I'm a senior at Harvard studying mathematics. I'm particularly interested in low-dimensional topology and symplectic geometry. Last summer, I researched a divide-and-conquer algorithm for computing the Khovanov homology of knots in RP3 with Ciprian Manolescu. This summer, I will conduct independent research on how one's health and wellness improves when one absorbs adequate sunlight and sleeps adequate sleep. Check out my resume here. (It is somewhat out of date, but I see no reason to update everyone on exactly how much my GPA has decreased.)
In fall 2025, I will be enrolling in a PhD program. If any school would like to recruit me to their PhD program, do let me know. Despite being a very successful athlete in my youth (and having, as Kendall Jenner once said, "over the normal limit of athleticness"), I have shockingly never had the pleasure of being recruited.
In my free time, I like doing the crossword, talking about poems, pretending to read more poems than I do, and drinking smoothies. Please send me smoothie recommendations. I am in desperate need.
In summer 2024, I worked with Ciprian Manolescu to find an efficient algorithm to compute the Khovanov homology of class-1 knots in RP3. The algorithm mimics Bar-Natan's tangle-theoretic algorithm, but uses the TQFT for RP3, as defined by Manolescu and Willis, rather than the standard Khovanov TQFT.
In summer 2023, I worked with Peter Kronheimer on understanding higher differentials in the Lee spectral sequence. I showed that the map taking a knot K to the n-th page of its Lee spectral sequence is functorial. One consequence is that the Lee spectral sequence of a band sum decomposes quite nicely. I presented this research at the Joint Mathematics Meetings in 2024.
An ardent Googler may also discover that I have a preprint on tight contact structures. Unfortunately, Lemma 3.4 from that preprint is utterly false. The closed form formula is probably still true though, based on computations using Honda's algorithm for tight contact structures. I sadly cannot offer much more information than that. I still have dreams of fixing this proof.
There is also a paper on regular matroids which has my name on it. I am sorry to say that I no longer know what a matroid is, nor what makes one regular. Please do not talk to me about this paper. It only reminds me of all the knowledge I've lost.
I am currently writing a senior thesis with Denis Auroux on bordered Heegaard Floer homology, with a particular emphasis on proving compactness results typically relegated to symplectic field theory texts. I will discuss Lipshitz's cylindrical reformulation of Heegaard Floer homology along the way.
I have published an expository paper on elliptic bootstrapping and the nonlinear Cauchy-Riemann operator. It is called, incredibly enough, "Elliptic bootstrapping and the nonlinear Cauchy-Riemann operator." It assumes relatively little background, mostly because I had incredibly little background myself when writing this.
I also have a short paper on Khovanov homology and Lee homology, as well as an even shorter paper on the relationship between knot Floer homology and grid homology. These were both written for classes. I have written other papers for math classes, but they are all so awful that I refuse to share them.
I have solutions to (most of) the first two parts of Bott and Tu's Differential Forms in Algebraic Topology. I'm not sure if I'll ever get around to typing the rest, but I'm sure solutions are all available if you Google intently enough.
I also have written up solutions to Rotman's Introduction to Algebraic Topology. It's missing Chapter 12 (on cohomology), and will definitely never be updated, because I am lazy.
