Research

Research papers

  1. Joint with Pierre Derbez, and Shicheng Wang, Volume of Seifert representations for graph manifolds and finite covers, J. London Math. Soc. (2), 109 (2024). doi:10.1112/jlms.1287
  2. Entropy versus volume via Heegaard diagrams, preprint, 50 pages, 2023: arXiv:2312.14255
  3. On Hempel pairs and Turaev--Viro invariants, preprint, 22 pages, 2023: arXiv:2303.14775
  4. Finite quotients, arithmetic invariants, and hyperbolic volume, Peking Math. J. (2023). doi:10.1007/s42543-023-00077-1
  5. Virtual homological eigenvalues and the Weil--Petersson translation length, Sci. China Math. 66 (2023), no. 9, 2119--2132. doi:10.1007/s11425-022-2051-8
  6. Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups, Invent. Math. 231 (2023), 741--804. doi:10.1007/s00222-022-01155-4
  7. Mapping classes are almost determined by their finite quotient actions, Duke Math. J. 173 (2023), no. 3, 569--631. doi:10.1215/00127094-2022-0047
  8. Virtual homological spectral radii for automorphisms of surfaces, J. Amer. Math. Soc. 33 (2020), no. 4, 1167--1227. doi:10.1090/jams/949
  9. Finiteness of nonzero degree maps between 3-manifolds, J. Topol, 13 (2020), 237--268. doi:10.1112/topo.12125
  10. Joint with Pierre Derbez, Hongbin Sun, and Shicheng Wang, Volume of representations and mapping degree, Adv. Math. 351 (2019), 570--613. doi:10.1016/j.aim.2019.05.015
  11. Immersing quasi-Fuchsian surfaces of odd Euler characteristic in closed hyperbolic 3-manifolds, J. Differ. Geom. 111 (2019), 475--493. doi:10.4310/jdg/1552442607
  12. Joint with Hongbin Sun, Virtual 1-domination of 3-manifolds, Compos. Math. 154 (2018), 621--639. doi:10.1112/S0010437X17007965
  13. Joint with Pierre Derbez, Hongbin Sun, and Shicheng Wang, Positive simplicial volume implies virtually positive Seifert volume for 3-manifolds, Geom. Topol. 21 (2017), no. 5, 3159--3190.  doi: 10.2140/gt.2017.21.3159
  14. Degree of L2--Alexander torsion for 3-manifolds, Invent. Math. 207 (2017), no. 3, 981--1030. doi:10.1007/s00222-016-0680-6
  15. A characterization of virtually embedded subsurfaces in 3-manifolds, Trans. Amer. Math. Soc. 369 (2016), no. 2, 1237--1264. doi:10.1090/tran/6707 [ Erratum ]
  16. Joint with Pierre Derbez and Shicheng Wang, Chern–Simons theory, surface separability, and volumes of 3-manifolds, J. Topol. 8 (2015), no. 4, 933--974. doi:10.1112/jtopol/jtv023
  17. Joint with Vladimir Markovic, Homology of curves and surfaces in closed hyperbolic 3-manifolds, Duke Math. J. 164 (2015), no. 14, 2723--2808. doi:10.1215/00127094-3167744
  18. Joint with Yi Ni, Hongbin Sun, and Shicheng Wang, On slope genera of knotted tori in the 4-space, Pacific J. Math. 261 (2013), no. 1, 117--144. 
  19. Virtual cubulation of nonpositively curved graph manifolds, J. Topol. 6 (2013), no. 4, 793--822. doi:10.1112/jtopol/jtt010
  20. A Jørgensen--Thurston theorem for homomorphisms, Algebr. Geom. Topol. 12 (2012), no. 3, 1301--1311. doi:10.2140/agt.2012.12.1301
  21. Joint with Ian Agol, Presentation length and Simon’s conjecture. J. Amer. Math. Soc. 25 (2012), no. 1, 151--187.;doi:10.1090/S0894-0347-2011-00711-X
  22. Joint with Fan Ding, Shicheng Wang, and Jiangang Yao, Extending Tp automorphisms over Rp+2 and realizing DE attractors, Discrete Contin. Dyn. Syst. 32 (2012), 1639--1655.
  23. Joint with Fan Ding, Shicheng Wang, and Jiangang Yao, Spin structure and codimension-two homeomorphism extensions, Math. Res. Lett. 19 (2012), 345--357.

Survey papers

  1. Surface automorphisms and finite covers. In: International Congress of Mathematicians: July 6–14, 2022, pp. 2792--2805, European Mathematical Society, 2023. doi:10.4171/ICM2022/70
  2. Joint with Hongbin Sun, Toward and after virtual specialization in 3-manifold topology, Surveys in Differential Geometry, 25 (2020), 215--252. doi: 10.4310/SDG.2020.v25.n1.a6
  3. Joint with Hongbin Sun, Toward and after virtual specialization in 3-manifold topology, Surveys in Differential Geometry, 25 (2020), 215--252. doi: 10.4310/SDG.2020.v25.n1.a6
  4. Joint with Vladimir Markovic, Construction of subsurfaces via good pants. In: What's Next? --- the mathematical legacy of William P. Thurston, pp. 233---243, Ann. of Math. Stud., 205, Princeton Univ. Press, Princeton, NJ, 2020. doi: 10.2307/j.ctvthhdvv.13

Talk slides

  1. Separability of surface subgroups for 3–manifold groups, Osaka, January 2016
  2. Bounded quasi-Fuchsian subsurfaces in closed hyperbolic 3-manifolds, Busan, August 2014
  3. A Jorgensen--Thurston theorem for homomorphisms, Houston, March 2011
  4. Presentation length and Simon's conjecture, Hiroshima, January 2011