Research papers — sorted by topics

List of Topics Teichmüller metric on Teichmüler space
  1. A characterization of short curves of a geodesic in Teichmüller space
    Geom. Topol. 9 (2005), 179-202. [pdf]

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

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

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

  5. Length of a curve is quasi-convex along a Teichmüller geodesic
    (With Anna Lenzhen)
    J. Differential Geom. 88 (2011), no. 2, 267-295. [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. Hyperbolicity in Teichmüller space
    Geometry & Topology 18-5 (2014) 3025--3053. [pdf]

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

  9. Counting closed geodesics in strata.
    (With Alex Eskin and Maryam Mirzakhani)
    To appear in Inventiones mathematicae pending revisions. [pdf]

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

  11. Rigidity of Teichmüller space
    (With Alex Eskin and Howard Masur) [pdf]

Flat surfaces
  1. Thick-thin decomposition for quadratic differentials
    Math. Res. Lett. 14 (2007), no. 2, 333-341. [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. Counting geodesics in a stratum
    (With Alex Eskin and Maryam Mirzakhani)
    To appear in Inventiones mathematicae pending revisions. [pdf]

Mapping class groups
  1. Covers and the curve complex
    (With Saul Schleimer)
    Geom. Topol. 13 (2009), no. 4, 2141-2162. [pdf]

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

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

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

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

  6. Geodesics Currents and Counting Problems
    (With Juan Souto) [pdf]

Curve complex
  1. Covers and the curve complex
    (With Saul Schleimer)
    Geom. Topol. 13 (2009), no. 4, 2141-2162. [pdf]

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

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

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

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

  2. Bounded combinatorics and the Lipschitz metric on Teichmüller space
    (With Anna Lenzhen and Jing Tao)
    Geom. Dedicata 159 (2012), 353-371. [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. Coarse and fine geometry of the Thurston metric
    (With David Dumas, Anna Lenzhen and Jing Tao) [pdf]

  5. Geodesics Currents and Counting Problems
    (With Juan Souto) [pdf]

Notions of straight lines in Teichmüler space
  1. A characterization of short curves of a geodesic in Teichmüller space
    Geom. Topol. 9 (2005), 179-202. [pdf]

  2. Lines of minima are uniformly quasi-geodesic
    (With Young-Eun Choi and Caroline Series)
    Pacific J. Math. 237 (2008), no. 1, 21-44. [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. Grafting rays fellow travel Teichmüller geodesics
    (With Young-Eun Choi and David Dumas)
    Int. Math. Res. Not. IMRN (2011). [pdf]

  5. 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]

Outer space and outer automorphism groups of free groups
  1. On hyperbolicity of free splitting and free factor complexes
    (With Ilya Kapovich)
    Groups Geom. Dyn. 8 (2014) no. 2, 391--414. [pdf]

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

  3. 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]

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

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

  6. Convexity of balls in the outer space
    (With Yulan Qing) [pdf]

Limit set of a Teichmüller geodesic
  1. 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]

  2. 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]

  3. Limit sets of Weil-Petersson geodesics
    (With Jeffrey Brock, Chris Leininger and Babak Modami)
    International Mathematics Research Notices
    Advance Access publication on February 9, 2018, doi:10.1093/imrn/rny002 [pdf]

  4. Teichmüller geodesics with d-dimensional limit sets
    (With Babak Modami and Anna Lenzhen) [pdf]

  5. Limit sets of Weil-Petersson geodesics with nonminimal ending laminations
    (With Jeffrey Brock, Chris Leininger and Babak Modami) [pdf]