Research

My research is in algebraic combinatorics.

I am interested in the intersection of algebraic combinatorics with representation theory, algebraic topology, algebraic geometry and probability. Some keywords of interest:

Representation theory and combinatorics of the symmetric group, Coxeter groups, and Hecke algebras
Hyperplane arrangements and matroids
Configuration spaces and their cohomology
Monoid and semigroup algebras, such as left regular bands
Random walks on permutations and generalizations

Papers and related talks

In preparation

Configuration spaces and peak representations (manuscript available upon request)

With Marcelo Aguiar and Vic Reiner

an extended abstract on this paper has been accepted to the FPSAC 2024 proceedings
Slides from a 50 minute talk on this paper

Preprints

Spectrum of random-to-random in the Hecke algebra

With Ilani Axelrod-Freed, Judy Chiang, Patty Commins, and Veronica Lang

Video of a 20 minute talk I gave on this paper at IPAM's Integrability and Algebraic Combinatorics Workshop
Slides and video for 25 minute talk I gave on this paper at ALCoVE 2024
Slides for a 50 minute talk I gave on this paper at VI Canada-Mexico-US meeting on Representation Theory, Noncommutative Algebra, and Categorification

Wondertopes, submitted.

With Chris Eur, Lizzie Pratt, and Raluca Vlad

A three-regime theorem for flow-firing, submitted.

With Galen Dorpalen-Barry, Selvi Kara, Carly Klivans, and Lisa Schneider

Slides from a talk on this paper at the JMM Special Session on Research Communities in Algebraic Combinatorics in Boston, MA in January 2023.

Publications

Left regular bands of groups and the Mantaci-Reutenauer algebra, Journal of Algebra (2024) Vol. 655, pg 29-94.

With Jose Bastidas and Franco Saliola

ArXiv preprint
Slides from a talk Franco gave on this paper at the MSU Combinatorics seminar

Invariant theory of the free left regular band and a q-analogue, Pacific Journal of Mathematics (2023) 322-2, 251--280.

With Patty Commins and Vic Reiner

ArXiv preprint
An extended abstract based on this paper was accepted to FPSAC 2023 as a poster.
Slides from a talk Vic gave on this paper
Slides from a talk Patty gave on this paper
Slides from a talk I gave on this paper (and extensions!)

A Type B analog of the Whitehouse representations, Mathematische Zeitschrift (2023), 303(3), 58.

ArXiv preprint
An extended abstract of this paper was accepted to FPSAC 2022 as a talk.
Slides from my talk at FPSAC 2022, and the recording of the talk.
Slides from a 50-minute version of the talk

Eulerian representations for real reflection groups, Journal of the London Mathematical Society (2022), 105(1): 412-444.

ArXiv preprint
An extended abstract of this paper was accepted to FPSAC 2021 as a talk, and awarded the Best Student Paper Award!
Slides from my talk at FPSAC 2021, and the recording of the talk.
Slides from a 50-minute version of the talk

Enumerating linear systems on graphs, Mathematische Zeitschrift (2020), 296(3): 1101-1134.

With Forrest Glebe and David Perkinson

ArXiv preprint
An extended abstract of this paper was accepted to FPSAC 2019 as a poster
Slides from a talk on this paper at the AMS Special Session on Combinatorial Algebraic Geometry at University of Wisconsin, Madison in September 2019.

A simplified presentation of Specht modules, Journal of Pure and Applied Algebra (2022), 226(7).

With Tamar Friedmann

ArXiv preprint
Slides from a talk on this paper at the AMS Special Session on Combinatorics in Algebra and Algebraic Geometry at University of Michigan, October 2018.

A workshop to build community and broaden participation in mathematics: reflections on the Mathematics Project at Minnesota, PRIMUS (2022) 32:6, 738-754

With Esther Banaian, Harini Chandramouli, Kim Klinger-Logan, Alice Nadeau, and McCleary Philbin.

Preprint of the paper
A recording of a talk Esther, McCleary and I gave about MPM
An article about MPM written by the UMN Department of Mathematics