Papers

Preprint versions of the published papers are made avaiable here.

          52. You can hear the shape of a billiard table: Symbolic dynamics and rigidity for flat surfaces., with M. Duchin, V. Erlandsson, and C. Sadanand, preprint.

          51. Pseudo-Anosov homeomorphisms not arising from branched covers., with A.W. Reid, preprint.

          50. Limit sets of Weil-Petersson geodesics with nonminimal ending laminations, with J. Brock, B. Modami, and K. Rafi, to appear in J. Topol. Anal.

          49. Limit sets of Weil-Petersson geodesics. with J. Brock, B. Modami, and K. Rafi, IMRN, online first.

          48. Quotients of mapping class groups from \(Out(F_n) \). with K. Bou-Rabee, to appear in Proc. Amer. Math. Soc..

          47. Undistorted purely pseudo-Anosov groups. with M. Bestvina, K. Bromberg, and A.E. Kent, J. Reine Agnew Math., published online first.

          46. Strict contractions and exotic \(\mbox{SO}_0(d,1)\) quotients. with G. Lakeland, J. Lond. Math. Soc. (2) 96 (2017), no. 3, 642-662.

          45. Limit sets of Teichmüller geodesics with minimal non-uniquely ergodic vertical foliation, II. with J. Brock, B. Modami, and K. Rafi, J. Reine Agnew Math., online first.

          44. An arc graph distance formula for the flip graph. with F. Gultepe, Proc. Amer. Math. Soc, 145 (2017), no. 7, 3179-3184.

          43. Endomorphisms, train track maps, and fully irreducible monodromies. with S. Dowdall and I. Kapovich, Groups Geom. Dyn. 11 (2017), no. 4, 1179-1200.

          42. Marked length spectral rigidity for flat metrics, with A. Bankovic, Trans. Amer. Math. Soc. 370 (2018), no. 3, 1867-1884.

          41. Exhausting curve complexes by finite rigid sets, with J. Aramayona, Pacific J. Math. 282 (2016), no. 2, 257-283.

          40. Pseudo-Anosov stretch factors and homology of mapping tori with I. Agol and D. Margalit, J. Lond. Math. Soc. (2) 93 (2016), no. 3, 664-682.

          39. Unbounded asymmetry of stretch factors. with S. Dowdall and I. Kapovich, C. R. Math. Acad. Sci. Paris 352 (2014), no. 11, 885-887.

          38. Conical limit points and Cannon-Thurston maps, with W. Jeon, I. Kapovich, and K. Ohshika, Conform. Geom. Dyn. 20 (2016), 58-80

          37. Limit sets of Teichmüller geodesics with minimal non-uniquely ergodic vertical foliations. with A. Lenzhen and K. Rafi, J. Reine Angew. Math. 737 (2018), 1-32.

          36. McMullen polynomials and Lipschitz flows for free-by-cyclic groups. with S. Dowdall and I. Kapovich, J. Eur. Math. Soc. 19 (2017), no. 11, 3253-3353.

          35. Abstract commensurators of right-angled Artin groups and mapping class groups with M. Clay and D. Margalit, Math. Res. Lett. 21 (2014), no. 3, 461-467.

          34. Systoles and Dehn surgery for hyperbolic 3-manifolds with G. Lakeland, Algebr. Geom. Topol. 14 (2014), no. 3, 1441-1460.

          33. Dynamics on free-by-cyclic groups. with S. Dowdall and I. Kapovich, Geom. Topol. 19 (2015) no. 5, 2801-2899.

          32. Lipschitz constants to curve complexes. with Vaibhav Gadre, Eriko Hironaka, and A.E. Kent, Math. Res. Lett. 20 (2013), no. 4, 647-656.

          31. Pseudo-Anosov subgroups of fibered 3-manifold groups. with S. Dowdall and A.E. Kent, Groups Geom. Dyn. 8 (2014), no. 4, 1247-1282.

          30. A geometric criterion to be pseudo-Anosov with A.E. Kent, Michigan Math. J. 63 (2014), no. 2, 227-251.

          29. Finite rigid sets in curve complexes, with J. Aramayona, J. Topol. Anal. 5 (2013), no.2, 183-203

          28. Hyperbolic spaces in Teichmüller spaces, with S. Schleimer, J. Eur. Math. Soc. (JEMS) 16 (2014), no. 12, 2669-2692.

             27.On the number and location of short geodesics in moduli space. with D. Margalit, J. Topol. 6 (2013), no. 1, 30-48.

             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 A.E. Kent, 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 A.E. Kent 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 A.E. Kent, Ergodic Theory and Dynamical Systems (2008), 28, 1177-1195.

             13.Shadows of mapping class groups: capturing convex cocompactness, with A.E. Kent, 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 A.E. Kent, 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

Lecture notes:

       3. Hyperbolic structures on surfaces and geodesic currents, Lecture notes from mini-course with J. Aramayona, at CRM (Barcelona), Fall 2012 to appear.

          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

Some other things...

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

             Graphs of Veech groups, in preparation.

Part of this material is based upon work supported by the National Science Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.


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