoc/Centre Mersenne in Annals of Representation Theory
- Vol. 3 (1) , 141-163
Open AccessGlobal Weyl modules for thin Lie algebras are finite-dimensional
The notion of Weyl modules, both local and global, goes back to Chari and Pressley in the case of affine Lie algebras, and has been extensively studied for various Lie algebras graded by root systems. We extend that definition to a certain class of Lie algebras graded by weight lattices and prove that if such a Lie algebra satisfies a natural “thinness” condition, then already the global Weyl modules are finite-dimensional. Our motivating example of a thin Lie algebra is the Lie algebra of polynomial Hamiltonian vector fields on the plane vanishing at the origin. We also introduce stratifications of categories of modules over such Lie algebras and identify the corresponding strata categories.
- Open Access
Global Weyl modules for thin Lie algebras are finite-dimensional
The notion of Weyl modules, both local and global, goes back to Chari and Pressley in the case of affine Lie algebras, and has been extensively studied for various Lie algebras graded by root systems. We extend that definition to a certain class of Lie algebras graded by weight lattices and prove that if such a Lie algebra satisfies a natural "thinness" condition, then already the global Weyl modules are finite-dimensional. Our motivating example of a thin Lie algebra is the Lie algebra of polynomial Hamiltonian vector fields on the plane vanishing at the origin. We also introduce stratifications of categories of modules over such Lie algebras and identify the corresponding strata categories.
Open AccessGlobal Weyl modules for thin Lie algebras are finite-dimensional
The notion of Weyl modules, both local and global, goes back to Chari and Pressley in the case of affine Lie algebras, and has been extensively studied for various Lie algebras graded by root systems. We extend that definition to a certain class of Lie algebras graded by weight lattices and prove that if such a Lie algebra satisfies a natural "thinness" condition, then already the global Weyl modules are finite-dimensional. Our motivating example of a thin Lie algebra is the Lie algebra of polynomial Hamiltonian vector fields on the plane vanishing at the origin. We also introduce stratifications of categories of modules over such Lie algebras and identify the corresponding strata categories.
- 1 April 2022
- Published by Elsevier in Journal of Algebra
- Vol. 596, 53-88
Operadic approach to wall-crossing
- 1 April 2022
- Published by Elsevier in Journal of Algebra
- Vol. 596, 53-88
Operadic approach to wall-crossing
- Open Access
Translation quiver varieties
We introduce a framework of translation quiver varieties which includes Nakajima quiver varieties as well as their graded and cyclic versions. An important feature of translation quiver varieties is that the sets of their fixed points under toric actions can be again realized as translation quiver varieties. This allows one to simplify quiver varieties in several steps. We prove that translation quiver varieties are smooth, pure and have Tate motivic classes. We also describe an algorithm to compute those motivic classes.
Open AccessTranslation quiver varieties
We introduce a framework of translation quiver varieties which includes Nakajima quiver varieties as well as their graded and cyclic versions. An important feature of translation quiver varieties is that the sets of their fixed points under toric actions can be again realized as translation quiver varieties. This allows one to simplify quiver varieties in several steps. We prove that translation quiver varieties are smooth, pure and have Tate motivic classes. We also describe an algorithm to compute those motivic classes.
- Open Access
Attractor invariants, brane tilings and crystals
Supersymmetric D-brane bound states on a Calabi-Yau threefold $X$ are counted by generalized Donaldsdon-Thomas invariants $\Omega_Z(\gamma)$, depending on a Chern character (or electromagnetic charge) $\gamma\in H^*(X)$ and a stability condition (or central charge) $Z$. Attractor invariants $\Omega_*(\gamma)$ are special instances of DT invariants, where $Z$ is the attractor stability condition $Z_\gamma$ (a generic perturbation of self-stability), from which DT invariants for any other stability condition can be deduced. While difficult to compute in general, these invariants become tractable when $X$ is a crepant resolution of a singular toric Calabi-Yau threefold associated to a brane tiling, and hence to a quiver with potential. We survey some known results and conjectures about framed and unframed refined DT invariants in this context, and compute attractor invariants explicitly for a variety of toric Calabi-Yau threefolds, in particular when $X$ is the total space of the canonical bundle of a smooth projective surface, or when $X$ is a crepant resolution of $C^3/G$. We check that in all these cases, $\Omega_*(\gamma)=0$ unless $\gamma$ is the dimension vector of a simple representation or belongs to the kernel of the skew-symmetrized Euler form. Based on computations in small dimensions, we predict the values of all attractor invariants, thus potentially solving the problem of counting DT invariants of these threefolds in all stability chambers. We also compute the non-commutative refined DT invariants and verify that they agree with the counting of molten crystals in the unrefined limit.Open AccessAttractor invariants, brane tilings and crystals
Supersymmetric D-brane bound states on a Calabi-Yau threefold $X$ are counted by generalized Donaldsdon-Thomas invariants $\Omega_Z(\gamma)$, depending on a Chern character (or electromagnetic charge) $\gamma\in H^*(X)$ and a stability condition (or central charge) $Z$. Attractor invariants $\Omega_*(\gamma)$ are special instances of DT invariants, where $Z$ is the attractor stability condition $Z_\gamma$ (a generic perturbation of self-stability), from which DT invariants for any other stability condition can be deduced. While difficult to compute in general, these invariants become tractable when $X$ is a crepant resolution of a singular toric Calabi-Yau threefold associated to a brane tiling, and hence to a quiver with potential. We survey some known results and conjectures about framed and unframed refined DT invariants in this context, and compute attractor invariants explicitly for a variety of toric Calabi-Yau threefolds, in particular when $X$ is the total space of the canonical bundle of a smooth projective surface, or when $X$ is a crepant resolution of $C^3/G$. We check that in all these cases, $\Omega_*(\gamma)=0$ unless $\gamma$ is the dimension vector of a simple representation or belongs to the kernel of the skew-symmetrized Euler form. Based on computations in small dimensions, we predict the values of all attractor invariants, thus potentially solving the problem of counting DT invariants of these threefolds in all stability chambers. We also compute the non-commutative refined DT invariants and verify that they agree with the counting of molten crystals in the unrefined limit. - 1 January 2022
