# notes

Various notes I've written. They all contain my confusions, mistakes, and/or TODOs, but hopefully are nevertheless useful.

## Course Notes

- APAW Notes
- Harvard 286 Algebraic Curves Notes
- UMich 679 Course on Mazur's Theorem Notes
- Étale cohomology and the Weil conjectures Notes
- Homological Stability Minicourse Notes
- UW 582C Introduction to Stacks and Moduli Notes
- 18.737 Algebraic Groups Notes
- 18.755 Lie Groups and Lie Algebras II Notes
- 18.786 Number Theory II Notes
- Fall 2020 Course Notes

These are notes I took during the 2022 APAW Graduate Instructional Workshop.

These are notes on Andrew Snowden’s course on Mazur’s theorem. All his lectures were recorded, so those are probably more useful than these notes.

These are notes on the recordings of an étale cohomology class by Daniel Litt.

These are notes on a homological stability minicourse taught by Alexander Kupers through eCHT.

These are notes on Jarod Alper’s stacks course at the University of Washington.

I put all the course notes I took in Fall 2020 in one document because I hadn’t yet realized that this was a bad idea. If you’re curious, this includes some Lie algebras, some number theory, some topology, some arithmetic statistics, and some abelian varieties.

## Notes for Talks

- Local Heights and Arithmetic Surfaces
- STAGE Vojta's Approach to the Mordell Conjecture Notes
- KanSem Formal Group Laws Notes
- Juvitop CFT Notes
- Forms of \(K\)-theory Notes

These are notes meant to accompany a talk I gave in a Gross-Zagier learning seminar.

These are notes meant to accompany my STAGE talks on (Bombieri’s simplification of) Vojta’s proof of the Mordell Conjecture.

These are notes meant to accompany my Kan Seminar talk on Quillen’s work on formal group laws and complex cobordism.

These are notes meant to accompany my Juvitop talk introducing class field theory.

These are notes meant to accompany my Kan Seminar talk on this paper by Morava.

## Seminar Notes

- Harvard Ax-Schanuel Seminar Notes

These are notes I took during a seminar on O-minimality and Ax-Schanuel. There was much I did not understand, so these are probably of limited use.

## Other Notes

- Counting Cubic Number Fields
- Singular Fibers on Elliptic Surfaces
- A Brief Intro to Fourier Series

This is an exposition on the sections of this paper which reprove Davenport-Heilbronn’s results on counting cubic number fields. Honestly, these notes ended up being little more than a slightly expanded version of the relevant sections of that paper, where I tried to give a few more details in places where the paper initially confused me. If you are going to look at these notes, probably the best thing to do is just read (the relevant sections of) the Bhargava-Shankar-Tsimerman paper, and then look at these notes whenever you would like to see more of the steps involved in some calculation.

This was my undergraduate thesis. Ostensibly, it is an exposition on Kodaira’s work on classifying singular fibers of elliptic surfaces over \(\mathbb C\). In practice though, it’s more of an introduction to 2-dimensional complex geometry w/ Kodaira’s result serving as a particular application of the general theory.

This was my WIM (Writing in the Major) assignment as an undergrad. It’s a short note proving that the Fourier series of a continuous function on \(S^1\) actually converges to the function you started with.