Below are some Math things I have (co-)written:

  1. Behavior of Infinitely Wide Neural Networks [link]
    • I discuss the neural tangent kernel, some RKHS theory, and what happens during initialization and throughout gradient descent for infinitely wide neural networks.
    • Work done as the final project for MATH 35607: Introduction to Machine Learning, November 2025.
  2. Ratatouille: RL for Micromouse [link]
    • This one is not really mathy, but I design an environment to make it conducive for an agent to learn the Micromouse task (which I do in real life!).
    • Work done as the final project for TTIC 31170: Robot Estimation and Learning, May 2025.
  3. Strong Law of Large Numbers and Kingman’s Subadditive Ergodic Theorem [link]
    • I approach the Strong Law of Large Numbers from the ergodic point of view, which is really interesting (and becomes perhaps more obvious). Plus Kingman’s Theorem, which is helpful in the case when “addition” is not commutative.
    • Work done as the final project for MATH 27600: Dynamical Systems, March 2025.
  4. Elliptic Functions and Plane Cubics [link]
    • I discuss this mysteriously fancy-sounding object called “elliptic functions”, and reveal that the plane cubics they induce admit a certain additive structure, which can be seen by just drawing straight (tangent) lines.
    • Work done as the final project for MATH 27000: Complex Analysis, May 2024.
  5. Risk-averse Dynamic Programming for Tree-based Controlled Markov Decision Processes [link]
    • With Cole Franklin, Denisse Garnica and Benjamin May. With guidance from Prof. Sebastian Jaimungal and Prof. Piotr Zwiernik.
    • We generalize a technique on using dynamic programming to minimize convex dynamic risk measures on controlled MDPs, from the sequential case to the tree-based case.
    • We also illustrate certain difficulties when generalizing this further to a DAG-based process.
    • Work done during the Fields Undergraduate Summer Research Program 2024, August 2024.
  6. Harmony in Randomness: the Laplacian and the Heat Equation[link]
    • With guidance from Prof. Beniada Shabani.
    • I discuss the heat equation, the analytical way to solve it, and its probabilistic interpretations. Personally I think complementing it with the probabilistic point of view is not only interesting, but it provides a very strong intuition as to what ought to be true.
    • Work done during the UChicago Math REU 2023, August 2023.