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I am a sixth-year Ph.D. student at Columbia working with Prof. Mikhail Khovanov and Prof. Joshua Sussan. I intend to graduate in May 2027. I'm broadly interested in representation theory, categorification, and anything relating to highest-weight/stratified structures. More specifically I do diagrammatic algebra and categorification, and in particular I am very interested in the representation theory of various diagrammatic algebras. For example, one long-term research program I have is to search for BGG resolutions over various algebras in categorification by using Koszul theory. It seems there are quite a few algebras appearing in nature (categorification) which are ``nil-Koszul'' (meaning that a ``half'' of the algebra is Koszul), and I intend to study more of them in the future. These days I am thinking about some coherent geometry related to KLR algebras.
I will be on the job market in Fall 2026.
I'm also something of an expert on pneumothoraces (lung collapses).
As a matter of principle I would like to make it public that I think Trump has and is continuing to run this country into the ground. Columbia will be remembered for its weakness during this era.
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.
(5) The coherent KLR sheaf. Joint work with Matthew Hase-Liu, to appear on arXiv in a few hours. This paper constructs the KLR algebras of type A as affine sections of a coherent sheaf on a projective space, thereby geometrically explaining the sl2-actions of Elias-Qi. We anticipate many sequels.
(4) Even and odd minimal categorifications of the nilpotent part of classical and quantum sl(2). Joint work with Mikhail Khovanov and Alvaro L. Martinez. This paper studies minimal/semisimple categorifications of U_q^+(sl_2) and is part of a broader hope to obtain semisimple categorifications.
(3) BGG resolutions, Koszulity, and stratifications, part II: the Jacobi-Trudi algebra. This is the second paper in this series. This paper categorifies the Jacobi-Trudi determinant formula by considering some special quasihereditary quotient of KLR. It turns out these JT algebras, as well as the Soergel calculi to which they are Morita equivalent, are all nil-Koszul, and Koszul duality with respect to the nilalgebra recovers BGG.
(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.
For those interested, here is a short summary of each of my papers. This is likely only useful for people in my field or adjacent fields.
There are some short notes/blurbs which would not make sense as submissions to arXiv, but which are interesting enough that I'd like to have them online. These I place here.
(2) Categorifying Jacobi-Trudi: a phenomenon in rank 1. This was meant as an appendix to the paper on categorifying the Jacobi-Trudi determinant formula. It now serves best as a sales pitch for that paper.
(1) Undergrad senior thesis. This was my undergraduate thesis, advised by Prof. Dennis Gaitsgory and Charles Fu. The first half is an exposition on the BGG resolution in category O and the second half is an alternative approach detailed to me by my advisor(s); this was where I learned the reconstruction-from-stratification idea. I have since learned about a paper by Gurbir Dhillon at this link.
In Fall of 2026, I am co-organizing the Representation Theory, Categorification, and Geometry seminar, website here.
In Spring of 2026, I co-organized the Representation Theory and Categorification seminar, renamed again to "Quantum Invariants of Links", website here.
In Fall of 2025, I co-organized the Representation Theory and Categorification seminar, renamed this semester to "Quantum Invariants of Links", website here.
In Spring of 2025, I co-organized the Representation Theory and Categorification seminar, website here.
In Fall of 2024, I co-organized 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 will give a talk at the AMS Fall Eastern Sectional conference at George Washington University in October 2026. The talk will be on my recent preprint with Matthew Hase-Liu on the coherent KLR sheaf.
I gave a talk at the 16th Southeastern Lie Theory conference at the University of Virginia in July 2026. The talk was on the same topic from a year prior, but the focus has been shifted to Koszul duality; the slides can be found here.
I gave a talk at the 2026 Beijing-Shanghai summer school at the Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS) in June 2026; I was also a copilot/TA for Mikhail Khovanov's minicourse on categorification there. The chalk talk was about categorifying Jacobi-Trudi; the video can be found here.
I gave a talk at the Combinatorics Seminar at UCLA in January 2026. The talk was about categorifying Jacobi-Trudi. There are no slides because it was a board talk.
I gave a talk at the KIAS Geometry, Algebra, and Physics conference in Seoul in January 2026. The talk was about Koszul duality and Jacobi-Trudi. The original slides can be found here. If you prefer a smaller file with no pauses, see here.
I gave a talk at the Topology Seminar at JHU in November 2025. The talk was about categorifying Jacobi-Trudi.
I gave a talk at the 15th Southeastern Lie Theory conference at Charleston (SC) in May 2025. The slides are more or less the same as those from the AMS Spring Sectional a month earlier, but they can be found here.
I gave a talk at the AMS Spring Eastern Sectional conference at Hartford (CT) in April 2025. The Jacobi-Trudi slides can be found here.
I gave another talk at the AMS Spring Eastern Sectional conference at Hartford (CT) in April 2025. The nil-Brauer slides can be found here.
I gave a talk at the Knots In Washington 50 conference at George Washington University in December 2024. The slides are essentially the same as those from the May 2024 AMS talk, except with a few more slides about categorifying Jacobi-Trudi via KLR.
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.
I have a couple of projects I am working on, and I'm pretty behind on writing things up. Here are a couple of the forthcoming works:
(6) "Categorifications of Hermite polynomials", joint work in progress with Mikhail Khovanov and Radmila Sazdanovic. In my mind, this paper is part 1.5 in terms of the Koszul trick.
In Spring of 2026, I was TAing Linear Algebra.
In Fall of 2025, I taught Math 3951, Undergraduate Seminar. The title of the class was ``Diagrammatic Algebra'', and the website is here.
In Spring of 2025, I was TAing Calculus IV (again).
In Fall of 2024, I was TAing Calculus IV.
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 was ``Topics in Representation Theory'', and the website is here.
I'm also interested in classical Chinese, e.g. poetry. More here.
Last updated: 09/10/26