Surely everything below will have typos and errors. Please email me about any you find.
For (more) Advanced Mathematicians
I.e. college upperclassman math majors or early grad students.
(Ongoing, in early draft) Big Book, in collaboration with Rawley Harrison. The goal is to exposit all the necessary algebraic geometry background for Faltings' proof of the Mordell Conjecture for someone who has just done a year-long algebraic geometry course, say. Updated every couple weeks or so.
Notes on DeJong's Alterations, written for a class in collaboration with Rawley Harrison, Miguel Machado and with a lot of useful input from Brian Conrad.
My Bachelor's Honors Thesis on adelic analysis. In particular I had not found a satisfactory exposition of Tate's thesis in the function field case, so this is an attempt to create one. At some (much later) point in the future I'll likely expand it to a general exposition on automorphic forms.
For Earlier Mathematicians
I.e. advanced high-schoolers or early undergraduates.
PROMYS 2022 Minicourse Notes
Some notes for mathematical talks that I gave as a PROMYS counselor.
AKS Algorithm; a proof of the validity of a polynomial-time prime-checking algorithm, along with a runtime analysis.
Constructible Polygons; the 'T-Shirt Talk' on proving (one direction, at least) of the constructbility criterion for regular polygons. (I brought a giant compass and constructed a pentagon on the chalkboard for this talk, it was a lot of fun!)
Googology; some fun vignettes of absurdly big finite numbers and how we construct them.
The Polynomial Trick; some examples of Alon's "polynomial method" used to generate combinatorial bounds via polynomial vector space dimension arguments.
Guided Readings for SUMaC 2025
Written for students to work through and internalize the material via several (doable!) exercises.
Pontryagin Duality; an outline following Rudin's arguments, handwaving some measure theory results and Plancherel for times' sake.
p-adic ''geometry''; a construction and exploration of the basic properties of the p-adic numbers, and some exercises to illustrate why they resists visualization (unlike the reals, for example).
Stanford Class Projects
Mostly very introductory material, done as practice for exposition in my early mathematical years.
Dinitz' theorem: written as a final expository paper for Math 107 (Graph Theory).
Probabilistic Method: a crash course, originally written as a series of mini-lectures for Math75SI students. The examples range from game theory to graph theory to Euclidean geometry.
Semidirect Products: written for the WiM paper in Math 120 (Groups and Rings).
How to Write Proofs, compiled by me and some fellow counselors at PROMYS 2022.
How to Give a Math Talk, by me and the wonderful Andrew Lee. While created for mini-talks, the advice generalizes. Also see: John McCarthy's How to Give a Good Colloquium (though I disagree with #12 and the sandwiched clause of #4).