Separating geodesics in hyperbolic 3-manifolds.
Universal length bounds for non-simple closed geodesics.
Moduli spaces of hyperbolic 3-manifolds and dynamics on character varieties.
Combinatorial length, geometric length and self-intersection of curves on surfaces.
Isoperimetric problems in the mapping class group.
Skinning maps are finite-to-one.
Dynamics of Thurston's pullback map on the Weil-Petersson boundary.
Coarse differentiation and the rank of Teichmuller space.