An exposition of Deligne's "Weil I" paper. Notes (written together with Alex Bertolini Meli) on the basics of p-divisible groups, for WCATSS 2016. Structure theory of unimodular lattices Explains the classification of indefinite unimodular lattices, following Serre. Notes from my talks in the 2015-2016 Number Theory Learning Seminar at Stanford on the Bloch-Kato conjecture:

- A "BSD-like" Conjecture of Mazur and Tate
- The Bloch-Kato Selmer Group.
- The Baby Bloch-Kato Conjecture.

Hodge-Tate Theory. My undergraduate thesis on the Hodge-Tate decomposition for abelian varieties.

Notes for talks delivered to the (Stanford) Student Algebraic Geometry Seminar. [Warning: these are still pretty rough.]

- Part I and Part II of talks on Brill-Noether theory and the Griffiths-Harris paper "On the variety of special linear systems on a general algebraic curve."
- Uniform Boundedness of Rational Points. Notes from a talk (May 18, 2015) on the Caporaso-Harris-Mazur theorem on uniform boundedness of rational points.
- Chow Groups of Classifying Spaces. Notes from a talk (January 30, 2015) covering a (small) subset of Totaro's paper "The Chow Ring of a classifying space."

Notes from talks on Vincent Lafforgue's construction of the global Langlands correspondence over function fields: Part 1, Part 2, Part 3, Part 4.

Notes from talks on the "Galois to Automorphic" direction of the global Langlands correspondence for GL(2) over function fields (following Drinfeld): Part 1, Part 2, Part 3, Part 4, Part 5.

Notes from talks on geometric class field theory: Part 1, Part 2, Part 3.