I've had the opportunity to work with some incredibly talented students! I have a collection of problems that could be potential REU (research experience for undergraduates) projects, so if you are a math major interested in seeing what actual math research is like, please Contact me. Here are some of my past REU projects:

• Braidings for Non-Split TY categories over R:
  • Mentee: Yoyo Jiang, JHU
  • Co-mentor: David Green, OSU
  • Continuing the investigation of the categories discovered in https://arxiv.org/abs/2303.17843, we follow the outline of Siehler in https://arxiv.org/abs/math/0011037 and classify all possible braidings that these categories can be equipped with. We discover that all possible braidings on real/quaternionic TY categories are necessarily symmetric, and that some real/complex TY categories appear as the Drinfel'd centers of real/quaternionic TY categories.
  • This was part of OSU's Research Opportunities in Mathematics for Underrepresented Students (ROMUS) Program in summer 2023.
• Pointed Fusion Categories Over Non-Algebraically Closed Fields:
  • Mentee: Sophie Zhu, Williamsville East High School (now at Harvard)
  • Co-mentor: Julia Plavnik
  • Slides from Sophie's presentation on the project can be found here
  • Sophie's project won multiple awards at the Regeneron International Science and Engineering Fair!
  • This was through MIT's Primes-USA Program for the year 2022
• Non-Split Tambara-Yamagami Categories Over the Reals:
  • Mentee: Dalton Sconce, IU
  • Co-mentor: Julia Plavnik
  • Current preprint available here
  • In 1998, Daisuke Tambara and Shigeru Yamagami investigated a simple set of fusion rules, and proved under which circumstances those rules could be given a coherent associator. In this project, we are investigating a generalization of such fusion rules to the setting where the simpleobjects are no longer required to be absolutely simple. Over the real numbers, this means that objects are either real, complex or quaternionic.
  • This was through IU's REU Program in summer 2021

• "M018 Lectures: Basic Algebra for Finite Math" This is a series of 66 mini-lectures developed during the covid-19 pandemic to accommodate my students who were learning from home for the first time.