Research Interests

Discrete subgroups of Lie groups, geometry of discrete groups, arithmetic lattices, hyperbolic geometry and topology, hyperbolic manifolds and orbifolds, hyperbolic reflection groups, Coxeter polytopes, arithmetic hyperbolic reflection groups, reflective Lorentzian lattices.

Preprints/submitted papers

    15. Quasi-arithmetic hyperbolic Coxeter prisms, with Khusrav Yorov, preprint, 2023.

    14. with Sami Douba and Jean Raimbault: “Infinitely many commensurability classes of compact Coxeter polyhedra in H^4 and $H^5$”, preprint, 2023.

    13. with Dmitry Guschin (MIPT) and Andrei Vesnin (Sobolev Inst. of Math.): “Arithmeticity of ideal hyperbolic right-angled polyhedra and hyperbolic link complements”, preprint pdf

    12. with Sami Douba: “Geometric and arithmetic properties of Löbell polyhedra”, arXiv:2304.12590.

    11. with Alexander Kolpakov: “Thin hyperbolic reflection groups”, arXiv:2112.14642

    10. with Misha Belolipetsky, Alexander Kolpakov & Leone Slavich: “Subspace stabilisers in hyperbolic lattices”, arXiv:2105.06897

Published/accepted papers

    9. with Alex Kontorovich & Sasha Kolpakov: “Kleinian sphere packings, reflection groups and arithmeticity”, arXiv:2203.01973, accepted to Math. Comp.

    8. with Stepan Alexandrov, Andrei Egorov & Andrei Vesnin: “On volumes of hyperbolic right-angled polyhedra”, arXiv:2111.08789, Sbornik: Math.

    7. with Liudmila Ostroumova-Prokhorenkova (Yandex & HSE & MIPT), Dima Baranchuk (Yandex), Yura Demidovich (MIPT), and Alexander Kolpakov: “Graph-based Nearest Neighbor Search in Hyperbolic Spaces”, accepted to ICLR 2022 (one of the top-3 ML & AI conference).

    6. “From geometry to arithmetic of compact hyperbolic Coxeter polytopes”, to appear in Transformation Groups, arXiv:2003.11944

• SageMath worksheet SmaRBA

    5. with Alexander Kolpakov: “On faces of quasi-arithmetic Coxeter polytopes”, IMRN – Int. Math. Res. Not., 2021, Vol. 2021, Issue 4, pp. 3078-3096. arXiv:2002.11445

• SageMath worksheet PLoF

    4. “On the Classification of Stably Reflective Hyperbolic Z[√2]-Lattices of Rank 4”, Doklady Math., 2019

    3. “Classification of (1,2)-Reflective Anisotropic Hyperbolic Lattices of Rank 4”, Izvestiya Math., 2019, Vol. 83:1, pp. 1–19, arXiv:1903.08147

    2. with Alexander Perepechko: “Vinberg’s Algorithm for Hyperbolic Lattices”, Math. Notes, 2018, Vol. 103:5, 836–840

    1. “Reflective Anisotropic Hyperbolic Lattices of Rank 4”, Russian Mathematical Surveys, 2017, vol. 1 (433), p. 179 - 181

PhD-Thesis

• Ph.D. in Mathematics of Higher School of Economics. Thesis: “Reflective Hyperbolic Lattices”.

Non-published preprints & notes

• Preprint 2016: “Reflective anisotropic hyperbolic lattices of rank 4”, arXiv:1610.06148

• Notes on determinantal point processes, 2015:

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