# Scribe notes

This is not an exhaustive list; if you're interested in something else you think I might have notes for, feel free to ask me via email (`ebelmont at ucsd dot edu`).
### Seminars and workshops

### MIT courses (taken as a graduate student)

- 18.917: The Gamma function and the field with one element, taught by Clark Barwick. Tate's thesis, $\mathbb{F}_1$, cyclotomic spectra, $THH$ and zeta functions. (pdf, tex) (Spring 2017)
- 18.786: Number theory II, taught by Bjorn Poonen. Tate's thesis, Galois cohomology, introduction to Galois representation theory, including the statement of the local Langlands correspondence. (pdf, tex) (Spring 2015)
- 18.785: Algebraic number theory, taught by Bjorn Poonen. Algebraic number theory (up through adèles, Dirichlet's unit theorem, and finiteness of the class group), and a short introduction to analytic number theory. (pdf, tex) (Fall 2014)
- 18.965: Geometry of manifolds, taught by Paul Seidel. Differential topology and differential geometry. (Fall 2013)

### Cambridge (Part III), 2012-2013

- Elliptic curves, taught by Tom Fisher. Introduction to elliptic curves over $\mathbb{F}_p$, local fields, and $\Q$.
- Lie algebras, taught by C. Brookes. Lie algebras, root systems, representation theory of Lie algebras.
- Algebraic geometry, taught by Caucher Birkar. Sheaves, schemes, sheaf cohomology.
- Commutative algebra, taught by Nick Shepherd-Barron. Roughly follows Atiyah-Macdonald, plus modules of differentials, and some homological algebra.

### Harvard (some courses I took as an undergraduate)

- Math 229: Analytic number theory, taught by Barry Mazur. Zeta functions and functional equations, the prime number theorem, Dirichlet $L$-functions, Artin $L$-functions, primes in arithmetic progressions. (Spring 2012)
- Math 232a: (Classical) Algebraic geometry, taught by Xinwen Zhu. Course on varieties, following Mumford's
* Complex Projective Varieties*. (Fall 2011)
- Math 114: Real analysis, taught by Peter Kronheimer. Measure, integrability, Fourier series, $L^p$ spaces. (Fall 2011)
- Math 231br: Algebraic topology (notes taken by Akhil Mathew and me), taught by Michael Hopkins. Serre spectral sequence, Eilenberg-Maclane spaces, model categories, simplicial sets, rational homotopy theory of spheres. (Spring 2011)