## Expository notes and articles

Please use at your own risk.

**From grad school**

I wrote a lot of unpolished notes, mostly for personal use. I might put them here one day.

**From early grad school** (when I still thought I might want to do number theory)

- Simpler form of the trace formula for GL_2(A), for the Number theory learning seminar 2013-2014 at Stanford.
- On spherical representations of p-adic groups and the classical Satake isomorphism, for the Number theory learning seminar 2013-2014 at Stanford.

**Things I wrote as an undergrad**

*Structure Theory of Reductive Groups through Examples*, summer study funded by Princeton University Mathematics Department, under advisor Tasho Kaletha (Summer 2011)*Expanders and Related Results*, for Princeton University's Junior Paper requirement, under advisor Alireza Salehi Golsefidy (Spring 2011)*An Application of the Weil Conjectures to PAC and Large Fields*[with Erick P. Knight], for the course*MAT 416: Algebraic Geometry*at Princeton University, taught by János Kollár (Fall 2010)

## Talk slides

*A Commutative Diagram of the Heavens*. For an invited talk at the high school math competition Math Day at the Beach at California State University, Long Beach (March 15, 2014).

A talk about the planetary days for a mathematical audience. The material here is certainly well known. The presentation is original and is inspired by conversations with Brian Lawrence. Here's an amusing application of this material: if you know Chinese and (say) French, you can figure out the days of the week in Japanese. With a little more effort, you don't even need French.