My research focuses on non-positive curvature in groups. I am especially interested in groups acting on cube complexes, as well as hierarchical hyperbolicity, which is 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 fundamental groups of special cube complexes;
  • mapping class groups and Teichmüller space;
  • 3-manifold groups containing no Nil or Sol components;
  • graph products of hyperbolic groups;
  • braid groups.

Recently, I have been studying random quotients of hierarchically hyperbolic groups and using cube complexes to study non-positive curvature in graph braid groups. I am also working on writing code to implement algorithms detailed in my paper on graph braid groups. For example, I have written a programme that computes free splittings of graph braid groups and, joint with Tomasz Maciazek, a programme that computes presentations of graph braid groups.

A copy of my research statement is available here.


  1. Graph of groups decompositions of graph braid groups
    Daniel Berlyne
    International Journal of Algebra and Computation, 2023
    (To appear)
  2. Random quotients of hierarchically hyperbolic groups
    Carolyn AbbottDaniel BerlyneThomas Ng, and Alexander Rasmussen
    In preparation, 2023


  1. Hierarchical hyperbolicity of graph products
    Daniel Berlyne, and Jacob Russell
    Groups, Geometry, and Dynamics, 2022


  1. Appendix to “Largest acylindrical actions and stability in hierarchically hyperbolic groups”
    Daniel Berlyne, and Jacob Russell
    Transactions of the American Mathematical Society, Series B, 2021
    Primary article by C. Abbott, J. Behrstock, and M. G. Durham
  2. Hierarchical hyperbolicity of graph products and graph braid groups
    Daniel Berlyne
    CUNY Academic Works, 2021
    Ph.D. thesis, City University of New York


  1. Teichmüller’s theorem and its applications
    Daniel Berlyne
    University of Warwick, 2015
    Master’s thesis


  1. Ideal Theory in Rings (Translation of “Idealtheorie in Ringbereichen” by Emmy Noether)
    Daniel Berlyne
    arXiv, 2014