Math works

Papers and preprints

[39] (*) A.Ayzenberg, M.Beketov, G.Magai, Coverings by open and closed hemispheres, preprint [arxiv]

[38] A.Ayzenberg, D.Gugnin, On actions of tori and quaternionic tori on products of spheres, 2023, to appear in Proc. Steklov Inst. Math. [jour | arxiv]

[37]  A.Ayzenberg, M.Beketov, A.Burashnikova, G.Magaj, A.Polevoi, I.Shanin, K.Sorokin, Chordal Embeddings Based on Topology of the Tonal Space, in proceedings of Artificial Intelligence in Music, Sound, Art and Design: 12th International Conference, EvoMUSART 2023, Ch.2. in Lecture Notes in Computer Science (LNCS) 13988 (2023), 20-33. [jour]

[36] A.A.Ayzenberg, V.V.Cherepanov, Dehn–Sommerville relations for complexity one torus actions, to appear in Russian Math. Surveys [jour]

[35] A.Ayzenberg, V.Gorchakov, Toric orbit spaces which are manifolds, Arnold Math J. (2024), https://doi.org/10.1007/s40598-023-00242-5 [jour].   preprint: [arxiv]

[34] (*) K.Sorokin, A.Ayzenberg, K.Anokhin, V.Sotskov, M.Beketov, A.Zaitsew, R.Drynkin, Topology of cognitive maps, preprint: [arxiv]

[33] (*) G.Magai, A.Ayzenberg, Topology and geometry of data manifold in deep learning, 2022, preprint: [arxiv]

[32] (*) A.Ayzenberg, K.Sorokin, Topological approach to diagonalization algorithms, 2022,  preprint: [arxiv]

[31] A.Ayzenberg, V.Buchstaber, Cluster-permutohedra and submanifolds of flag varieties with torus actions, Int. Math. Res. Notices 2024:3, 2024, 1931–1967. [jour | arxiv] 

[30] A.Ayzenberg, M.Masuda, T.Sato, The second cohomology of regular semisimple Hessenberg varieties from GKM theory, Proc. of Steklov Inst. Math. 317 (2022), 5-26. [jour | arxiv] 

[29] A.Ayzenberg, M.Masuda, G.Solomadin, How is a graph not like a manifold?, Sbornik: Mathematics, 214:6 (2023), 793-815. [jour | arxiv] 

[28] (*) A.Ayzenberg, V.Cherepanov, Matroids in toric topology, 2022, preprint: [arxiv]

[27] A.Ayzenberg, A.Rukhovich, Clique complexes of multigraphs, edge inflations, and tournaplexes, to appear in Homology, Homotopy and Applications [jour(prelim) | arxiv]

[26] A.Ayzenberg, M.Masuda, Orbit spaces of equivariantly formal torus actions, Transformation Groups 2023 [jour | arxiv] 

[25] A.Ayzenberg, D.Gugnin, Topology of misorientation spaces, Proc. Steklov Inst. Math. 325, 1-20 (2024),  preprint: [jour | arxiv]

[24] (*) A.Ayzenberg, Topology of nerves and formal concepts, preprint: [arxiv] 

[23] A.Ayzenberg, V.Cherepanov, Torus actions of complexity one in non-general position, Osaka J. Math. 58:4 (2021), 839-853. [jour | arxiv] 

[22] A.Ayzenberg, Torus action on quaternionic projective plane and related spaces, Arnold Math. J. 7 (2021), 243-266. [jour | arxiv]

[21] A.Ayzenberg, Space of isospectral periodic tridiagonal matrices, Algebraic and Geometric Topology 20 (2020), 2957-2994.  [jour | arxiv]

[20] A.Ayzenberg, Dimensions of multi-fan algebras, J. Math. Soc. Japan 72:3  (2020), 777-794. [jour | arxiv]

[19] A.A.Ayzenberg, V.M.Buchstaber, Manifolds of isospectral matrices and Hessenberg varieties, Int. Math. Res. Notices 2021:21 (2021), 16671-16692. [jour | arxiv] 

[18] A.A.Ayzenberg, V.M.Buchstaber, Manifolds of isospectral arrow matrices, Sbornik: Mathematics 212:5 (2021), 3-36. [mathnet | arxiv]

