Research

Geometric Group Theory

       For a non-technical audience: My current research uses hyperbolic geometry to study algebra. Hyperbolic geometry is the study of geometric spaces of negative curvature. Think of a space with negative curvature like a giant infinitely curly kale leaf. I study the symmetries of such spaces and use these geometric techniques to solve traditionally algebraic problems. 

Here is an article about closely related research aimed at a non-technical audience. Here is a nice video introduction to my field (Credit: 3Blue1Brown). 

    For my fellow mathematicians: I am a geometric group theorist, meaning I use techniques from hyperbolic geometry to study infinite but finitely presented groups.  I study Artin groups, a vast generalization of braid groups, which provide a rich field of examples and counterexamples for many geometric, topological, and algebraic properties. My methods are chiefly geometric, using CAT(0) cube complexes and the action of an Artin group on these cube complexes. 

Recent Papers

1. R. Boyd, R. Charney, R. Morris-Wright, and S. Rees, The Artin Monoid Cayley Graph. to appear in Journal of Computational Algebra. ArXiv Link 

2. R. Blasco, M. Cumplido, and R. Morris-Wright, A Solution to the Word Problem for 3-free Artin Groups in Quadratic Time. Pre-print.  April 2022. ArXiv link 

3. R. Boyd, R. Charney, and R. Morris-Wright, A Deligne Complex for Artin Monoids. Journal of Algebra: Special Edition in Memory of Patrick Dehorney, 2021. ArXiv link 

4. Dissertation: Geometric Structures on Infinite Type Artin groups. Click here for the abstract.

5. R. Morris-Wright, Parabolic Subgroups of FC-Type Artin groups. Journal of Pure and Applied Algebra, 2020. ArXiv link 

6. R. Charney and R. Morris-Wright, Artin groups of infinite type: trivial centers and acylindrical hyperbolicity.  Proceedings of the  AMS. 2019. ArXiv link. 

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