Algebra vs. geometry in hyperbolic 3-manifolds. pdf

PhD thesis, University of Chicago.
The Three Gap Theorem and Riemannian Geometry.
Arxiv

Joint with Benjamin Schmidt. Geometriae Dedicata, vol. 136 (2008).

Geometry and Rank of Fibered Hyperbolic 3-Manifolds.
Arxiv

Algebr. Geom. Topol. 9 (2009).

Algebraic and Geometric Convergence of Discrete Representations into PSL(2,C).
Arxiv

Joint with Juan Souto. Geometry and Topology 14 (2010).

A finiteness theorem for closed hyperbolic 3-manifolds.
Arxiv

Joint with Juan Souto. Journal of the London mathematical society (2011).

Extending pseudo-Anosov maps to compression bodies.
Arxiv

Joint with Yair Minsky, Jesse Johnson. Journal of Topology (2013).

On the growth of L2-invariants for sequences of lattices in Lie groups. Arxiv

Joint with M. Abert, N. Bergeron, T. Gelander, N. Nikolov, J. Raimbault and I. Samet.

A research announcement is available here.

Intersection growth in groups.
Arxiv

Joint with Khalid Bou-Rabee, Martin Kassabov and Francesco Mattucci.

Unimodularity of invariant random subgroups.
Arxiv

Joint with Omer Tamuz.

Rank of mapping tori via the curve complex.
Arxiv

Joint with Juan Souto.

Rank and topology of hyperbolic 3-manifolds.

Joint with Juan Souto. (in preparation)

Invariant measures on the space of all Riemannian manifolds.

Joint with Miklos Abert. (in preparation)