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List of Topics Teichmüller metric on Teichmüller space
  1. A characterization of short curves of a Teichmüller geodesic
    Geometry & Topology 9 (2005), 179--202 [pdf]

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

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

  4. 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]

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

  6. 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]

  7. Hyperbolicity in Teichmüller space
    Geometry & Topology 18 (2014), no. 5, 3025--3053 [pdf]

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

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

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

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

  12. Genericity of sublinearly Morse directions in CAT(0) spaces and the Teichmüller space
    (With Ilya Gekhtman and Yulan Qing)
    Mathematische Zeitschrift 311 (2025), article no. 79 [pdf]

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

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

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

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

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

  6. Fibered 3-manifolds and Veech groups
    (With Chris Leininger, Nicholas Rouse, Emily Shinkle and Yvon Verberne)
    Algebraic & Geometric Topology 25 (2025), no. 3, 1897--1915 [pdf]

  7. Lengths of saddle connections on random translation surfaces of large genus
    (With Howard Masur and Anja Randecker)
    to appear in Commentarii Mathematici Helvetici [pdf]

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

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

  2. 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]

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

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

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

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

  7. 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]

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

  9. Large Scale Geometry of Big Mapping Class Groups
    (With Kathryn Mann)
    Geometry & Topology 27 (2023), no. 6, 2237--2296 [pdf]

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

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

  12. Two results on the end spaces of infinite type surfaces
    (With Kathryn Mann)
    Michigan Mathematical Journal 74 (2024), no. 5, 1109--1116 [pdf]

  13. Classification of Stable Surfaces with respect to Automatic Continuity
    (With Mladen Bestvina and George Domat)
    to appear in Compositio Mathematica [pdf]

  14. The non-peripheral curve graph and divergence in big mapping class groups
    (With Assaf Bar-Natan and Yulan Qing) [pdf]

  15. Random walks on groups and superlinear-divergent geodesics
    (With Kunal Chawla, Inhyeok Choi and Vivian He)
    Ergodic Theory and Dynamical Systems 45 (2025), no. 5, 1403--1443 [pdf]

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

  2. Curve complexes are rigid
    (With Saul Schleimer)
    Duke Mathematical Journal 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 (2014), no. 6, 3325--3344 [pdf]

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

  5. The non-peripheral curve graph and divergence in big mapping class groups
    (With Assaf Bar-Natan and Yulan Qing) [pdf]

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

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

  3. 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]

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

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

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

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

  2. 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]

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

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

  5. 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]

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

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

  2. Mapping tori of small dilatation expanding 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)
    Geometry & Topology 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)
    Algebraic & Geometric Topology 18 (2018), no. 4, 1883--1916 [pdf]

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

  7. Quasi-geodesics in Out(F_n) and their shadows in sub-factors
    (With Yulan Qing)
    Journal of the London Mathematical Society (2) 104 (2021), no. 1, 147--168 [pdf]

Limit sets of Teichmüller and Weil-Petersson geodesics
  1. 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]

  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)
    International Mathematics Research Notices (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 die reine und angewandte Mathematik 758 (2020), 1--66 (Crelle's Journal) [pdf]

  5. 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]

Boundaries
  1. Sublinearly Morse Boundary I: CAT(0) Spaces
    (With Yulan Qing and Giulio Tiozzo)
    Advances in Mathematics 404 (2022), part B, Paper No. 108442 [pdf]

  2. Sublinearly Morse Boundary II: Proper geodesic spaces
    (With Yulan Qing and Giulio Tiozzo)
    Geometry & Topology 28 (2024), no. 4, 1829--1889 [pdf]

  3. Genericity of sublinearly Morse directions in CAT(0) spaces and the Teichmüller space
    (With Ilya Gekhtman and Yulan Qing)
    Mathematische Zeitschrift 311 (2025), article no. 79 [pdf]

  4. Random walks on groups and superlinear-divergent geodesics
    (With Kunal Chawla, Inhyeok Choi and Vivian He)
    Ergodic Theory and Dynamical Systems 45 (2025), no. 5, 1403--1443 [pdf]

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

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

  2. Fibered 3-manifolds and Veech groups
    (With Chris Leininger, Nicholas Rouse, Emily Shinkle and Yvon Verberne)
    Algebraic & Geometric Topology 25 (2025), no. 3, 1897--1915 [pdf]

  3. 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]

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

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