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  1. 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.
  2. Simple groups separated by finiteness properties (with Rachel Skipper and Stefan Witzel)
    Invent. Math. Vol. 215 (2019), No. 2, 713-740. View on arXiv.
  3. 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.
  4. 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. 251, 173-194, Cambridge University Press (2018). View on arXiv.
  5. 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
  6. On normal subgroups of the braided Thompson groups
    Groups Geom. Dyn. Vol. 12 (2018), No. 1, 65-92. View on arXiv.
  7. Symmetric automorphisms of free groups, BNSR-invariants, and finiteness properties
    Michigan Math. J, Vol. 67 (2018), No. 1, 133-158. View on arXiv.
  8. A user's guide to cloning systems
    Topology Proc, Vol. 52, 13-33, 2018. 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.)
  9. 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.
  10. Separation in the BNSR-invariants of the pure braid groups
    Pub. Mat, Vol. 61, No. 2, 337-362, 2017. View on arXiv
  11. On Belk's classifying space for Thompson's group F (with Lucas Sabalka)
    Forum Math, Vol. 29, No. 3, 681-691, 2017. View on arXiv
  12. 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
  13. HNN decompositions of the Lodha-Moore groups, and topological applications
    J. Topol. Anal, Vol. 8, No. 4, 627-653, 2016. View on arXiv
  14. A free subgroup in the image of the 4-strand Burau representation (with Stefan Witzel)
    J. Knot Theory Ramifications, Vol. 24, No. 12, 2015. View on arXiv. (16 pages)
  15. Division algebras and transitivity of group actions on buildings
    Adv. Geom, Vol. 15, No. 2, 133-142, 2015. View on arXiv
  16. Rational homological stability for groups of partially symmetric automorphisms of free groups
    Algebr. Geom. Topol, Vol. 14, 1845-1879, 2014. View on arXiv
  17. A combinatorial proof of the Degree Theorem in Auter space (with Robert McEwen)
    New York J. Math, Vol. 20, 217-228, 2014. View paper
  18. Representatives of elliptic Weyl group elements in algebraic groups
    J. Group Theory, Vol. 17, No. 1, 49-71, 2014. View on arXiv
  19. The Brin-Thompson groups sV are of type F (with Martin Fluch, Marco Marschler and Stefan Witzel)
    Pacific J. Math, Vol. 266, No. 2, 283-295, 2013. View on arXiv
  20. Waffles: Irreducible Representations of Metacyclic Groups (with Andrea Heald and Mark Pearson)
    Pi Mu Epsilon Journal, Issue 13:2, 93-104, 2010. (Undergraduate publication)
  21. Generalized Thue-Morse sequences and the von Koch Curve (with Judy Holdener and Lee Kennard)
    Int. J. Pure Appl. Math., Volume 47, No. 3, 397-403, 2008. View paper. (Undergraduate publication)

    To appear

  1. Almost-automorphisms of trees, cloning systems and finiteness properties (with Rachel Skipper)
    J. Topol. Anal. View on arXiv. (44 pages)
  2. The BNSR-invariants of the Houghton groups, concluded
    Proc. Edinb. Math. Soc. View on arXiv. (11 pages)
  3. The Basilica Thompson group is not finitely presented (with Stefan Witzel)
    Groups Geom. Dyn. View on arXiv. (14 pages)


  1. Equivariant Morse theory on Vietoris-Rips complexes & universal spaces for proper actions (with Marco Varisco)
    View on arXiv. Submitted September 2019. (17 pages)
  2. Bestvina-Brady discrete Morse theory and Vietoris-Rips complexes
    View on arXiv. Submitted January 2019. (21 pages)
  3. Geometric structures related to the braided Thompson groups
    View on arXiv. Submitted March 2018. (25 pages)

    In preparation

    Various projects, in various, ever-changing degrees of preparation/progress. Details gladly available upon request.

    Other work

  1. 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")
  2. 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)
  3. 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)