research
Click here to see the list of publications.
Some 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).
Conferences co-organized
- Metrics on higher Teichmüller spaces, (co-organized with Christian El Emam and Nathaniel Sagman), August 28th-September 1st, 2023.
- NCNGT 2022 Conference, session on Anosov representations (co-organized with Gabriele Viaggi), September 19th-25th, 2022.
- Virginia Topology Conference 2021 (co-organized with Thomas Koberda, Sara Maloni, and Mark Pengitore), November 5th-7th, 2021.
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.