Research

My research is in geometric group theory. I am mainly interested in the theory of groups acting on CAT(0) cube complexes. Here are some of my papers:

  • Relatively Geometric Cubulations of Small Cancellation Free Products, with Thomas Ng. Preprint.
  • Separation and Relative Quasiconvexity Criteria for Relatively Geometric Actions, with Daniel Groves and Thomas Ng. arXiv.
  • Relatively geometric actions on CAT(0) cube complexes, with Daniel Groves. To appear in J. Lond. Math Soc. (Accepted 9/23/21). arXiv.
  • Relative cubulations and groups with a 2-sphere boundary, with Daniel Groves. Published 2020 in Compositio Mathematica. Journal. arXiv.
  • Hierarchies for Relatively Hyperbolic Virtually Special Groups. Submitted. arXiv.
  • Taming the Hydra: the word problem and extreme integer compression, with Will Dison and Tim Riley. Published 2018 in International Journal of Algebra and Computation. DOI, arXiv paper
  • Ackermannian integer compression and the word problem for hydra groups, with Will Dison and Tim Riley. Version of the above submitted to a computer science conference. Published in LIPIcs. Leibniz International Proceedings in Informatics (2016). MR Link.
  • The ratio field of values, with Charles Johnson, Brian Lins and Ilya Spitkovsky. Published 2011 in Linear Algebra and its Applications. MR link.