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Summary and Selected Papers

My research is in algebraic combinatorics, centered around reflection, braid, and Lie groups. I have been very fortunate to have had many brilliant collaborators, with whom I have written some very nice papers. Here are a few of my favorites:


Promotion and Rowmotion unifies various results in what J. Propp calls "Dynamical Algebraic Combinatorics" (with J. Striker). Later related work includes Rowmotion in Slow Motion and Independence Posets (with H. Thomas)
Doppelgängers uses K-theoretic jeu-de-taquin to give an explicit bijection between plane partitions in a rectangle and plane partitions in a trapezoid
(with Z. Hamaker, R. Patrias, and O. Pechenik)
Sweeping up Zeta inverts D. Armstrong, N. Loehr, and G. Warrington's sweep map, with applications to (q,t)-combinatorics. Inverting sweep is unexpectedly equivalent to a different problem that Hugh and I solved in 2012.
(with H. Thomas)
Cataland: Why the Fuss? is a 132-page monograph that extends N. Reading's Coxeter-sortable elements and the cluster complex to the positive braid monoid---very much in the spirit of completing D. Armstrong's generalization of noncrossing partitions
(with C. Stump and H. Thomas)

Rational Noncrossing Catalan Combinatorics is a 42-page preprint that gives the first uniform construction of rational noncrossing Catalan objects and the first uniform enumeration of noncrossing objects
(with P. Galashin, T. Lam, and M.-T. Trinh)

Papers and Preprints

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Selected Recorded Talks

Recording Event/Slides Year
Rational Noncrossing Catalan Combinatorics
OPAC
2022
Semidistrim Lattices
BIRS
2021
Strange Expectations
UCLA Combinatorics Seminar
2020
Independence Posets
Triangle Lectures in Combinatorics
2020

Selected Posters

Poster Event Year
Strange Checkspectations
FPSAC
2021
Independence Posets
FPSAC
2020