My research interests lie in number theory, specifically using analytic methods. I am now exploring different aspects of quantum chaos on the 2-sphere using automorphic representations of inner twists of GL(2).
Ongoing Projects
Large fluctuations of arithmetic spherical harmonics (with Sun Kai Leung).
Orders in the Euclidean court, II (with Enrique Treviño). Preprint available upon request.
Arthur's explicit formula and applications to Sato-Tate (with Kristaps Balodis, Melissa Emory, Daniel Mora Mora, Pankaj Singh, and Tian An Wong).
Research Papers
Equidistribution on shrinking sets for arithmetic spherical harmonics, 2026.
On the geodesic restriction problem for arithmetic spherical harmonics, 2025.
Selecting balls from urns with partial replacement rules (with Julian Burden, Chandramauli Chakraborty, Qizhou Fang, Lisa Lin, Nasser Malibari, Sammi Matoush, Isaiah Milbank, Zahan Parekh, Martín Prado, Rachael Ren, Qizhao Rong, Eli Sun, Enrique Treviño, and Daisuke Yamada), 2024.
On a sequence related to the factoradic representation of an integer (with Enrique Treviño), 2021.
Expository Papers
Pi is Transcendental, 2020.
Notes
Spherical harmonics and automorphic representations (in progress). Last version: December 16, 2024.
El Teorema de Erdős-Kac (undergraduate thesis in Spanish, never defended). Last version: December 17, 2022.
Research Talks
The Geodesic Restriction Problem for Arithmetic Spherical Harmonics, Fouvry-73 Summer School, August 18, 2026
The Geodesic Restriction Problem for Arithmetic Spherical Harmonics, 38° Automorphic Forms Workshop, May 19, 2026
The Geodesic Restriction Problem for Arithmetic Spherical Harmonics, UVA Ramanujan-Serre Seminar, April 3, 2026
The Geodesic Restriction Problem for Arithmetic Spherical Harmonics, Palmetto Number Theory Series XL, December 7, 2025
Una sucesión relacionada a la representación factorádica de un entero, 54° National Congress of the Mexican Mathematical Society, October 4, 2021.
Una sucesión relacionada a la representación factorádica de un entero, VIII Young Researchers Meeting in the State of Nuevo Leon, November 18, 2020.
Expository Talks
Chebyshev's Bias, UVA Math Graduate Students Seminar, September 20, 2024.
A Failed Proof of Fermat's Last Theorem, UVA Math Graduate Students Seminar, September 8, 2023.
The Erdős-Kac Theorem, UVA Math Graduate Students Seminar, January 20, 2023.
Pi es Trascendente, 2° Mathematics' Week - UANL, March 13, 2020.
Sistemas Dinámicos Discretos y el Teorema de Sharkovskii, 1° Mathematics' Week - UANL, September 10, 2019.