- Published by International Press of Boston in Mathematical Research Letters
- Vol. 29 (5) , 1551-1570
Counting twisted Higgs bundles
International Press of Boston - publishers of scholarly mathematical and scientific journals and books
- 1 January 2022
- Published by International Press of Boston in Mathematical Research Letters
- Vol. 29 (5) , 1551-1570
Counting twisted Higgs bundles
International Press of Boston - publishers of scholarly mathematical and scientific journals and books
- Open Access
DT invariants from vertex algebras
We obtain a new interpretation of the cohomological Hall algebra $\mathcal{H}_Q$ of a symmetric quiver $Q$ in the context of the theory of vertex algebras. Namely, we show that the graded dual of $\mathcal{H}_Q$ is naturally identified with the underlying vector space of the principal free vertex algebra associated to the Euler form of $Q$. Properties of that vertex algebra are shown to account for the key results about $\mathcal{H}_Q$. In particular, it has a natural structure of a vertex bialgebra, leading to a new interpretation of the product of $\mathcal{H}_Q$. Moreover, it is isomorphic to the universal enveloping vertex algebra of a certain vertex Lie algebra, which leads to a new interpretation of Donaldson--Thomas invariants of $Q$ (and, in particular, re-proves their positivity). Finally, it is possible to use that vertex algebra to give a new interpretation of CoHA modules made of cohomologies of non-commutative Hilbert schemes.Open AccessDT invariants from vertex algebras
We obtain a new interpretation of the cohomological Hall algebra $\mathcal{H}_Q$ of a symmetric quiver $Q$ in the context of the theory of vertex algebras. Namely, we show that the graded dual of $\mathcal{H}_Q$ is naturally identified with the underlying vector space of the principal free vertex algebra associated to the Euler form of $Q$. Properties of that vertex algebra are shown to account for the key results about $\mathcal{H}_Q$. In particular, it has a natural structure of a vertex bialgebra, leading to a new interpretation of the product of $\mathcal{H}_Q$. Moreover, it is isomorphic to the universal enveloping vertex algebra of a certain vertex Lie algebra, which leads to a new interpretation of Donaldson--Thomas invariants of $Q$ (and, in particular, re-proves their positivity). Finally, it is possible to use that vertex algebra to give a new interpretation of CoHA modules made of cohomologies of non-commutative Hilbert schemes. - Top Cited Papers
- 27 February 2020
- Published by Cambridge University Press (CUP) in Compositio Mathematica
- Vol. 156 (4) , 744-769
Counting Higgs bundles and type quiver bundles
We prove a closed formula counting semistable twisted (or meromorphic) Higgs bundles of fixed rank and degree over a smooth projective curve of genus $g$ defined over a finite field, when the twisting line bundle degree is at least $2g-2$ (this includes the case of usual Higgs bundles). This yields a closed expression for the Donaldson–Thomas invariants of the moduli spaces of twisted Higgs bundles. We similarly deal with twisted quiver sheaves of type $A$ (finite or affine), obtaining in particular a Harder–Narasimhan-type formula counting semistable $U(p,q)$ -Higgs bundles over a smooth projective curve defined over a finite field.- 27 February 2020
- Published by Cambridge University Press (CUP) in Compositio Mathematica
- Vol. 156 (4) , 744-769
Top Cited PapersCounting Higgs bundles and type quiver bundles
We prove a closed formula counting semistable twisted (or meromorphic) Higgs bundles of fixed rank and degree over a smooth projective curve of genus $g$ defined over a finite field, when the twisting line bundle degree is at least $2g-2$ (this includes the case of usual Higgs bundles). This yields a closed expression for the Donaldson–Thomas invariants of the moduli spaces of twisted Higgs bundles. We similarly deal with twisted quiver sheaves of type $A$ (finite or affine), obtaining in particular a Harder–Narasimhan-type formula counting semistable $U(p,q)$ -Higgs bundles over a smooth projective curve defined over a finite field. - 1 January 2020
- Published by Elsevier in Journal of Algebra
- Vol. 541, 35-50
Quiver representations in abelian categories
- 1 January 2020
- Published by Elsevier in Journal of Algebra
- Vol. 541, 35-50
Quiver representations in abelian categories
- Open Access
Commuting matrices and volumes of linear stacks
A conjecture by Higman asserts that the number of conjugacy classes in the unipotent group of upper triangular matrices over a finite field depends polynomially on the number of elements of the field. We will study several alternative counting problems arising from quiver representations and prove explicit formulas relating the corresponding invariants to the invariants of Higman's conjecture. To do this, we develop a general framework of linear stacks over small etale sites and study volumes of these stacks and of their substacks of absolutely indecomposable objects.
Open AccessCommuting matrices and volumes of linear stacks
A conjecture by Higman asserts that the number of conjugacy classes in the unipotent group of upper triangular matrices over a finite field depends polynomially on the number of elements of the field. We will study several alternative counting problems arising from quiver representations and prove explicit formulas relating the corresponding invariants to the invariants of Higman's conjecture. To do this, we develop a general framework of linear stacks over small etale sites and study volumes of these stacks and of their substacks of absolutely indecomposable objects.