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  1. Von Neumann algebras of Thompson-like groups from cloning systems (with Eli Bashwinger)
    J. Operator Theory. Vol. 89 (2023), No. 1, 23-48. View on arXiv.
  2. Random subcomplexes of finite buildings, and fibering of commutator subgroups of right-angled Coxeter groups (with Eduard Schesler)
    J. Topol. Vol. 16 (2023), No. 1, 20-56. View on arXiv.
  3. The BNSR-invariants of the Lodha--Moore groups, and an exotic simple group of type F (with Yash Lodha)
    Math. Proc. Cambridge Philos. Soc. Vol. 174 (2023), No. 1, 25-48. View on arXiv.
  4. Bestvina-Brady discrete Morse theory and Vietoris-Rips complexes
    Amer. J. Math. Vol. 144 (2022), No. 5, 1177-1200. View on arXiv.
  5. Twisted Brin-Thompson groups (with James Belk)
    Geom. Topol. Vol. 26-3 (2022), 1189-1223. View on arXiv.
  6. Higher connectivity of the Morse complex (with Nicholas A. Scoville)
    Proc. Amer. Math. Soc. Ser. B. Vol. 9 (2022), 135-149. View on arXiv.
  7. Geometric structures related to the braided Thompson groups
    Math. Z. Vol. 300 (2022), No. 3, 2591-2610. View on arXiv.
  8. Equivariant Morse theory on Vietoris-Rips complexes & universal spaces for proper actions (with Marco Varisco)
    Bull. Lond. Math. Soc. Vol. 53 (2021), No. 6, 1724-1739. View on arXiv.
  9. The BNSR-invariants of the Stein group F2,3 (with Robert Spahn)
    J. Group Theory. Vol. 24 (2021), No. 6, 1149-1162. View on arXiv.
  10. Almost-automorphisms of trees, cloning systems and finiteness properties (with Rachel Skipper)
    J. Topol. Anal. Vol. 13 (2021), No. 1, 101-146. View on arXiv.
  11. A short account of why Thompson's group F is of type F
    Topology Proc. Vol. 57 (2021), 77-86. View on arXiv.
  12. The BNSR-invariants of the Houghton groups, concluded
    Proc. Edinb. Math. Soc. Vol. 63 (2020), No. 1, 1-11. View on arXiv.
  13. The Basilica Thompson group is not finitely presented (with Stefan Witzel)
    Groups Geom. Dyn. Vol. 13 (2019), No. 4, 1255-1270. View on arXiv.
  14. Commensurability invariance for abelian splittings of right-angled Artin groups, braid groups and loop braid groups
    Algebr. Geom. Topol. Vol. 19, Issue 3 (2019), 1247-1264. View on arXiv.
  15. Simple groups separated by finiteness properties (with Rachel Skipper and Stefan Witzel)
    Invent. Math. Vol. 215 (2019), No. 2, 713-740. View on arXiv.
  16. Groups of fast homeomorphisms of the interval (with Collin Bleak, Matthew G. Brin, Martin Kassabov, and Justin Tatch Moore)
    J. Comb. Algebra. Vol. 3 (2019), No. 1, 1-40. View on arXiv.
  17. The Σ-invariants of Thompson's group F, via Morse theory (with Stefan Witzel)
    Topological Methods in Group Theory, London Math. Soc. Lecture Note Ser. Vol. 451, 173-194, Cambridge University Press (2018). View on arXiv.
  18. Thompson groups for systems of groups, and their finiteness properties (with Stefan Witzel)
    Groups Geom. Dyn. Vol. 12 (2018), No. 1, 289-358. View on arXiv. See "A user's guide to cloning systems" below for a short note summarizing this long paper
  19. On normal subgroups of the braided Thompson groups
    Groups Geom. Dyn. Vol. 12 (2018), No. 1, 65-92. View on arXiv.
  20. Symmetric automorphisms of free groups, BNSR-invariants, and finiteness properties
    Michigan Math. J. Vol. 67 (2018), No. 1, 133-158. View on arXiv.
  21. A user's guide to cloning systems
    Topology Proc. Vol. 52 (2018), 13-33. View on arXiv. (This is a short expository note summarizing the long paper Thompson groups for systems of groups, and their finiteness properties, listed above.)
  22. On the Σ-invariants of generalized Thompson groups and Houghton groups
    Int. Math. Res. Not. IMRN. Vol. 2017, Issue 19, 5861-5896. View on arXiv.
  23. Separation in the BNSR-invariants of the pure braid groups
    Pub. Mat. Vol. 61 (2017), No. 2, 337-362. View on arXiv
  24. On Belk's classifying space for Thompson's group F (with Lucas Sabalka)
    Forum Math. Vol. 29 (2017), No. 3, 681-691. View on arXiv
  25. The braided Thompson's groups are of type F (with Kai-Uwe Bux, Martin Fluch, Marco Marschler, and Stefan Witzel). With appendix Higher generation for pure braid groups
    J. Reine Angew. Math. (Crelle's Journal). Vol. 2016, Issue 718, 59-101. View on arXiv. View erratum (also in arXiv version).
  26. HNN decompositions of the Lodha-Moore groups, and topological applications
    J. Topol. Anal. Vol. 8 (2016), No. 4, 627-653. View on arXiv
  27. A free subgroup in the image of the 4-strand Burau representation (with Stefan Witzel)
    J. Knot Theory Ramifications. Vol. 24 (2015), No. 12. View on arXiv. (16 pages)
  28. Division algebras and transitivity of group actions on buildings
    Adv. Geom. Vol. 15 (2015), No. 2, 133-142. View on arXiv
  29. Rational homological stability for groups of partially symmetric automorphisms of free groups
    Algebr. Geom. Topol. Vol. 14 (2014), 1845-1879. View on arXiv
  30. A combinatorial proof of the Degree Theorem in Auter space (with Robert McEwen)
    New York J. Math. Vol. 20 (2014), 217-228. View paper
  31. Representatives of elliptic Weyl group elements in algebraic groups
    J. Group Theory. Vol. 17 (2014), No. 1, 49-71. View on arXiv
  32. The Brin-Thompson groups sV are of type F (with Martin Fluch, Marco Marschler, and Stefan Witzel)
    Pacific J. Math. Vol. 266 (2013), No. 2, 283-295. View on arXiv
  33. Waffles: Irreducible Representations of Metacyclic Groups (with Andrea Heald and Mark Pearson)
    Pi Mu Epsilon Journal. Issue 13:2 (2010), 93-104. View paper. (Undergraduate publication)
  34. Generalized Thue-Morse sequences and the von Koch Curve (with Judy Holdener and Lee Kennard)
    Int. J. Pure Appl. Math. Volume 47 (2008), No. 3, 397-403. View paper. (Undergraduate publication)

