Research papers — sorted by topics

List of Topics Teichmüller metric on Teichmüler space
  1. Rigidity of Teichmüller space
    (With Alex Eskin and Howard Masur) [pdf]

  2. Non-convex balls in the Teichmüuller metric
    (With Maxime Fortier Bourque)
    to appear in Journal of Differential Geometry. [pdf]

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

  4. Counting geodesics in a stratum
    (With Alex Eskin and Maryam Mirzakhani)
    To appear in Inventiones mathematicae pending revisions. [pdf]

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

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

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

  8. Divergence rate of geodesics in Teichmüller space and mapping class groups
    (With Moon Duchin)
    Geom. Funct. Anal. 19 (2009), no. 3, 722-742. [pdf]

  9. Comparison between Teichmüller and Lipschitz metrics
    (With Young-Eun Choi)
    J. Lond. Math. Soc (2) 76 (2007), no. 3, 739-756. [pdf]

  10. A combinatorial model for the Teichmüller metric
    Geom. Funct. Anal. 17 (2007), no. 3, 936-959. [pdf]

  11. A characterization of short curves of a geodesic in Teichmüller space
    Geom. Topol. 9 (2005), 179-202. [pdf]
Flat surfaces
  1. Counting geodesics in a stratum
    (With Alex Eskin and Maryam Mirzakhani)
    To appear in Inventiones mathematicae pending revisions. [pdf]

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

  3. Thick-thin decomposition for quadratic differentials
    Math. Res. Lett. 14 (2007), no. 2, 333-341. [pdf]
Mapping class groups
  1. Geodesics Currents and Counting Problems
    (With Juan Souto) [pdf]

  2. Isomorphisms between big mapping class groups
    (With Juliette Bavard and Spencer Dowdall) [pdf]

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

  4. Uniform growth rate
    (With Jing Tao)
    Proc. Amer. Math. Soc. 144 (2016), no. 4, 1415--1427. [pdf]

  5. Divergence rate of geodesics in Teichmüller space and mapping class groups
    (With Moon Duchin)
    Geom. Funct. Anal. 19 (2009), no. 3, 722-742. [pdf]

  6. Covers and the curve complex
    (With Saul Schleimer)
    Geom. Topol. 13 (2009), no. 4, 2141-2162. [pdf]
Curve complex
  1. Uniform hyperbolicity of the curve graph via surgery sequences
    (With Matt Clay and Saul Schleimer)
    Algebraic & Geometric Topology 14-6 (2014), 3325--3344. [pdf]

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

  3. Covers and the curve complex
    (With Saul Schleimer)
    Geom. Topol. 13 (2009), no. 4, 2141-2162. [pdf]
Thurston metric on Teichmüler space
  1. Geodesics Currents and Counting Problems
    (With Juan Souto) [pdf]

  2. Coarse and fine geometry of the Thurston metric
    (With David Dumas, Anna Lenzhen and Jing Tao) [pdf]

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

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

  5. Comparison between Teichmüller and Lipschitz metrics
    (With Young-Eun Choi)
    J. Lond. Math. Soc (2) 76 (2007), no. 3, 739-756. [pdf]
Notions of straight lines in Teichmüler space
  1. The shadow of a Thurston geodesic to the curve graph
    (With Anna Lenzhen and Jing Tao)
    J. Topol. 8 (2015), no. 4, 1085--1118. [pdf]

  2. Grafting rays fellow travel Teichmüller geodesics
    (With Young-Eun Choi and David Dumas)
    Int. Math. Res. Not. IMRN (2011). [pdf]

  3. Lines of minima and Teichmüller geodesics
    (With Young-Eun Choi and Caroline Series)
    Geom. Funct. Anal. 18 (2008), no. 3, 698-754. [pdf]

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

  5. A characterization of short curves of a geodesic in Teichmüller space
    Geom. Topol. 9 (2005), 179-202. [pdf]
Outer space and outer automorphism groups of free groups
  1. Convexity of balls in the outer space
    (With Yulan Qing) [pdf]

  2. Algebraic ending laminations and quasi-convexity
    (With Mahan Mj) [pdf]

  3. Uniform fellow traveling between surgery paths in the sphere graph
    (With Matt CLay and Yulan Qing)
    to appear in Algebraic and Geometric Topology. [pdf]

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

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

  6. On hyperbolicity of free splitting and free factor complexes
    (With Ilya Kapovich)
    Groups Geom. Dyn. 8 (2014) no. 2, 391--414. [pdf]
Limit set of a Teichmüller geodesic
  1. Limit sets of Weil-Petersson geodesics
    (With Jeffrey Brock, Chris Leininger and Babak Modami) [pdf]

  2. Two-dimensional limit sets of Teichmüller geodesics
    (With Babak Modami and Anna Lenzhen) [pdf]

  3. Limit sets of Teichmüller geodesics with minimal nonuniquely ergodic vertical foliation, II
    (With Jeffrey Brock, Chris Leininger and Babak Modami)
    to appear in Journal für reine und angewandte Mathematik (Crelle's Journal). [pdf]

  4. Limit sets of Teichmüller geodesics with minimal non-uniquely ergodic vertical foliation
    (With Christopher Leininger and Anna Lenzhen)
    To appear in Crelle's Journal. [pdf]