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:
Quantum ergodicity on the 2-sphere for arithmetic Laplacian eigenfunctions.
Geodesic restriction problem for arithmetic Laplacian eigenfunctions of the 2-sphere.
Research Papers
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 16th, 2024.
El Teorema de Erdős-Kac (undergraduate thesis in Spanish, never defended). Last version: December 17th, 2022.
Research Talks
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.