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
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Continuous Noncrossing Partitions and the Dual Braid Complex
Preprint, 2024 -
Noncrossing Partition Lattices from Planar Configurations
Preprint, 2023 -
The Polyhedral Tree Complex
Combinatorial Theory, 2022 -
Geometric Combinatorics of Polynomials I: The Case of a Single Polynomial
Journal of Algebra, 2022 -
Critical Points, Critical Values, and a Determinant Identity for Complex Polynomials
Proceedings of the American Mathematical Society, 2020 -
Boundary Braids
Algebraic & Geometric Topology, 2020 -
Undesired Parking Spaces and Contractible Pieces of the Noncrossing Partition Link
Electronic Journal of Combinatorics, 2018 -
A Decomposition of Parking Functions by Undesired Spaces
Electronic Journal of Combinatorics, 2016 -
Hankel Transforms of Linear Combinations of Catalan Numbers
Journal of Integer Sequences, 2011
In Preparation
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Geometric Combinatorics of Polynomials II: The Branched Annulus Complex