Projects

These are my projects, both research and personal.

The work I've done below is a mix of mathematics and programming. You can click the names of the projects below to view technical documents or source code when applicable.

• This site: Click here for a development log of this website and to see what sorts of changes have happened over time.
• Khovanov Homology and Quantum Error Correction: This project was done through the Columbia mathematics REU, under Professor Rostislav Akhmechet, and supported by both the math department and the I. I. Rabi Scholars program at Columbia. Khovanov Homology is a powerful invariant in knot theory that categorifies the Jones polynomial of a link diagram, and we used it to investigate families of homological CSS codes arising from quantum error theory.
• Lubin Tate Theory and the Local Kronecker-Weber Theorem: This is an expository paper I wrote on Lubin-Tate formal groups, which provide an elementary way to prove the theorems known as "local class field theory," which are usually proven by using cohomological methods.
• Grid Diagrams of Knots: This is a short expository paper I wrote on the grid diagrams of topological knots, and a simple way to compute the Wirtinger presentation (a presentation of the fundamental group of the knot complement, which is a very strong invariant).
• NASA SPEARS 3D Microscope: This is the abstract for the research I counducted through my internship at NASA Ames. I created a machine-learning based data quality evaluator and am working on segmenting the data into distinct regions. I also reimplemented prototyped MATLAB 3D reconstruction algorithms into performant C++ code for use on embedded hardware. You can read more about the SPEARS 3D microscope project here.
• Deep Learning & Protein Allostery: I did some research at the Glasgow Lab at the Columbia University Medical Center during my freshman year on diffusion models in deep learning for protein allostery. This was funded by the I.I Rabi Scholars Program at Columbia. Attached is my poster that I presented at the Undergraduate Research Symposium at Columbia.
• Young Tableaux, Representation Theory, and Algebraic Flag Varieties: I studied Young Tableaux, a combinatorial object, and their applications to representation theory of the general and special linear groups and some of their applications to flag varities in algebraic geometry. Done through the Directed Reading Program at Columbia. I then gave a talk on the RSK correspondence and its applications.
• Sagashi: This is an in-progress command line utility which provides sentence parsing, dictionary lookup, and Anki (a popular flashcard program) integration for the study of the Japanese language. I've mainly implemented this for myself, as having a CLI utility enables scripting with other handy programs, such as an accessory script I wrote in Python to get text in images via OCR. Perfect for studying any kind of media! Written in C++.
• F(ast)TeX: A lightweight and minimal language-spec and transpiler written around LaTeX to make taking short notes much much faster. By simplifying syntax with user customization, one is able to focus solely on the math (or anything) at hand. Planned support for slides with beamer. Written in C++.
• Partially Ordered Sets (Posets): These are the slides from a talk I gave to high school students on introducing partially ordered sets and associated combinatorial problems with them, including graded posets.