    To appear

  • Finitely presented left orderable monsters (with Francesco Fournier-Facio and Yash Lodha)
    Ergodic Theory Dynam. Systems View on arXiv. (12 pages)
  • Braiding groups of automorphisms and almost-automorphisms of trees (with Rachel Skipper)
    Canad. J. Math. View on arXiv. (39 pages)
  • Braided Thompson groups with and without quasimorphisms (with Francesco Fournier-Facio and Yash Lodha)
    Algebr. Geom. Topol. View on arXiv. (22 pages)
  • A taste of twisted Brin-Thompson groups
    Sémin. Congr. Conference proceedings for Beyond Hyperbolicity/Charneyfest. View on arXiv. (13 pages)


  • Hyperbolic groups satisfy the Boone-Higman Conjecture (with James Belk, Collin Bleak, and Francesco Matucci)
    View on arXiv. Submitted October 2023. (69 pages)
  • Progress around the Boone-Higman Conjecture (with James Belk, Collin Bleak, and Francesco Matucci)
    View on arXiv. Submitted July 2023. (21 pages)
  • Finitely presented simple groups with at least exponential Dehn function
    View on arXiv. Submitted June 2023. (10 pages)
  • Non-inner amenability of the Higman-Thompson groups (with Eli Bashwinger)
    View on arXiv. Submitted April 2022. (10 pages)
  • Houghton-like groups from "shift-similar" groups (with Brendan Mallery)
    View on arXiv. Submitted February 2022. (32 pages)

    Other work

  • Rational homological stability for groups of symmetric automorphisms of free groups
    View on arXiv. 2012. (Subsumed by "Rational homological stability for groups of partially symmetric automorphisms of free groups")
  • Some reductive anisotropic groups that admit no split spherical BN-pairs (with Peter Abramenko)
    View on arXiv. 2011. Not intended for publication. Our techniques are unique, but the results have since been proved via entirely different methods, in vastly more generality, by Gopal Prasad in "Weakly-split spherical Tits systems in pseudo-reductive groups" (Amer. J. Math. Vol. 136, no.3, 807-832, 2014)
  • Strongly and Weyl transitive group actions on buildings arising from Chevalley groups (with Peter Abramenko)
    View on arXiv. Unpublished preprint.


  • Strong Transitivity and Weyl Transitivity of Group Actions on Affine Buildings, PhD thesis (2011). View
  • Beyond Complex: An Inspection of Quaternions, Kenyon College Senior Thesis (2007; received distinction). (view)