Papers


Papers in .pdf format.

Erratum to "On the density of geometrically finite Kleinian groups."
(With Ken Bromberg). Preprint (2017).

Local topology in deformation spaces of hyperbolic 3-manifolds II. (arXiv).
(With Ken Bromberg, Richard Canary, Cyril Lecuire, and Yair Minsky). Preprint (2017).

Schwarzian derivatives, projective structures, and the Weil-Petersson gradient flow for renormalized volume. (arXiv).
(With Martin Bridgeman and Ken Bromberg). Preprint (2017).

Machine learning algorithm for automatic detection of CT-identifiable hyperdense lesions associated with traumatic brain injury.
Krishna N. Keshavamurthy ; Owen P. Leary ; Lisa H. Merck ; Benjamin Kimia ; Scott Collins ; David W. Wright ; Jason W. Allen ; Jeffrey F. Brock ; Derek Merck. Proc. SPIE 10134, Medical Imaging 2017: Computer-Aided Diagnosis, 101342G (March 23, 2017); doi:10.1117/12.2254227.

Limit sets of Weil-Petersson geodesics. (arXiv).
(With Christopher Leininger, Babak Modami, and Kasra Rafi). Preprint (2017).

Windows, cores, and skinning maps. (arXiv).
(With Ken Bromberg, Dick Canary, and Yair Minsky). Preprint (2016).

Limit sets of Teichmüller geodesics with minimal nonuniquely ergodic vertical foliation, II. (arXiv).
(With Chris Leininger, Babak Modami, and Kasra Rafi). Crelle's Journal, DOI: https://doi.org/10.1515/crelle-2017-0024.

Norms on the cohomology of hyperbolic 3-manifolds. (arXiv).
(With Nathan Dunfield). Inventiones Mathematicae, pp. 1-28. DOI: 10.1007/s00222-017-0735-3.

Geometric inflexibility of hyperbolic cone-manifolds. (arXiv).
(With Ken Bromberg). To appear, Proceedings of the 2014 MSJ-SI.

Inflexibility, Weil-Petersson distance, and volumes of fibered 3-manifolds. (arXiv).
(With Ken Bromberg). Math. Res. Lett. 23 (2016) pp. 649-674.

Recurrent Weil-Petersson geodesic rays with non-uniquely ergodic ending laminations. (arXiv).
(With Babak Modami). Geometry & Topology 19, (2015) pp. 3565-3602.

Convergence and divergence of Kleinian groups. (arXiv).
(With Ken Bromberg, Richard Canary, Cyril Lecuire). J. Topology 8 (2015) 811-841.

Bounded combinatorics and uniform models for hyperbolic 3-manifolds. (arXiv).
(With Yair Minsky, Hossein Namazi, and Juan Souto). Preprint (2013). To appear, Journal of Topology.

Injectivity radii of hyperbolic integer homology 3-spheres. (arXiv).
(With Nathan Dunfield). Geometry & Topology, 19 (2015) 497–523.

Convergence properties of end invariants. (arXiv).
(With Ken Bromberg, Dick Canary, and Yair Minsky). Geometry & Topology, 17 (2013) pp. 2877-2922.

The classification of Kleinian surface groups II: the ending lamination conjecture. (arXiv).
(With Dick Canary and Yair Minsky). Annals of Math.
176 (2012), pp. 1-149.

Assembling surfaces from random pants: mixing, matching and correcting in the proofs of the surface-subgroup and Ehrenpreis conjectures.
In AMS Current Events Bulletin (2012)

Local topology of deformation spaces of hyperbolic 3-manifolds.
(With Ken Bromberg, Richard Canary, and Yair Minsky). Geometry & Topology 15 (2011) pp. 1169–1224.

Asymptotics of Weil-Petersson geodesics II: bounded geometry and unbounded entropy.
(With Howard Masur and Yair Minsky). Geom. & Funct. Anal. 21 (2011) pp. 820-850.

Taming the Field of Hyperbolic 3-Manifolds.
In the Annual Report of the Clay Mathematics Institute, 2009 pp. 10-18.

Geometric inflexibility and 3-manifolds that fiber over the circle.
(With Ken Bromberg). Journal of Topology, 4 (2011) pp. 1-38. (doi: 10.1112/jtopol/jtq032).

Asymptotics of Weil-Petersson geodesics I: ending laminations, recurrence and flows.
(With Howard Masur and Yair Minsky). Geom. & Funct. Anal. 19 (2010) pp. 1229-1257.

Coarse and synthetic Weil-Petersson geometry: quasi-flats, geodesics, and relative hyperbolicity.
(With Howard Masur). Geometry & Topology, 12 (2008) 2453-2495.

Heegaard splittings, pants decompositions and volumes of hyperbolic 3-manifolds.
(With Juan Souto). In Preparation.

Weil-Petersson isometries via the pants complex.
(With Dan Margalit). Proc. A.M.S. 135 (2007) pp. 795-803

Algebraic limits of geometrically finite manifolds are tame.
(With Juan Souto). Geom. & Funct. Anal. 16 (2006) pp. 1-39.

Curvature and rank of Teichmüller space.
(With Benson Farb). Amer. J. Math. 128 (2006), pp. 1-22 .

The Weil-Petersson visual sphere.
Geometriae Dedicata, 1, (2005), pp. 1-18

On the density of geometrically finite Kleinian groups.
(With Ken Bromberg). Acta Math., 192 (2004), pp. 33-93.

Tameness on the boundary and Ahlfors' measure conjecture.
(With Ken Bromberg, Richard Evans, and Juan Souto). Publ. Math. I.H.E.S., 98 (2003), pp. 145-166.

Pants decompositions and the Weil-Petersson metric.
In Complex Manifolds and Hyperbolic Geometry, American Mathematical Society, Providence, 2002, 343 pp.

Cone-manifolds and the density conjecture.
(With Ken Bromberg). In Kleinian Groups and Hyperbolic 3-Manifolds, London Math Society Lecture Note Series, Cambridge Univesrity Press, 2003.

Weil-Petersson translation distance and volumes of mapping tori.
Preprint (2001). Comm. Anal. Geom. 11 (2003), pp. 987-999.

The Weil-Petersson metric and volumes of 3-dimensional hyperbolic convex cores.
J. Amer. Math. Soc., 16 (2003), pp. 495-535.

Boundaries of Teichmüller spaces and end-invariants for hyperbolic 3-manifolds.
Duke Math. J., 106 (2000), pp. 527-552.

Continuity of Thurston's length function.
Geom. & Funct. Anal., 10 (2000), pp. 741-797.

Iteration of mapping classes and limits of hyperbolic 3-manifolds.
Invent. Math. 143 (2001), pp. 523-570.

Iteration of mapping classes on a Bers slice: examples of algebraic and geometric limits of hyperbolic 3-manifolds.
In Lipa's Legacy, J. Dodziuk, L. Keen, ed., Proceedings of the Bers Colloquium, 1997, pp. 81-106.

The standard double bubble in R^2 uniquely minimizes perimeter.
(with M. Alfaro et. al.) Pacific Journal of Mathematics, 159, (1993), no. 1, 47-59.

Almost Alternating Links.
(with C. Adams et. al.) Topology and its Applications 46, (1992), no. 2, 151 165.