Research Interests

My research lies at the intersection of hyperbolic geometry, geometric topology, and arithmetic groups. I am particularly interested in the topology and geometry of arithmetic hyperbolic manifolds, with an emphasis on torsion phenomena in homology. My work combines geometric constructions with tools from Coxeter groups and the combinatorics of polytopes.

Current Projects

  • Hyperbolic manifolds and homological torsion growth
    Geometric constructions producing large torsion subgroups in homology, including towers of covers and arithmetic methods.
  • Coxeter polytopes and reflection groups
    Combinatorial and geometric properties of hyperbolic Coxeter polytopes and their applications to arithmetic lattices.

Publications

  • Lannér diagrams and combinatorial properties of hyperbolic Coxeter polytopes
    Transactions of the American Mathematical Society, 2023
    doi:10.1090/tran/8967
  • On volumes of hyperbolic right-angled polyhedra
    with N. Bogachev, A. Egorov, and A. Vesnin
    Sbornik: Mathematics, 2023
    doi:10.4213/sm9740e

Preprints

  • Family of hyperbolic manifolds with exponential homology torsion growth
    ariv:2512.08915
  • On ideal vertices of right-angled hyperbolic polyhedra
    ariv:2303.09533