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I participated in the Directed Reading Program as a Graduate Mentor for the project on Hecke Operator Theory (February 2026 - May 2026).
In this role, I guided a team (Srijan Raghunath (senior math major)) in exploring the Hecke operator theory.
Abstract: An introduction to higher-level modular forms, Ramanujan’s tau-function, and Hecke operators. It explores the arithmetic properties of Hecke eigenforms and the role of newforms in the theory of higher-level modular forms.
Slides & Final Report
I participated in the Directed Reading Program as a Graduate Mentor for the project parity of the partition function and Rademacher’s exact formulas(September 2025 - December 2025).
In this role, I guided a team (Srijan Raghunath (senior math major)) in exploring the intricate integer partitions.
Abstract: We outline the path from Ramanujan’s partition congruences to Rademacher’s exact formula for p(n), highlighting the generating-function ideas that reveal the modular structure of the partition function. As an application, we show that p(n) takes both even and odd values infinitely often.
I participated in the Knox Math Lab as a Team Leader for the research project Symmetry and Geometric Variational Problems, led by Dr. Letian Chen(January 2025 - May 2025).
In this role, I guided a team(Michael Rice (junior math major) and Emma Upton(freshman math major)) in exploring the intricate connections between symmetry, geometry, and variational methods. The project allowed me to develop my leadership skills while contributing to groundbreaking research in mathematics.
Abstract: The minimal surface equation defines a PDE, but under suitable symmetry assumptions, it can be reduced to a simpler ODE. This project explores problems arising from minimal surface theory and mean curvature flow, focusing on the existence and (non)uniqueness of symmetric solutions through ODEs.
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