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:

• Invariant theory for the face algebra of the braid arrangement

  • arXiv preprint, 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, arXiv preprint, FPSAC 2023 proceedings

  • Slides and a recording of an earlier version of this talk

  • 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.

• 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.

• University of Minnesota Combinatorics REU 2018:

Recovering Conductances of Resistor Networks in a Punctured Disk (with Yulia Alexandr, B 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.