NOTE: This website is unlikely to be updated any more. By August 2013 I should have a website at Binghamton.

Publications

Thompson's groups

• The Brin-Thompson groups sV are of type F_∞ (with Martin Fluch, Marco Schwandt and Stefan Witzel)
  To appear in Pacific J. Math. View on arXiv.
  


• The braided Thompson's groups are of type F_∞ (with Kai-Uwe Bux, Martin Fluch, Marco Schwandt and Stefan Witzel)
  Submitted. View on arXiv.
  


• Higher generation for pure braid groups
  View on arXiv. (This has been added as an appendix to "The braided Thompson's groups are of type F_∞," but they are currently separate on arXiv.)
  


• Classifying spaces for Thompson's group F and braided F (with Lucas Sabalka)
  In preparation.
  


• Splitting and merging circles: A Thompson group for the loop braid groups
  In preparation.
  

Automorphisms of free groups

• Rational homological stability for groups of partially symmetric automorphisms of free groups
  Submitted. View on arXiv.
  


• A combinatorial proof of the Degree Theorem in Auter space (with Robert McEwen)
  Submitted. View on arXiv.
  

Buildings and algebraic groups

• Representatives of elliptic Weyl group elements in algebraic groups
  Submitted. View on arXiv.
  


• Division algebras and transitivity of group actions on buildings
  Submitted. View on arXiv.
  


• Strongly and Weyl transitive group actions on buildings arising from Chevalley groups (with Peter Abramenko)
  In preparation. View on arXiv.
  

Undergraduate papers

• Waffles: Irreducible Representations of Metacyclic Groups (with Andrea Heald and Mark Pearson)
  Appeared in the Pi Mu Epsilon Journal, Issue 13:2, pages 93-104 (Spring 2010).
  


• Generalized Thue-Morse sequences and the von Koch Curve (with Judy Holdener and Lee Kennard)
  Appeared in the International Journal of Pure and Applied Mathematics, Volume 47, No. 3, pages 397-403 (2008).
  View paper.
  

Other work

• Rational homological stability for groups of symmetric automorphisms of free groups
  View on arXiv.
  (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. 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."
  

Theses

• 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)