Home Topics

Research papers — in chronological order

Preprints
  1. Benjamini-Schramm limits of high genus translation surfaces: research announcement
    (With Lewis Bowen and Hunter Vallejos) [pdf]

  2. Lengths of saddle connections on random translation surfaces of large genus
    (With Howard Masur and Anja Randecker) [pdf]

  3. Classification of Stable Surfaces with respect to Automatic Continuity
    (With Mladen Bestvina and George Domat) [pdf]

  4. Thurston geodesics: no backtracking and active intervals
    (With Anna Lenzhen, Babak Modami and Jing Tao) [pdf]

  5. The quasi-redirecting boundary
    (With Yulan Qing) [pdf]

  6. Random walks on groups and superlinear divergent geodesics
    (With Kunal Chawla, Inhyeok Choi and Vivian He) [pdf]

  7. Asymptotic Dimension of Big Mapping Class Groups
    (With Curtis Grant and Yvon Verberne) [pdf]

Refereed
  1. Genericity of sublinearly Morse directions in CAT(0) spaces and the Teichmüller spae
    (With Ilya Gekhtman and Yulan Qing)
    to appear in Mathematische Zeitschrift [pdf]

  2. Fibered 3-manifolds and Veech groups
    (With Chris Leininger, Nicholas Rouse, Emily Shinkle and Yvon Verberne)
    to appear in Algebraic & Geometric Topology [pdf]

  3. Two results on the end spaces of infinite type surfaces
    (With Kathryn Mann)
    to appear in Michigan Mathematical Journal [pdf]

Published
  1. Sublinearly Morse Boundary II: Proper geodesic spaces
    (With Yulan Qing and Giulio Tiozzo)
    Geometry & Topology 28:4 (2024) 1829--1889 [pdf]

  2. Large Scale Geometry of Big Mapping Class Groups
    (With Kathryn Mann)
    Geometry & Topology 27 (2023) 2237--2296. [pdf]

  3. Big mapping class groups with hyperbolic actions: classification and applications
    (With Camillie Horbez and Yulan Qing)
    Journal of the Institute of Mathematics of Jussieu 21 (2022), no. 6, 2173--2204. [pdf]

  4. Benjamini-Schramm convergence of periodic orbits
    (With Amir Mohammadi)
    Geometriae Dedicata 216 (2022), no. 5, Paper No. 57. [pdf]

  5. Sublinearly Morse Boundary I: CAT(0) Spaces
    (With Yulan Qing and Giulio Tiozzo)
    Advances in Mathematics 404 (2022) 108442 [pdf]

  6. Expected covering radius of a translation surface
    (With Howard Masur and Anja Randecker)
    International Mathematics Research Notices 2022, no. 10, 7967--8002 [pdf]

  7. Local maxima of the systole function
    (With Maxime Fortier Bourque)
    Journal of the European Mathematical Society (JEMS) 24 (2022), no. 2, 623--668. [pdf]

  8. Quasi-geodesics in Out(F_n) and their shadows in sub-factors
    (With Yulan Qing)
    Journal of the London Mathematical Society, 104 (1), (2022), 147--168. [pdf]

  9. Geodesics in the Mapping Class Group
    (With Yvon Verberne)
    Algebraic & Geometric Topology 21 (2021) 2995--3017 [pdf]

  10. Convexity of balls in the outer space
    (With Yulan Qing)
    Groups, Geometry, and Dynamics 15 (2021), no. 3, 893--934. [pdf]

  11. Centralizers in Mapping Class Group and decidability of Thurston Equivalence
    (With Nikita Selinger and Michael Yampolsky)
    Arnold Mathematical Journal 6 (2020), no. 2, 271--290 [pdf]

  12. Renormalizing an infinite rational IET
    (With W. Patrick Hooper and Anja Randecker)
    Discrete and Continuous Dynamical Systems - Series A (2020), 40, no. 9, 5105--5116 [pdf]

  13. Coarse and fine geometry of the Thurston metric
    (With David Dumas, Anna Lenzhen and Jing Tao)
    Forum of Mathematics, Sigma (2020), Vol. 8, e28, 58 pages [pdf]

  14. Isomorphisms between big mapping class groups
    (With Juliette Bavard and Spencer Dowdall)
    International Mathematics Research Notices (2020), no. 10, 3084--3099 [pdf]

  15. Limit sets of Weil-Petersson geodesics with nonminimal ending laminations
    (With Jeffrey Brock, Chris Leininger and Babak Modami)
    Journal of Topology and Analysis 12 (2020), no. 1, 1-28 [pdf]

  16. Limit sets of Teichmüller geodesics with minimal nonuniquely ergodic vertical foliation, II
    (With Jeffrey Brock, Chris Leininger and Babak Modami)
    Journal für reine und angewandte Mathematik, 758 (2020), 1-66 (Crelle's Journal) [pdf]

  17. Limit sets of Weil-Petersson geodesics
    (With Jeffrey Brock, Chris Leininger and Babak Modami)
    International Mathematics Research Notices (2019), no. 24, 7604-7658 [pdf]

  18. Geodesics Currents and Counting Problems
    (With Juan Souto)
    Geometric and Functional Analysis 29 (2019), no. 3, 871-889 [pdf]

