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  1. 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.

  2. 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 below.)

  3. Separation in the BNSR-invariants of the pure braid groups
    Pub. Mat, Vol. 61, No. 2, 337-362, 2017. View on arXiv

  4. 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

  5. HNN decompositions of the Lodha-Moore groups, and topological applications
    J. Topol. Anal, Vol. 8, No. 4, 627-653, 2016. View on arXiv

  6. 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

  7. 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)

  8. Division algebras and transitivity of group actions on buildings
    Adv. Geom, Vol. 15, No. 2, 133-142, 2015. View on arXiv

  9. Rational homological stability for groups of partially symmetric automorphisms of free groups
    Algebr. Geom. Topol, Vol. 14, 1845-1879, 2014. View on arXiv

  10. A combinatorial proof of the Degree Theorem in Auter space (with Robert McEwen)
    New York J. Math, Vol. 20, 217-228, 2014. View paper

  11. Representatives of elliptic Weyl group elements in algebraic groups
    J. Group Theory, Vol. 17, No. 1, 49-71, 2014. View on arXiv

  12. 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

  13. Waffles: Irreducible Representations of Metacyclic Groups (with Andrea Heald and Mark Pearson)
    Pi Mu Epsilon Journal, Issue 13:2, 93-104, 2010. (Undergraduate publication)

  14. 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. Symmetric automorphisms of free groups, BNSR-invariants, and finiteness properties
    To appear, Michigan Math. J. View on arXiv. (25 pages)

  2. The Σ-invariants of Thompson's group F, via Morse theory (with Stefan Witzel)
    To appear, proceedings of Topological Methods in Group Theory: A conference in honor of Ross Geoghegan's 70th birthday, London Math. Soc. Lecture Note Ser. View on arXiv. (17 pages)

  3. Thompson groups for systems of groups, and their finiteness properties (with Stefan Witzel)
    To appear, Groups Geom. Dyn. View on arXiv. (50 pages.) See "A user's guide to cloning systems" above for a short note summarizing this long paper


  1. Almost-automorphisms of trees, cloning systems and finiteness properties (with Rachel Skipper)
    View on arXiv. Submitted October 2017. (44 pages)

  2. Commensurability invariance for abelian splittings of right-angled Artin groups, braid groups and loop braid groups
    View on arXiv. Submitted August 2017. (14 pages)

  3. Groups of fast homeomorphisms of the interval (with Collin Bleak, Matthew G. Brin, Martin Kassabov and Justin Tatch Moore)
    View on arXiv. Submitted January 2017. (32 pages)

  4. The Basilica Thompson group is not finitely presented (with Stefan Witzel)
    View on arXiv. Submitted March 2016. (14 pages)

  5. On normal subgroups of the braided Thompson groups
    View on arXiv. Submitted April 2014. (21 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)


  • 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)