Pavel Osipov

@hse.ru

International Laboratory for Mirror Symmetry and Automorphic Forms
HSE universitry

Pavel Osipov


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https://researchid.co/pavelosipov

RESEARCH, TEACHING, or OTHER INTERESTS

Geometry and Topology, Algebra and Number Theory
5

Scopus Publications

9

Scholar Citations

2

Scholar h-index

Scopus Publications

  • Special Vinberg cones of rank 4
    D. V. Alekseevsky, P. Osipov
    Journal of High Energy Physics, 2026
    A bstract E.B. Vinberg developed a theory of homogeneous convex cones $$C\\subset V={\\mathbb{R}}^{n}$$ , which has many applications. He gave a construction of such cones in terms of non-associative rank n matrix T-algebras $$\\mathcal{T}$$ , that consist of vector-valued n × n matrices X = || x ij ||, x ij ∈ V ij where V ij are Euclidean vector spaces. The multiplication in a T-algebra is determined by a system of isometric maps V ij × V jk → V ik , s.t. | v ij · v jk | = | v ij | · | v jk | that satisfies some axioms. A T-algebra is determined by its associative subalgebra of upper triangular matrices $$\\mathcal{G}$$ or its niladical $$\\mathcal{N}$$ , called the Nil-algebra. The connected Lie group $$G\\subset \\mathcal{G}$$ of the upper triangular (non-degenerate) matrices acts in the vector space $$Her{m}_{n}\\subset \\mathcal{T}$$ of Hermitian matrices and the orbit C = G ( I ) ⊂ Herm n of the identity matrix I is a convex cone with a simply transitive action of G . Conversely, any homogeneous convex cone is obtained by this construction. Generalizing the notion of rank 3 Clifford T-algebra [1, 2], we define notions of rank n special T-algebra and Clifford Nil-algebra, which define a special Vinberg cone. We associate with a Clifford Nil-algebra $$\\mathcal{N}$$ a directed acyclic graph $$\\Gamma =\\Gamma (\\mathcal{N})$$ of diameter 1 and show that Clifford Nil-algebras with given graph Γ bijectively correspond to its admissible equipments. This gives an effective method of classification of Clifford Nil-algebras and associated special Vinberg cones. We apply this approach for explicit classification of rank 4 special Vinberg cones.
  • Locally conformally Hessian and statistical manifolds
    Pavel Osipov
    Journal of Geometry and Physics, 2023
  • Selfsimilar Hessian manifolds
    Pavel Osipov
    Journal of Geometry and Physics, 2022
  • Self-similar Hessian and conformally Kähler manifolds
    Pavel Osipov
    Annals of Global Analysis and Geometry, 2022
  • Statistical Lie algebras of constant curvature and locally conformally Kahler Lie algebras
    Bulletin Mathematique De La Societe Des Sciences Mathematiques De Roumanie, 2022

RECENT SCHOLAR PUBLICATIONS

  • Kunneth formula for Hessian manifolds
    P Osipov
    arXiv preprint arXiv:2605.10743 , 2026
    2026.0
  • Special Vinberg cones of rank 4
    DV Alekseevsky, P Osipov
    Journal of High Energy Physics 2026 (1), 1 , 2026
    2026.0
  • Locally conformally Hessian and statistical manifolds
    P Osipov
    Journal of Geometry and Physics 193, 104989 , 2023
    2023.0
    Citations: 5
  • Self-similar Hessian and conformally Kähler manifolds
    P Osipov
    Annals of Global Analysis and Geometry 62 (3), 479-488 , 2022
    2022.0
    Citations: 2
  • Selfsimilar Hessian manifolds
    P Osipov
    Journal of Geometry and Physics 175, 104476 , 2022
    2022.0
    Citations: 1
  • Statistical Lie algebras of constant curvature and locally conformally Kähler Lie algebras
    P Osipov
    Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie … , 2022
    2022.0
    Citations: 1
  • Компактные вайсмановы многообразия и их вещественный аналог
    PS Osipov

MOST CITED SCHOLAR PUBLICATIONS

  • Locally conformally Hessian and statistical manifolds
    P Osipov
    Journal of Geometry and Physics 193, 104989 , 2023
    2023.0
    Citations: 5
  • Self-similar Hessian and conformally Kähler manifolds
    P Osipov
    Annals of Global Analysis and Geometry 62 (3), 479-488 , 2022
    2022.0
    Citations: 2
  • Selfsimilar Hessian manifolds
    P Osipov
    Journal of Geometry and Physics 175, 104476 , 2022
    2022.0
    Citations: 1
  • Statistical Lie algebras of constant curvature and locally conformally Kähler Lie algebras
    P Osipov
    Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie … , 2022
    2022.0
    Citations: 1
  • Kunneth formula for Hessian manifolds
    P Osipov
    arXiv preprint arXiv:2605.10743 , 2026
    2026.0
  • Special Vinberg cones of rank 4
    DV Alekseevsky, P Osipov
    Journal of High Energy Physics 2026 (1), 1 , 2026
    2026.0
  • Компактные вайсмановы многообразия и их вещественный аналог
    PS Osipov