Research


Papers

  • 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, accepted, to appear in Memoirs of the American Mathematical Society.
  • Constant Gaussian curvature foliations and Schläfli formulas of hyperbolic 3-manifolds, accepted, to appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (preprint arXiv:1910.06203).
  • 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

In preparation



Selected talks

  • Introduction to minimal surfaces and harmonic maps, Workshop "Minimal surfaces in symmetric spaces and Labourie's conjecture" in Autrans. August 22-26, 2022 (notes).
  • Shear-bend coordinates for pleated surfaces in PSL(d,C), AMS-SMF-EMS Special Meeting in Grenoble. July 20, 2022 (slides).
  • A para-hyperKähler structure on the space of GHMC anti-de Sitter 3-manifolds, Heidelberg University. June 10, 2022 (slides).
  • Pleated surfaces for SO(2,n)-maximal representations, University of Virginia. April 5, 2022 (slides).
  • Pleated surfaces for SO(2,n)-maximal representations, 55th Spring Topology & Dynamical Systems Conference. March 12, 2022 (recording).
  • Infima of volumes of convex co-compact hyperbolic 3-manifolds, NCNGT 2021 Conference (recording).
  • Constant Gaussian curvature surfaces in hyperbolic 3-manifolds, Pangolin seminar. November 3, 2020 (slides).


REU Project (Summer 2021, University of Virginia)

    Katherine Betts, Troy Larsen, Jeffrey Utley, Avalon Vanis, The Tri-Pants graph of the twice-punctured torus, preprint 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.