Research Interests

Coxeter polytopes, right-angled polytopes, hyperbolic geometry, arithmetic groups, combinatorics of polytopes, hyperbolic manifolds, reflection groups.

Current Projects

  • Dimension bounds and classification of hyperbolic Coxeter polytopes
  • Arithmetic, geometry, and topology of hyperbolic orbifolds
    with Nikolay Bogachev, Andrei Egorov, Dmitry Gushchin, and Andrei Vesnin
  • Topology of random simplicial complexes
    with Nikolay Bogachev and Maksim Zhukovskii

Preprints

  • On ideal vertices of right-angled hyperbolic polyhedra
    ariv:2303.09533
  • Lannér diagrams and combinatorial properties of hyperbolic Coxeter polytopes
    ariv:2203.07248—accepted to Transactions of the AMS
  • On volumes of hyperbolic right-angled polyhedra
    ariv:2111.08789—accepted to Sbornik: Mathematics
    doi:10.4213/sm9740—published in Russian in Matematicheskii Sbornik