# 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).

### 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)