Research

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Publications

Cutting the Möbius Strip (The College Mathematics Journal MAA, vol. 55, no. 2, 2024): Using tools from algebraic topology and algebraic geometry (fundamental polygons and blowups, respectively), we prove that cutting along the center of a Möbius strip yields a cylinder.

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.

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?”