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

Course Notes

Notes for Talks

Seminar Notes

Other Notes

  • Counting Cubic Number Fields
  • 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.

  • Singular Fibers on Elliptic Surfaces
  • 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.

  • A Brief Intro to Fourier Series
  • 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.