I am a fifth year mathematics PhD student at UC Berkeley. I am primarily interested in number theory, especially algebraic number theory and p-adic aspects of the Langlands program. My research interests currently include: the categorical p-adic Langlands program; Galois deformation theory; p-adic representation theory of p-adic groups; p-adic Hodge theory, especially reductions of crystalline and semistable representations; and overconvergent modular forms. My advisor is Professor Sug Woo Shin. I passed my qualifying exam on August 22nd, 2023; here is my syllabus. If you are one of my students, you can find section resources under the teaching section below. Here is my resume.
I have a blog! You can find some of my expository writing here---mainly notes on what I am currently learning.
Jump to:The 3-adic Steinberg and a categorical 3-adic local Langlands correspondence for GL_2(Q_p). 2026.
We extend results of Johansson-Newton-Wang-Erickson on a categorical p-adic Langlands correspondence for GL_2(Q_p) to p = 3. This work will be the main result in my PhD dissertation.
Arborescences of covering graphs, with Sunita Chepuri, Andrew Hardt, Gregory Michel, Sylvester W. Zhang, and Valerie Zhang, in Algebraic Combinatorics, Volume 5 (2022) no. 2, pp. 319-346. Based on our work from the 2019 UMN REU. Also presented at the University of Illinois Chicago Undergraduate Mathematics Symposium, November 2, 2019; here is our poster.
We prove a formula describing a combinatorial relationship between the set of spanning trees of a graph vs. the set of spanning trees of a covering graph.
On parameterizations of cyclic N-isogenies and strict K-curves lying above rational points of Y_0^+(N). My undergraduate thesis, submitted in 2021. Unfortunately I later discovered that my supposedly novel result had been done before in a paper by Josep González (Isogenies of polyquadratic Q-curves to their Galois conjugates, see especially Proposition 3.1).
I give an exposition of Ligozat's formulas for Hauptmoduln of rational modular curves in terms of eta products and use them to tabulate rational expressions for the coefficients of the corresponding elliptic curves. Additionally, I give a Diophantine condition that describes when the isogeny between two elliptic K-curves can be defined over the base field.
Virtual resolutions of general points in smooth Fano toric varieties, with Sean McNally from the 2019 UMN REU.
We prove the existence of virtual resolutions of length dim X for general points in several smooth Fano toric varieties.