Research

My main research lies in arithmetic geometry where I investigate number-theoretic problems and objects through the lens of algebraic geometry. My current research involves investigating the difference between two distinct integral structures (one coming from arithmetic, the other from geometry) on the space of modular forms. I have also recently been investigating Selmer groups via graph theoretic methods.

My recent work (joint w/ Ben Savoie) has involved investigating Selmer groups via graph theoretic methods. Here's a link to a talk I gave at Rice University (2023) on our current progress.

My thesis computes the precise difference between two integral structures of modular forms. Here's a link to a talk I gave at UCSD in 2022 and my preprint.

In 2018, my comprehensive exam focused on understanding Coleman's paper on classical and overconvergent modular forms. Here you can find my write-up and my presentation.

In 2016, my RTG focused on Kedlaya's algorithm and point counting using Monsky-Washnitzer cohomology. Here you can find my report and my presentation.

During Summer 2020, I held live online lectures twice a week on an introduction to algebraic geometry to graduate students. Video lectures and notes can be found on the site.

During Fall 2018, I helped organize a graduate student lead seminar on cryptography. You can find our website here. Here are my slides on Number Field Sieves.

In 2017, I gave a talk on modular forms and the Ramanujan congruences at the UoA grad student colloquium. Here are my slides.