Research
I am interested in algebraic combinatorics and representation theory.
My thesis work focuses on a special class of semigroups called left regular bands. I specifically like to study the structure of these semigroups under group actions. Left regular bands appear a surprising amount in algebraic combinatorics and have connections with card shuffling and poset topology.
Projects
Spectrum of random-to-random on the Hecke algebra (with Ilani Axelrod-Freed, Sarah Brauner, Judy Chiang, and Veronica Lang)
in preparation
Superspace invariants and hyperpane arrangements (with Robbie Angarone, Trevor Karn, Satoshi Murai, and Brendon Rhoades)
Invariant theory for the face algebra of the braid arrangement
Extended abstract (to appear in FPSAC 2024 proceedings)
Slides from a 20 min talk and a recording from a longer version
Invariant theory for the free left-regular band and a q-analogue (with Sarah Brauner and Vic Reiner)
Journal article (Pacific Journal of Mathematics), arXiv preprint
Extended abstract (FPSAC 2023 proceedings)
As an undergraduate, through REU's and other programs, I was fortunate to have the opportunity to learn about other areas of algebraic combinatorics, knot theory, and theoretical computer science. These projects can be found below.
University of Washington, Bothell Mathematics REU 2017
Hexagonal Mosaic Links Generated by Saturation (with John Bush, Tamara Gomez, and Jennifer McLoud-Mann): journal article (Journal of Knot Theory and its Ramifications).
Undergraduate Research at Carleton College in Computer Science
Summarizing Diverging String Sequences with Applications to Chain-Letter Petitions (with David Liben-Nowell, Tina Liu, and Kiran Tomlinson): conference proceedings (CPM 2020).
University of Minnesota Combinatorics REU 2018:
Recovering Conductances of Resistor Networks in a Punctured Disk (with Yulia Alexandr, Naomi Burks, and Sunita Chepuri): arXiv link.
Deformations of the Weyl Character Formula for SO(2n + 1) via Ice Models (with Yulia Alexandr, Alexandra Embry, Sylvia Frank, Yutong Li, and Alexander Vetter): arXiv link.