The mid-prism of a simplex generalises the notion of a midcube. The main focus of my research is hierarchical hyperbolicity of groups, a tool to study groups from a geometric point of view by exploiting patterns of hyperbolic behaviour occurring within them. This tool applies to a wide range of groups, including:

  • right-angled Artin groups, right-angled Coxeter groups and other cubical groups;
  • mapping class groups and Teichmüller space;
  • 3-manifold groups containing no Nil or Sol components;
  • graph products of hyperbolic groups.

Recently I have been using hierarchical hyperbolicity to study graph braid groups. My research statement can be found here.

Publications

  • Hierarchical hyperbolicity of graph products. Joint with Jacob Russell. (2021)
    (to appear in Groups, Geometry, and Dynamics | arXiv)
  • Hierarchical hyperbolicity of graph products and graph braid groups. (2021)
    (PhD thesis, CUNY Graduate Center | pdf)
  • Appendix to Largest acylindrical actions and stability in hierarchically hyperbolic groups. Joint with Jacob Russell. Primary article by Carolyn Abbott, Jason Behrstock, and Matthew Gentry Durham. (2021)
    (Transactions of the American Mathematical Society, Series B, vol. 8, pp. 66–104 | pdf)

Preprints

  • Hierarchical hyperbolicity, relative hyperbolicity, and thickness in graph braid groups.
    (in preparation | N/A)
  • Ideal Theory in Rings (Translation of "Idealtheorie in Ringbereichen" by Emmy Noether). (2014)
    (preprint | arXiv)

Notes and more

  • Slides from my PhD thesis defence.
  • Slides from my graph products talk at the Fall 2020 AMS Sectional Meeting.