Projects
Directed Reading Program (UMN)
Fall 2024
After being a mentee in my undergrad, I had the opportunity to mentor one student through their reading of [B&D]. I found our discussions of manifolds and Lie theory to be extremely rewarding. Throughout the program, we made an effort to reinterpret elements of this theory categorically, i.e., in terms of categories, functors, natural transformations, etc. Out of this program came the following exposition: Clarifying The Tangent Space.
Manifold Institute
Summer 2024
An attempt at bringing advanced mathematics to a wider audience. This program did not run in 2024, but there is hope for subsequent summers.
Directed Reading Program (McGill)
Spring 2024
This program pairs undergraduates with graduate mentors for a semester-long investigation into a chosen topic. This semester, I have been paired with Alexis Leroux-Lapierre to study categorification—the process of instantiating an algebraic structure in the rich environment of category theory. We began with Alexis presenting a crash course on the relevant ideas in categorification following [Savage]. We are now working on an approachable exposition particularly focussing on the categorification of the Hopf \& Heisenberg algebras of Sym, and the corresponding Fock space representation.
Fibrations Podcast
Fall 2022 - Summer 2023
The idea stemmed from my own curiosity regarding both the content and process of academic research. As an undergraduate student dreaming of a future in mathematical research, I often found myself on the websites of various McGill departments reading through the current work being done. I was surprised by the vast number of unique subfields, each professor with their own questions and methods of investigation. Naturally, much of language used was unkown to me, especially as I ventured outside of mathematics and physics into the realms of neuroscience, computer science, philosophy, etc. I became very interested in first deciphering this cryptic academic code and second, understanding why professors chose these seemingly arbitrary, niche questions. These two queries, along with a desire to share the answers with my fellow undergraduates, were exactly the seeds for Fibrations.
Over the course of the fall 2022 semester, I sent out over ninety emails to McGill Professors resulting in a mere five recordings—Interesting to consider why more professors weren’t interested. The first episode was released in December 2022 and after an interim abroad, I returned to Montreal in September 2023 where I proceeded to release the remaining four. An important remark is that without the help of a great friend, Elliott Dwyer, the podcast would be far less rich for he pioneered the theme song in which I contributed only to the drums :)
Lecture On Lie Theory
June 2023
A Qualitative Introduction To Lie Theory (with applications to quantum physics)
A month into my semester abroad in Prague, my friend informed me that a course she was taking, Advanced Concepts in Symmetry (a physics course), was one that I would really love. I reached out to the Professor and ultimately participated in the course, without credit, for the remainder of the semester. The course lived up to its title and by the last few lectures, my friend and I were completely lost in an unfamiliar world of gauge theory. The final assessment was to present a lecture on symmetry in physics. Considering we had been dancing around Lie Theory for the last month, I decided to enlighten my physics-minded classmates with a proper mathematical introduction to the topic.
25-Hour Physics Hackathon
October 2022
Certainly a period of great bonding and learning, but I do remember feeling tired for five days after this competition. Nonetheless, it was a semi-rewarding, messy, thrilling journey that I would probably venture into again.