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I'm currently a fourth-year Ph.D. student at Columbia working with Prof. Mikhail Khovanov and Prof. Joshua Sussan. I'm broadly interested in representation theory and categorification, and more specifically anything related to highest-weight/stratified structures. I am also interested in foams/diagrammatics from the representation theory side, especially the representation theory of diagrammatic algebras/path algebras. One of the things I am currently thinking about is a stratification of appropriate blocks of certain cyclotomic KLR algebras. After translating to the Hecke side via Brundan-Kleshchev, this is supposed to categorify Jacobi-Trudi.
I don't have many papers yet, so I suppose the order in which I list them does not matter so much. I'll list them in reverse chronological order.
(2) BGG Resolutions, Koszulity, and Stratifications, Part I: the nilBrauer Algebra. The paper is ambitiously named in anticipation of sequels. EDIT: I am currently in the process of (procrastinating on) replacing this paper with a significantly updated version, in which I give more context/history on previous work in the circle of triangular-based algebras and give some additional results/points of view. The first sequel will be about KLR and Jacobi-Trudi.
(1) On Eventually Periodic Sets as Minimal Additive Complements, published in Volume 30, Issue 4 (2023) of Electronic Journal of Combinatorics. This work was done in the COVID summer of 2020 at the (online) Duluth REU.
In Fall of 2024, I am co-organizing the Representation Theory and Categorification seminar, website here.
In Spring of 2024, I co-organized the Representation Theory and Categorification seminar, website here.
In Fall of 2023, I co-organized the Representation Theory and Categorification seminar, website here. I have pretended to live-TeX notes here
In Fall of 2022, I co-organized the joint Yale-Columbia representation theory seminar, website here.
In Spring of 2022, I co-organized the "GeometRic sEquel to lAst semesTer's inFormal categOry O graD seminar" (this is the actual name), website here. Patrick Lei had been very kind to live-TeX notes here.
In Fall of 2021, I co-organized the "inFormal categOry O graDuate seminar" (this is the actual name), website here. Patrick Lei had been very kind to live-TeX notes here.
I also attend some other seminars, some of which I give talks in, e.g. the Lie superalgebras seminar in Spring of 2023.
I gave a talk at the CUNY combinatorics seminar in September 2024, and a recording of the talk can be found here. The talk is about forthcoming work on categorifying Jacobi-Trudi via KLR.
I had a poster at the Canada-Mexico-USA representation theory conference in Mexico City in June 2024, and the poster can be found here. This is probably the most concise portrayal of that paper.
I gave a talk at the diagrammatic algebra special session at the AMS Sectional in California in May 2024, and the slides can be found here. I am also to give (a truncated version of) this talk at the Nakano birthday conference in Georgia, but the slides will remain almost unchanged.
I've written various sets of notes on various topics of various quality (they tend to be worse rather than better) throughout the last few years. Here are a couple that might be of limited use/interest to people.
Short notes on some basics for representations of Lie superalgebras.
Extremely short notes on some extremely basic basics of degenerate affine Hecke algebras.
Longer notes on the BGG resolution. This was my undergraduate thesis, advised by Prof. Dennis Gaitsgory and Charles Fu. The first half is an exposition on the BGG resolution and the second half is an alternative approach detailed to me by my advisor(s). I have since learned about a paper by Gurbir Dhillon at this link.
Here's a couple that might be of especially limited use.
Short note about combinatorial species. This is a subject dear to my heart but these notes were written early on in undergrad so they're probably not very good.
Short notes on quantum Schubert polynomials. I was recently reminded of the existence of these notes and had to reference them; for this reason I am uploading them. They were written during COVID in my junior year, so they are also not very good.
In Spring of 2024, I was teaching Math 1102, Calculus II.
In Fall of 2023, I was TAing Math 2030, Ordinary Differential Equations.
In Spring of 2023, I was TAing Math 3020, Number Theory and Cryptography. The website is here.
In Fall of 2022, I was teaching Math 3951, Undergraduate Seminar. The title of the class is ``Topics in Representation Theory'', and the website is here.
I'm also interested in classical Chinese, e.g. poetry. More here.
Last updated: 10/02/24