Research Notes
Genera of Congruence Subgroups (2021): A revisit to my undergraduate junior paper where I work towards showing that congruence subgroups of SL(2, Z) don’t attain every genus.
Torsion in the Cohomology of Arithmetic Subgroups (2020): My undergraduate senior thesis, which explains the literature on a conjecture by Bergeron and Venkatesh that predicts the growth of torsion in the cohomology of arithmetic subgroups.
Finding subgroups of SL(2, Z) with Arbitrary Genus (2019): My undergraduate junior paper, which explains how to construct non-congruence subgroups with any given genus and details one method of approaching the open question “do congruence subgroups of SL(2, Z) attain every genus?”
Expository Papers
The Role of Ribet’s Theorem in the Proof of FTL (2022): An overview of how Ribet’s theorem applies to Frey curves and how, with the Modularity Theorem, the proof of Fermat’s Last Theorem was attained.
An Introduction to Iwasawa Theory (2021): A brief introduction to classical Iwasawa Theory, as well as an introduction to Iwasawa Theory for elliptic curves at both ordinary and supersingular primes.
An Exposition of Elliptic Curve Cryptography (2021): A joint paper summarizing elliptic curve cryptography, including ECDH, ECDSA, the ECDHP, and vulnerabilities.
An Exposition of the First and Second Theorems in GAGA (2019): My translation of the first two major theorems in Jean-Pierre Serre’s Géométrie Algébrique et Géométrie Analytique.