My research interests lie primarily in geometric group theory, combinatorics, and topology, with a particular interest in the braid group and its relatives. Some of my recent work has focused on the geometric and combinatorial connections between braids, complex polynomials, and noncrossing partitions. My other interests include Coxeter groups, Artin groups, mapping class groups, and configuration spaces.

Publications and Preprints

  1. Continuous Noncrossing Partitions and the Dual Braid Complex
    (with Jon McCammond)
    Preprint, 2024
  2. Noncrossing Partition Lattices from Planar Configurations
    (with Stella Cohen, Andrew D. Harsh, and Spencer Park Martin)
    Preprint, 2023
  3. The Polyhedral Tree Complex
    Combinatorial Theory, 2022
  4. Geometric Combinatorics of Polynomials I: The Case of a Single Polynomial
    (with Jon McCammond)
    Journal of Algebra, 2022
  5. Critical Points, Critical Values, and a Determinant Identity for Complex Polynomials
    (with Jon McCammond)
    Proceedings of the American Mathematical Society, 2020
  6. Boundary Braids
    (with Jon McCammond and Stefan Witzel)
    Algebraic & Geometric Topology, 2020
  7. Undesired Parking Spaces and Contractible Pieces of the Noncrossing Partition Link
    (with Jon McCammond)
    Electronic Journal of Combinatorics, 2018
  8. A Decomposition of Parking Functions by Undesired Spaces
    (with Melody Bruce, Max Hlavacek, Ryo Kudo, and Ian Nicolas)
    Electronic Journal of Combinatorics, 2016
  9. Hankel Transforms of Linear Combinations of Catalan Numbers
    (with Christopher French, Benjamin Saderholm, and Wenyang Qian)
    Journal of Integer Sequences, 2011

In Preparation

  • Geometric Combinatorics of Polynomials II: The Branched Annulus Complex
    (with Jon McCammond)