  19. Counting closed geodesics in strata.
    (With Alex Eskin and Maryam Mirzakhani)
    Inventiones Mathematicae 215 (2019), no. 2, 535-607 [pdf]

  20. Rigidity of Teichmüller space.
    (With Alex Eskin and Howard Masur)
    Geometry & Topology 22 (2018) 4259-4306, [pdf]

  21. Non-convex balls in the Teichmüller metric
    (With Maxime Fortier Bourque)
    Journal of Differential Geometry 110 (2018) 379-412 [pdf]

  22. Teichmüller geodesics with d-dimensional limit sets
    (With Babak Modami and Anna Lenzhen)
    Journal of Modern Dynamics, 12 (2018), 261-283 [pdf]

  23. Algebraic ending laminations and quasi-convexity
    (With Mahan Mj)
    Algebraic & Geometric Topology 18 (2018), no. 4, 1883-1916 [pdf]

  24. Limit sets of Teichmüller geodesics with minimal non-uniquely ergodic vertical foliation. (With Christopher Leininger and Anna Lenzhen)
    Journal für die reine und angewandte Mathematik 737 (2018), 1-32 (Crelle's Journal) [pdf]

  25. Uniform fellow traveling between surgery paths in the sphere graph
    (With Matt Clay and Yulan Qing)
    Algebraic & Geometric Topology 17 (2017) 3751-3778 [pdf]

  26. Large scale rank of Teichmüller space.
    (With Alex Eskin and Howard Masur)
    Duke Mathematical Journal 166 (2017), no. 8, 1517-1572 [pdf]

  27. Uniform growth rate.
    (With Jing Tao)
    Proceedings of the American Mathematical Society 144 (2016), no. 4, 1415-1427 [pdf]

  28. The shadow of a Thurston geodesic to the curve graph.
    (With Anna Lenzhen and Jing Tao)
    Journal of Topology 8 (2015), no. 4, 1085-1118 [pdf]

  29. Digraphs and cycle polynomials for free-by-cyclic groups.
    (With Yael Algom-Kfir and Eriko Hironaka)
    Geometry & Topology 19 (2015), no. 2, 1111-1154 [pdf]

  30. Mapping tori of small dilatation irreducible train-track maps.
    (With Yael Algom-Kfir)
    Topology and its Applications 180 (2015) 44-63 [pdf]

  31. Uniform hyperbolicity of the curve graph via surgery sequences.
    (With Matt Clay and Saul Schleimer)
    Algebraic & Geometric Topology 14-6 (2014), 3325-3344 [pdf]

  32. Hyperbolicity in Teichmüller space.
    Geometry & Topology 18-5 (2014) 3025-3053 [pdf]

  33. On hyperbolicity of free splitting and free factor complexes.
    (With Ilya Kapovich)
    Groups, Geometry, and Dynamics 8 (2014) no. 2, 391-414 [pdf]

  34. Diameter of the thick part of moduli space and simultaneous Whitehead moves.
    (With Jing Tao)
    Duke Mathematical Journal 162 (2013), no. 10, 1833-1876 [pdf]

  35. Bounded combinatorics and the Lipschitz metric on Teichmüller space.
    (With Anna Lenzhen and Jing Tao)
    Geometriae Dedicata 159 (2012), 353-371 [pdf]

  36. Grafting rays fellow travel Teichmüller geodesics.
    (With Young-Eun Choi and David Dumas)
    International Mathematics Research Notices (2012), no. 11, 2445-2492 [pdf]

  37. Length of a curve is quasi-convex along a Teichmüller geodesic.
    (With Anna Lenzhen)
    J. Differential Geom. 88 (2011), no. 2, 267-295 [pdf]

  38. Curve complexes are rigid.
    (With Saul Schleimer)
    Duke Math. J. 158 (2011), no. 2, 225-246 [pdf]

  39. Length spectra and degeneration of flat metrics.
    (With Moon Duchin and Christopher Leininger)
    Inventiones Mathematicae 182 (2010), no. 2, 231-277 [pdf]

  40. Divergence rate of geodesics in Teichmüller space and mapping class groups.
    (With Moon Duchin)
    Geometric and Functional Analysis 19 (2009), no. 3, 722-742 [pdf]

  41. Covers and the curve complex.
    (With Saul Schleimer)
    Geometry & Topology 13 (2009), no. 4, 2141-2162 [pdf]

  42. Lines of minima and Teichmüller geodesics.
    (With Young-Eun Choi and Caroline Series)
    Geometric and Functional Analysis 18 (2008), no. 3, 698-754 [pdf]

  43. Lines of minima are uniformly quasi-geodesic.
    (With Young-Eun Choi and Caroline Series)
    Pacific Journal of Mathematics 237 (2008), no. 1, 21-44 [pdf]

  44. Comparison between Teichmüller and Lipschitz metrics.
    (With Young-Eun Choi)
    Journal of the London Mathematical Society (2) 76 (2007), no. 3, 739-756 [pdf]

  45. A combinatorial model for the Teichmüller metric.
    Geometric and Functional Analysis 17 (2007), no. 3, 936-959 [pdf]

  46. Thick-thin decomposition for quadratic differentials.
    Mathematical Research Letters 14 (2007), no. 2, 333-341 [pdf]

  47. A characterization of short curves of a geodesic in Teichmüller space.
    Geometry & Topology 9 (2005), 179-202 [pdf]