Research

I currently work on modular forms, cusp forms, twisting, the Rankin–Selberg method, the analytic computation of the constant term of non-holomorphic Eisenstein series, local fields, adeles, p-adic integration, and the special functions that arise in explicit computations.

I also study the computation of all Fourier coefficients and encountered the Whittaker function in the big Bruhat cell. To understand this construction more thoroughly, I studied the relevant representation-theoretic background, including degenerate principal series and the Schrödinger model of the Weil representation, following Yang’s CM Number Fields and Modular Forms and Kudla–Yang’s Eisenstein Series for SL(2), which I am currently reading in depth. These studies have shaped my current project on generalizing Whittaker function constructions.

In Algebraic Topology I studied free resolutions using augmented chain complexes, which gave me helpful intuition for homological tools that appear in the study of arithmetic groups.

In Algebraic Geometry I explored the connection between the j-invariant and ring class fields, following portions of Gross–Zagier and Cox.

In Matrix Analysis I studied the correspondence between ideal classes and similarity classes of matrices through the Latimer–MacDuffee theorem, discovering a surprising link to class numbers.

In Summer 2023, I completed a Directed Reading Program on the Dirichlet Class Number Formula under the guidance of Gaurish Korpal.

In Spring 2023, I worked on a project focused on application of category theory, under the supervision of Prof. Olcay Coskun. In this project we studied the Prof. Tom Leinster's paper called Entropy and Diversity: The Axiomatic Approach. Here I learned about how to grasp physical concepts like entropy in pure algebraic ways.