[17] A.Ayzenberg, Torus actions of complexity one and their local properties, Proc. Steklov Inst. Math. 302 (2018), 23-40. [mathnet | arxiv]

[16] A.Ayzenberg, Toric manifolds over 3-polytopes, In: Bahri, A., Jeffrey, L., Panov, T., Stanley, D., Theriault, S. (eds) Toric Topology and Polyhedral Products. Fields Institute Communications, vol 89. Springer  [jour | arxiv] 

[15] A.Ayzenberg, M.Masuda, S.Park, H.Zeng, Cohomology of toric origami manifolds with acyclic proper faces, J. Symplectic Geom. (2017) 15:3, 645-685. [jour | arxiv]

[14] A.Ayzenberg, Locally standard torus actions and sheaves over Buchsbaum posets, Sbornik: Mathematics (2017) 208:9, 3-25. [mathnet | arxiv].

[13] A.Ayzenberg, M.Masuda, Volume polynomials and duality algebras of multi-fans, Arnold Math. J. (2016), 2:3, 329-381. [jour | arxiv]

[12] A.Ayzenberg, Locally standard torus actions and h'-vectors of simplicial posets, J. Math. Soc. Japan 68:4 (2016), 1-21. [jour |  arxiv] 

[11] A.Ayzenberg, Topological model for h''-vectors of simplicial manifolds, Bol. Soc. Mat. Mexicana 23, 413–421 (2017). [jour | arxiv]

[10] A.Ayzenberg, Homology cycles in manifolds with locally standard torus actions, Homology, Homotopy Appl. 18:1 (2016), 1-23. [jour | arxiv]

[9] A.Ayzenberg, Buchstaber invariant, minimal non-simplices and related topics, Osaka J. Math. 53:2 (2016). [jour | arxiv]

[8] A.Ayzenberg, M.Masuda, S.Park, H.Zeng, Toric origami structures on quasitoric manifolds, Proc. Steklov Inst. Math. 288:1 (2015), 10-28. [mathnet | arxiv]

[7] (*) A.Ayzenberg, M.Masuda, S.Park, H.Zeng, Quasitoric manifolds which are not toric origami, at "The Topology and the Algebraic Structures of Transformation Groups", RIMS Kokyuroku, 2014. [download].

[6] (*) A.Ayzenberg, Simplicial complexes Alexander dual to boundaries of polytopes, preprint [arxiv]

[5] A.A.Ayzenberg, Substitutions of polytopes and of simplicial complexes, and multigraded betti numbers, Trans. Moscow Math. Soc. (2013), 175-202. [mathnet | arxiv]

[4] A.A.Aizenberg, Topological applications of Stanley-Reisner rings of simplicial complexes, Trans. Moscow Math. Soc. (2012), 37-65. [mathnet]

[3] A.A.Aizenberg, Connection between Buchstaber invariants and generalized chromatic numbers, Dal'nevost. Mat. Zh. 11:2 (2011), 113-139. [mathnet] (in Russian) А.А.Айзенберг, Связь инвариантов Бухштабера и обобщённых хроматических чисел, Дальневост. матем. журн., 11:2, (2011), 113–139  (roughly corresponds to this preprint).

[2] A.A.Ayzenberg, V.M.Buchstaber, Nerve complexes and moment-angle spaces of convex polytopes, Proc. Steklov Inst. Math. 275(1), 15-46. [mathnet | arxiv] 

[1] A.Aizenberg, Exponential law for the K-power, Russian Math. Surveys (2009), 64(4):745. [mathnet]

Some other math works (in Russian)

• Кандидатская диссертация Теория нерв-комплексов и ее приложения, мехмат МГУ 2012 (phd thesis "Theory of nerve complexes and its applications" MSU, October 2012).

• Дипломная работа "f-векторы и число Бухштабера симплициальных комплексов", мехмат МГУ, 2009 (diploma work "f-vectors and Buchstaber number of simplicial complexes" at MSU, 2009).

• Курсачи 3 курс, 4 курс (term papers).

• Драфт так и не защищенной докторской диссертации (draft of doctoral thesis, yet undefended)