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
The q-deformed random-to-random family in the Hecke algebra (with Sarah Brauner, Darij Grinberg, and Franco Saliola)
Spectrum of random-to-random shuffling in the Hecke algebra (with Ilani Axelrod-Freed, Sarah Brauner, Judy Hsin-Hui Chiang, and Veronica Lang)
Superspace coinvariants and hyperplane arrangements (with Robbie Angarone, Trevor Karn, Satoshi Murai, and Brendon Rhoades)
To appear in Advances in Mathematics
Invariant theory for the face algebra of the braid arrangement
To appear in Algebraic Combinatorics
Extended abstract (FPSAC 2024 proceedings)
Invariant theory for the free left-regular band and a q-analogue (with Sarah Brauner and Vic Reiner)
Journal article (Pacific Journal of Mathematics)
Extended abstract (FPSAC 2023 proceedings)
Slides and a recording of an earlier version of this talk, and a Poster
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.