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)
    Invent. Math. 215 (2019), no. 2, 535--607 [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)
    Geometry & Topology 22 (2018) 4259--4306, DOI: 10.2140/gt.2018.22.4259 [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 closed geodesics in strata.
    (With Alex Eskin and Maryam Mirzakhani)
    Invent. Math. 215 (2019), no. 2, 535--607 [pdf]


  4. The shape of a generic translation surface in the minimal stratum
    (With Howard Masur and Anja Randecker) [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)
    International Mathematics Research Notices (2020), no. 10, 3084--3099 [pdf]

  6. Geodesics Currents and Counting Problems
    (With Juan Souto)
    Geom. Funct. Anal. 29 (2019), no. 3, 871--889 [pdf]

  7. Geodesics in the Mapping Class Group
    (With Yvon Verberne) [pdf]

  8. Centralizers in Mapping Class Group and decidability of Thurston Equivalence
    (With Nikita Selinger and Michael Yampolsky)
    to appear in Arnold Mathematical Journal [pdf]

  9. Large Scale Geometry of Big Mapping Class Groups
    (With Kathryn Mann) [pdf]

  10. Big mapping class groups with hyperbolic actions: classification and applications
    (With Camillie Horbez and Yulan Qing) [pdf]

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

  2. Curve complexes 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)
    to appear in International Mathematics Research Notices [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)
    Forum of Mathematics, Sigma (2020), Vol. 8, e28, 58 pages [pdf]

  5. Geodesics Currents and Counting Problems
    (With Juan Souto)
    Geom. Funct. Anal. 29 (2019), no. 3, 871--889 [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)
    Algebr. Geom. Topol. 18 (2018), no. 4, 1883--1916. [pdf]

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

  7. Quasi-geodesics in Out(F_n) and their shadows in sub-factors
    (With Yulan Qing) [pdf]

Limit set of a Teichmüller geodesic
  1. Limit sets of Teichmüller geodesics with minimal non-uniquely ergodic vertical foliation.
    (With Christopher Leininger and Anna Lenzhen)
    J. Reine Angew. Math. 737 (2018), 1--32 (Crelle's Journal). [pdf]

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

  3. Limit sets of Weil-Petersson geodesics
    (With Jeffrey Brock, Chris Leininger and Babak Modami)
    Int. Math. Res. Not. IMRN (2019), no. 24, 7604--7658. [pdf]

  4. 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 [pdf]

  5. Limit sets of Weil-Petersson geodesics with nonminimal ending laminations
    (With Jeffrey Brock, Chris Leininger and Babak Modami)
    J. Topol. Anal. 12 (2020), no. 1, 1--28 [pdf]

Miscellaneous
  1. Sub-linearly Morse Boundary I: CAT(0) Spaces
    (With Yulan Qing and Giulio Tiozzo) [pdf]

  2. Centralizers in Mapping Class Group and decidability of Thurston Equivalence
    (With Nikita Selinger and Michael Yampolsky)
    to appear in Arnold Mathematical Journal [pdf]

  3. Local maxima of the systole function
    (With Maxime Fortier Bourque) [pdf]

  4. Renormalizing an infinite rational IET
    (With W. Patrick Hooper and Anja Randecker) [pdf]