Most of my work is in hyperbolic geometry and low-dimensional topology, although I am also interested in combinatorial, measurable and geometric group theory, and Gromov-style Riemannian geometry. Here is my CV.

I co-organize the Geometry/Topology seminar at Boston College.

I am working on an online book Geometry in Two Dimensions that is suitable for students with only a multivariable calculus background. Currently, it discusses Euclidean, spherical and hyperbolic geometry, and touches on additional topics like scissors congruence, isoperimetric inequalities, and tilings.

This semester, I am teaching MATH 2211: Linear Algebra (Honors).

Algebra vs. geometry in hyperbolic 3-manifolds
PhD thesis, University of Chicago.
The Three Gap Theorem and Riemannian Geometry
Joint with Benjamin Schmidt.
Geometriae Dedicata, vol. 136 (2008).
Algebraic and Geometric Convergence of Discrete Representations into PSL(2,C)
Joint with Juan Souto.
Geometry and Topology 14 (2010).
A finiteness theorem for closed hyperbolic 3-manifolds
Joint with Juan Souto.
Journal of the London mathematical society (2011).
Extending pseudo-Anosov maps to compression bodies
Joint with Yair Minsky, Jesse Johnson.
Journal of Topology (2013).
On the growth of L2-invariants for sequences of lattices in Lie groups
Joint with M. Abert, N. Bergeron, T. Gelander, N. Nikolov, J. Raimbault and I. Samet.
An announcement, published in Comptes Rendus Mathematique, is available here.
On the growth of L2-invariants of locally symmetric spaces, II: exotic invariant random subgroups in rank one
Joint with M. Abert, N. Bergeron, T. Gelander, N. Nikolov, J. Raimbault and I. Samet.
Intersection growth in groups
Joint with Khalid Bou-Rabee, Martin Kassabov and Francesco Mattucci.
To appear in Transactions of the AMS.
Unimodularity of invariant random subgroups
Joint with Omer Tamuz.
To appear in Transactions of the AMS.
Rank of mapping tori via the curve complex
Joint with Juan Souto.
To appear in Journal fur die reine und angewandte Mathematik.
Automorphisms of the compression body graph
Joint with Nicholas Vlamis.
To appear in JLMS.
Ends of unimodular random manifolds
Joint with Jean Raimbault.
To appear in PAMS.
Packing curves on surfaces with few intersections.
Joint with Tarik Aougab and Jonah Gaster.
Iteration in Schottky space
Joint with Cyril Lecuire. (in preparation)
Rank and topology of hyperbolic 3-manifolds.
Joint with Juan Souto. (in preparation)