Papers

Preprint versions of the published papers are made avaiable here.

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          33. Dynamics on free-by-cyclic groups. with S. Dowdall and I. Kapovich, preprint.

          32. Lipschitz constants to curve complexes. with Vaibhav Gadre, Eriko Hironaka, and R. P. Kent IV, preprint.

          31. Pseudo-Anosov subgroups of fibered 3-manifold groups. with S. Dowdall and R. P. Kent IV, preprint.

          30. A geometric criterion to be pseudo-Anosov with R. P. Kent IV, preprint.

          29. Finite rigid sets in curve complexes, with J. Aramayona, preprint.

          28. Hyperbolic spaces in Teichmüller spaces, with S. Schleimer, to appear in JEMS.

             27.On the number and location of short geodesics in moduli space. with D. Margalit, to appear in Journal of Topology.

             26.The geometry of right angled Artin subgroups of mapping class groups, with M. Clay and J. Mangahas, Groups Geom. Dyn. 6 (2012), no. 2, 249–278.

             25. Small dilatation pseudo-Anosovs and 3-manifolds. with B. Farb and D. Margalit, Adv. Math. 228 (2011), no. 3, 1466–1502.

             24. Commensurators of non-free finitely generated Kleinian groups, with D. Long and A. Reid, Algebr. Geom. Topol. 11 (2011) 605–624

             23. The universal Cannon--Thurston map and the boundary of the curve complex. with Mahan Mj and S. Schleimer. Comment. Math. Helv. 86 (2011), no. 4, 769–816. slides from a talk at the Ahlfors--Bers Colloquium

             22.Length spectra and degeneration of flat metrics. with M. Duchin and K. Rafi, Invent. Math., 182 (2010) No. 2, 231--277.

             21.Two-generator subgroups of the pure braid group, with D. Margalit, Geom. Dedicata 147 (2010) 107--113.

             20.A fake Schottky group in Mod(S) with R. P. Kent IV, In the tradition of Ahlfors-Bers. V, 185--196, Contemp. Math., 510, Amer. Math. Soc., Providence, RI, 2010.

             19.Injections of mapping class groups with J. Aramayona and J. Souto, Geometry & Topology 13 (2009) 2523--2541.

             18. Connectivity of the space of ending laminations. with S. Schleimer, Duke Math. J. 150 (2009) no. 3, 533--575.

             17. Accidental parabolics and mapping class groups, Proc. Amer. Math. Soc. 137 (2009) no. 3, 1153--1160.

             16. Trees and mapping class groups with R. P. Kent IV and S. Schleimer, J. Reine Angew Math. 637 (2009), 1--21.

             15. The lower central series and pseudo-Anosov dilatations with B. Farb and D. Margalit, Amer. J. Math. 130 (2008), no. 3, 799-827.

             14. Uniform convergence in the mapping class group with R. P. Kent IV, Ergodic Theory and Dynamical Systems (2008), 28, 1177--1195.

             13.Shadows of mapping class groups: capturing convex cocompactness, with R. P. Kent IV, Geom. Funct. Anal. 18 (2008), 1270--1325.

             12. Length and eigenvalue equivalence with D. B. McReynolds, W. D. Neumann., and A. W. Reid, Int. Math. Res. Not. volume 2007, article ID rnm135, 24 pages, doi:10.1093/imrn/rnm135.

             11. Subgroups of the mapping class group from the geometrical viewpoint a survey with R. P. Kent IV, In the tradition of Ahlfors--Bers IV, Contemp. Math., 432, Amer. Math. Soc. Providence, RI, 2007.

             10. Kleinian groups with discrete length spectrum, with R. D. Canary, Bull. London Math. Soc. 39 (2007), 189--193.

             9. Separable subgroups of the mapping class group, with D. B. McReynolds, Toplogy Appl. 154 (2007), no 1, 1--10.

             8. Abstract commensurators of braid groups, with D. Margalit, J. Algebra 299 (2006), no. 2, 447--455.

             7. A combination theorem for Veech subgroups of the mapping class group, with A. W. Reid, Geom. Funct. Anal. 16 (2006) 403--436.

             6. Small curvature surfaces in hyperbolic 3-manifolds, J. Knot Theory Ramifications 15 (2006), 379--411.

             5. On groups generated by two positive multi-twists: Teichmüller curves and Lehmer's number, Geom. Topol. 8 (2004) 1301--1359.

             4. Equivalent curves in surfaces, Geom. Dedicata 102 (2003), 151--177.

             3. The co-rank conjecture for 3-manifold groups, with A. W. Reid, Algebr. Geom. Topol. 2 (2002), 37--50.

             2. Compressing totally geodesic surfaces, Topology Appl. 118 (2002), 309--328.

             1. Surgeries on one component of the Whitehead link are virtually fibered, Topology 41 (2002), 307--320.

             0. Essential surfaces in hyperbolic three-manifolds, Thesis, U.T. Austin, May 2002

          2. From metrics to moduli space, Preliminary draft of Lecture notes from the Undergraduate Summer School in Park City Math Institute, July 2011.

          1. Degenerations of hyperbolic structures on surfaces, Lecture notes from Summer School in Singapore, July 2010, to appear. See the companion notes by J. Aramayona

             One-ended subgroups of right-angled Artin groups, preprint (4 pages).

             Graphs of Veech groups, in preparation.