My research focuses on: low-dimensional topology; hyperbolic geometry; mapping class groups and outer automorphisms of free groups; Teichmuller theory; and problems arising at the intersection of combinatorics and surface topology.
On fixed points of pseudo-Anosov maps; with Dave Futer and Sam Taylor. Arxiv
The arc complex is not quasi-isometric to the sphere complex; with Marissa Loving. Arxiv
From arcs to curves: quadratic growth of 1-systems; with Jonah Gaster. Arxiv
Subgraph Entropy; with Matt Clay and Tawfiq Hamed. Arxiv
Constructing reducibly geometrically finite subgroups of the mapping class group; with Harry Bray, Spencer Dowdall, Hannah Hoganson, Sara Maloni, and Brandis Whitfield. Arxiv. To appear in Groups, Geometry, and Dynamics.
On the monodromy and spin parity of of single cylinder origamis in the minimal stratum; with Adam Friedman-Brown, Luke Jeffreys, and Jiajie Ma. Arxiv
Effective bounds between divergence and Morse functions; with Cameron Gavaler and Dorothea Rugg. In preparation
Currents with corners and counting weighted triangulations; with Jayadev Athreya. Arxiv
A note on an effective characterization of covers with an application to higher rank representations; with Maxie Lahn, Marissa Loving, and Nick Miller. Arxiv. To appear in Groups, Geometry, and Dynamics.
Combinatorially random curves on surfaces; with Jonah Gaster. Arxiv . To appear in Transactions of the American Mathematical Society.
Unmarked simple length spectral rigidity for covers; with Maxie Lahn, Marissa Loving, and Nick Miller. Arxiv . To appear in Mathematische Annalen
Origamis associated to minimally intersecting filling pairs; with Bill Menasco and Mark Nieland. Pacific Journal of Mathematics. ArXiv
Thermodynamic metrics on Outer Space; with Matthew Clay and Yo'av Rieck. To apear in Ergodic Theory and Dynamical Systems. ArXiv
Curves on the torus intersecting at most k times; with Jonah Gaster. To appear in Mathematical Proceedings of the Cambridge Philosophical Society. ArXiv
Isometry groups of infinite genus hyperbolic surfaces; with Priyam Patel and Nicholas Vlamis. Mathematische Annalen. ArXiv
Characterizing covers via simple closed curves; with Max Lahn, Marissa Loving, and Yang Xiao. ArXiv. Accepted to Geometriae Dedicata.
Automorphisms of the k-curve graph; with Shuchi Agrawal, Yassin Chandran, Marissa Loving, Rob Oakley, Roberta Shapiro, and Yang Xiao. ArXiv . Accepted to Michigan Mathematical Journal.
Covers of surfaces, Kleinian groups, and the curve complex; with Priyam Patel and Samuel Taylor. To appear in Journal of Topology. ArXiv
Isolas versus snaking of localized rolls; with Margaret Beck, Paul Carter, Surabhi Desai, Bjorn Sandstede, Melissa Stadt, and Aric Wheeler. Journal of Dynamics and Differential Equations, vol. 31, pp 1119-1222 (2019) Journal article
Effective Masur-Minsky distance formulas and applications to hyperbolic 3-manifolds; with Samuel Taylor and Richard Webb. pdf draft (comments welcome)
Determining the finite subgraphs of curve graphs; with Ian Biringer and Jonah Gaster. Groups, Geometry, & Dynamics, vol. 13, no. 1, pp. 31-45 (2018) ArXiv
Packing curves on surfaces with few intersections; with Ian Biringer and Jonah Gaster. International Mathematics Research Notices, iss. 16, pp. 5205-5217 (2017) ArXiv
Pulling back stability with applications to Out(F_n); with Matthew Durham and Samuel Taylor. Journal of the London Mathematical Society, vol. 96, iss. 3 (2017) ArXiv
Counting curve types; with Juan Souto. American Journal of Mathematics, vol. 140, no. 6, pp. 1423-1441 (2018). Arxiv
Building hyperbolic metrics suited to closed curves and applications to lifting simply; with Jonah Gaster, Priyam Patel, and Jenya Sapir. Mathematical Research Letters, vol. 24, no. 3, pp. 593-617 (2017) ArXiv
Pseudo-Anosovs optimizing the ratio of curve graph to Teichmuller translation length; with Samuel Taylor. In the Tradition of Ahlfors-Bers, VII, Contemporary Mathematics, vol. 696, pp. 17-28 (2017) ArXiv
Local geometry of the k-curve graph. Transactions of the American Mathematical Society, vol. 370, no. 4, pp. 2657-2678 (2018) ArXiv
Curves intersecting exactly once and their dual cube complexes; with Jonah Gaster. Groups, Geometry, & Dynamics, vol. 11, no. 3, pp. 1061-1101 (2017) ArXiv
Constructing large k-systems on surfaces. Topology & Its Applications, vol. 176, pp. 1-9 (2014) ArXiv
Minimally intersecting filling pairs on closed surfaces; with Shinnyih Huang. Algebraic & Geometric Topology, vol. 15, pp. 903-932 (2014) ArXiv
Small intersection numbers in the curve graph; with Samuel Taylor. Bulletin of the London Mathematical Society, vol. 46, no. 5, pp. 989-1002 (2014) ArXiv
On curves and polygons with the equiangular chord property; with Xidian Sun, Serge Tabachnikov, and Yuwen Wang. Pacific Journal of Mathematics, vol. 274, no. 2, pp. 305-324 (2015) ArXiv
Quadratic bounds on the quasiconvexity of nested train track sequences. Topology Proceedings, vol. 44, pp. 365-388 (2014) ArXiv
Uniform hyperbolicity of the graphs of curves. Geometry & Topology, vol. 17, pp. 2855-2875 (2013) ArXiv
Large collections of curves pairwise intersecting exactly once. Geometriae Dedicata, vol. 172, no. 1, pp. 293-302 (2013) ArXiv
Laplacians on a family of quadratic Julia Sets, II; with Stella Dong and Robert Strichartz. Communications in Pure and Applied Analysis, vol. 12, no. 1 (2012) Journal article
Infinitesimal rigidity of a compact hyperbolic 4-orbifold with totally geodesic boundary; with Peter Storm. Algebraic & Geometric Topology, vol. 9, pp. 537-548 (2009) ArXiv
What's the Biggest Number You Can Think Of? Public lecture at Yale Math Mornings (2016)
Effective short conjugators and volumes of 3-manifolds from the curve and pants complexes. Geometric Structures on 3-Manifolds, Institute for Advanced Study (2016)
Effective geometry of combinatorial complexes. Georgia Topology Conference (2014)