Summer Projects
A Mathematical Analysis of Machine Learning Algorithms
This 2023 summer research project focused on the mathematical analysis of machine learning algorithms. I studied theoretical ML literature integrating statistical physics and probability, analyzed neural network approximation quality and trainability using SGD, and performed numerical experiments on toy models and datasets such as MNIST, recording practical insights.
Random Constructions in the Plane
I studied the notion of harmonic measure in the plane, its various formulations involving conformal maps and Brownian motion, culminating in the study of the so-called conformally balanced trees following work from Professor Christopher Bishop. This experience helped me refine analytical problem-solving, decomposition, and communication skills through weekly meetings with my supervisor, where feedback was incorporated into the project.
Imperial College Second Year Project
This is a report of our group’s study of Darboux Transformations and its role in the spectral analysis of one-dimensional Schrödinger operators. We developed the Hilbert space formalism and applied the method to three Schrödinger operator eigenvalue problems: the simple harmonic oscillator, the reflectionless potential, and the Coulomb potential. This work has broad implications in quantum mechanics and mathematical physics.
Imperial College First Year Project - Solitary Waves and the KdV Equation
In this poster project, I discussed a mathematical model that accounts for the phenomenon of solitons in shallow water. I examined some of its analytical as well as numerical properties.