Research

I'm mostly interested in geometric group theory and low dimensional topology.

Here are my mathematics papers, organized in mostly chronological order.

Reviews (if your institution has access) of some of these papers can be found at MathSciNet (see also here) or Zentrallblatt MATH.

Published

  1. "Algorithmic detection and description of hyperbolic structures on 3-manifolds with solvable word problem." Geometry & Topology 6 (2002) 1–26. (journal, arXiv)

  2. "Geometry of pseudocharacters." Geometry & Topology 9 (2005) 1147–1185. (journal,arXiv)

  3. (with an appendix by Nicolas Monod and Bertrand Rémy) "Quasi-actions on trees and Property (QFA)."Journal of the London Mathematical Society 73 (2006) 84-108. (journal, arXiv)

  4. (with Daniel Groves) "Fillings, finite generation and direct limits of relatively hyperbolic groups." Groups, Geometry, and Dynamics 1 (2007) 329-342. (journal, arXiv)

  5. "Actions of certain arithmetic groups on Gromov hyperbolic spaces." Algebraic & Geometric Topology 8 (2008) 1371-1402. (journal,arXiv)

  6. (with Daniel Groves) "Dehn filling in relatively hyperbolic groups." Israel Journal of Mathematics 168 (2008) 317–429. (journal, arXiv)

  7. (with Ian Agol and Daniel Groves) "Residual finiteness, QCERF, and fillings of hyperbolic groups." Geometry & Topology 13 (2009) 1043-1073. (journal, arXiv)

  8. (with Eduardo Martínez-Pedroza) "Separation of relatively quasiconvex subgroups." Pacific Journal of Mathematics 244 (2010), no. 2, 309–334. (journal, arXiv)

  9. "Virtually geometric words and Whitehead's algorithm." Mathematical Research Letters 17, no. 5 (2010) pp. 917-925. (journal, arXiv).

  10. (with Koji Fujiwara) "CAT(0) and CAT(-1) fillings of hyperbolic manifolds." Journal of Differential Geometry 85, no. 2 (2010) pp. 229–270 ( journal, arXiv).

  11. (with Koji Fujiwara) "Simplicial volume and fillings of hyperbolic manifolds." Algebraic & Geometric Topology 11, (2011) pp. 2237–2264 (journal, arXiv).

  12. (with Ian Agol and Daniel Groves) "Filling virtually special subgroups." Appendix to "The virtual Haken conjecture" by Ian Agol. Documenta Mathematica 18 (2013) pp. 1045–1087 (journal, arXiv).

  13. (with Daryl Cooper)"Non-faithful representations of surface groups into SL(2,C) which kill no simple closed curve." Geometriae Dedicata 177 (2015), 165–187 (arXiv, journal).

  14. (with Chris Cashen) "Virtual geometricity is rare." LMS Journal of Computation and Mathematics 18 (2015), no. 1, pp. 444-455 (journal, arXiv). The associated code has been moved from Bitbucket to GitHub.

  15. (with Ian Agol and Daniel Groves) "An alternate proof of Wise's Malnormal Special Quotient Theorem." Forum of Mathematics, Pi 4 (2016) e1, 54 pp. (journal, arXiv).

  16. (with Daniel Groves) "Dehn fillings and elementary splittings." Transactions of the American Mathematical Society 370 (2018), 3017-3051. (journal, arXiv, pdf).

  17. (with Alex Lubotzky and Henry Wilton) "Generalized triangle groups, expanders, and a problem of Agol and Wise." Commentarii Mathematici Helvetici 94 (2019), Issue 1, pp. 53-66. (journal, arXiv).

  18. (with Daniel Groves and Alessandro Sisto) "Boundaries of Dehn fillings." Geometry & Topology 23 (2019) 2929-3002 (journal, arXiv, pdf).

  19. (with Oliver Wang) "Cohomology and the Bowditch boundary." Michigan Mathematical Journal 63 (2020), Issue 3, pp. 633-669. (journal, arXiv).

  20. (with Daniel Groves) "Quasiconvexity and Dehn filling." American Journal of Mathematics. 143 (2021), Number 1, pp. 95-124. (journal, pdf updated 2019-10-24, arXiv )

  21. (with Daniel Groves) "Specializing cubulated relatively hyperbolic groups." Journal of Topology. 15 (2022), Issue 2, pp. 398-442. (journal, pdf updated 2022-01-05, arXiv)

  22. (with Daniel Groves) "Special IMM groups." Bull. Lond. Math. Soc. 55 (2023), Issue 2, pp. 717-722. (journal , arXiv)

  23. (with Kathryn Mann) "Stability for hyperbolic groups acting on boundary spheres." Forum Math., Sigma (2023) 11:e83 1-25. (journal, arXiv)

  24. (with Daniel Groves) "Hyperbolic groups acting improperly." Geom. Topol. 27:9 (2023) 3387-3460. (journal, arXiv).

Preprints

(see also the arXiv, though the versions below are sometimes more up to date):

  1. "The Bowditch boundary of (G,H) when G is hyperbolic" (pdf updated 2019-10-24, arXiv).

  2. (with Daniel Groves and Henry Wilton) "Recognizing geometric 3-manifold groups using the word problem." (arXiv).

  3. (with Carolyn Abbott) "Boundaries of coned-off hyperbolic spaces." (arXiv). Note this work is subsumed in the paper "Acylindrically hyperbolic groups and their quasi-isometrically embedded subgroups."

  4. (with Mahan Mj and Michah Sageev) "Tracks and cubulations," appendix to "Cubulating surface-by-free groups" by Mahan Mj (arXiv).

  5. (with Carolyn Abbott) "Acylindrically hyperbolic groups and their quasi-isometrically embedded subgroups." To appear in Michigan Mathematical Journal. (pdf updated 2022-08-08, arXiv)

  6. (with Kathryn Mann and Theodore Weisman) "Stability of hyperbolic groups acting on their boundaries." (arXiv)

  7. (with Daniel Groves) "A criterion for residual finiteness," appendix to "Relative cubulation of relative strict hyperbolization" by J.-F. Lafont and L. Ruffoni. (arXiv)

Other

You may also be interested in these (incomplete) draft notes entitled Cubulating spaces and groups, last updated 2024-02-23.

More information

My Google Scholar profile.

My current research is supported in part by the Simons Foundation, under Collaboration Grants 942496 and 524176.

Last modified 2024-02-23