Expository manuscripts

Please send me any mistakes you find in these manuscripts!

• p-adicity. Slides accompanying a talk for undergraduates at the Barbara T. Faires Allegheny Mountain Colloquium (2024), similar to slides I prepared for Young Mathematicians Conference (Ohio State University, 2024).
• Prime numbers and the Riemann zeta function. A talk in the Undergraduate Mathematics Seminar at Pitt. (2019)
• Derived structures in the Langlands program -- Introduction II. The second half of an introduction to the topic of the London number theory study group (Spring term, 2019). The first half (by James Newton), and other notes from the study group, are available here.
• The Milnor conjecture and the motivic Bloch-Kato conjecture. An expository talk in the London Number Theory Study Group. (2018)
• A summary of some of the results of an earlier version of "Deformations of residually reducible Galois representations via A-infinity algebra structure on Galois cohomology". (2015) [pdf]
• Thesis: Moduli of Galois Representations. Version 1.1. (2013) [pdf] [Harvard] [video]
• Formal Groups A brief introduction to formal groups in number theory, intended for Harvard Math 223a students. (2008)
• Ribet's Converse to Herbrand's Theorem An essay written for the Cambridge Part III program, covering Ribet's article. (2008)
• Prime Numbers and the Riemann Hypothesis, notes for a talk to advanced high schoolers in the PROMYS program. (2008)
• Cyclotomic Fields, a talk discussing the connection between Kummer's criterion and Fermat's last theorem. (2008)

You can also take a look at my research manuscripts page and arXiv page.

Main page.