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.
Preprints
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Noncrossing Partitions from Cones and Semicircles
Preprint, 2025 -
Geometric Combinatorics of Polynomials II: Polynomials and Cell Structures
Preprint, 2024 -
Continuous Noncrossing Partitions and Weighted Circular Factorizations
Preprint, 2024
Publications
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Noncrossing Partition Lattices from Planar Configurations
Discrete & Computational Geometry, 2024 -
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