Research

Number Theory & Automorphic Forms

About My Research

I am currently working on Automorphic Forms in my PhD at Columbia University. I mainly focus on applications of the Orbit Method and Microlocal Analysis to problems in Automorphic forms. For example, subconvexity of automorphic L-functions. My undergraduate research focused on a variety of areas within Number Theory, exploring fundamental questions about prime distributions and the Riemann zeta function.


I am organizing a learning seminar in Orbit Method, Microlocal Analysis and Subconvexity of Automorphic L-functions this Fall (2025) at Columbia University. If you're interested, please check out the seminar page.

Publications & Preprints

Published
A general approach for deriving zero-free half-planes for the Riemann zeta function ζ by identifying topological vector spaces of analytic functions with specific properties. Published in Advances in Mathematics, Volume 455.
View in Journal
Counting prime ideals of a given degree in Number Fields
We obtain error terms which are much smaller polynomial bounds involving only the field itself, not the Galois closure. This work provides sharper estimates for the distribution of prime ideals in algebraic number fields.
Report
We investigate approximations ζ_X of the ζ-function introduced in Gonek's work, analyzing how close the approximate zeroes are to the actual zeroes and studying their statistical properties.
View on arXiv

Seminars Organised

A learning seminar at Columbia University to investigate these various approaches to subconvexity of automorphic L-functions, especially the recent results by Paul Nelson and Akshay Venkatesh which incorporate microlocal analysis and the orbit method to prove subconvex bounds for high rank.
View Seminar Page
A continuation of the Fall 2024 learning seminar at Columbia University exploring foundational and advanced topics in automorphic forms, covering both classical and modern perspectives.
View Seminar Page
A learning seminar at Columbia University exploring foundational and advanced topics in automorphic forms, covering both classical and modern perspectives.
View Seminar Page

Academic Profiles

For a comprehensive list of my publications and citations, visit my Google Scholar profile.

Google Scholar Profile