Research


Papers

  • The infimum of the dual volume of convex co-compact hyperbolic 3-manifolds,
    accepted, to appear in Geometry & Topology, Preprint arXiv:2101.09380.
  • The dual volume of quasi-Fuchsian manifolds and the Weil-Petersson distance,
    Transactions of the American Mathematical Society 375 (2022), 695--723. DOI 10.1090/tran/8521.
    Preprint arXiv:1808.08936.
  • The dual Bonahon-Schläfli formula, Algebraic & Geometric Topology 21-1 (2021), 279--315.
    DOI 10.2140/agt.2021.21.279. Preprint arXiv:1808.08936.

Preprints

  • SO(2,n+1)-maximal representations and hyperbolic surfaces, (joint work with Gabriele Viaggi)
    Preprint arXiv:2206.06946.
  • Quasi-Fuchsian manifolds close to the Fuchsian locus are foliated by constant mean curvature surfaces, (joint work with Diptaishik Choudhury and Andrea Seppi)
    Preprint arXiv:2107.10363, submitted.
  • Para-hyperKähler geometry of the deformation space of MGHC anti-de Sitter 3-manifolds,
    (joint work with Andrea Seppi and Andrea Tamburelli) Preprint arXiv:2107.10363, submitted.
  • Constant Gaussian curvature foliations and Schläfli formulas of hyperbolic 3-manifolds,
    Preprint arXiv:1910.06203, submitted.
  • Intertwining operators of the quantum Teichmüller space,
    Preprint arXiv:1610.06056, under revision.


REU Project (Summer 2021, University of Virginia)

    Katherine Betts, Troy Larsen, Jeffrey Utley, Avalon Vanis, The Tri-Pants graph of the twice-punctured torus, arXiv:2111.07136
    Abstract: We investigate the structure of the tri-pants graph, a simplicial graph introduced by Maloni and Palesi, whose vertices correspond to particular collections of homotopy classes of simple closed curves of the twice-punctured torus, called tri-pants, and whose edges connect two vertices whenever the corresponding pants differ by suitable elementary moves. In particular, by examining the relationship between the tri-pants graph and the dual of the Farey complex, we prove that the tri-pants graph is connected and it has infinite diameter.