Articles
The following notes were written down as a part of projects for courses or for giving presentations. On average, these are highly unoriginal and derive heavily from one or two sources. There are probably errors in all of these, and the quality of writing could use some improvement. When I’m not feeling lazy, I might come back and proofread and/or edit these in the future.
Characteristic Classes: This implicitly assumes you know what a Riemannian metric and a connection on a manifold is, even though this is not a strict prerequisite. It starts off with defining connections on vector bundles and goes on to talk about various characteristic classes.
Model Categories: Starts of with some topological motivation and then develops the theory of Model Categories. Ends with an introduction to simplicial sets and a brief discussion on the model structures on Top and sSet.
K-Theory, Bott Periodicity and the Atiyah-Singer Index Theorem: Implicitly assumes some knowledge of the analytic side of the Index Theorem, and tries to introduce the K-theoretic aspects with a brief excursion into Bott periodicity. Overall, pretty light on the details.
- A Brisk Jaunt to Supersingular Elliptic Curves
- Hilbert’s 17th Problem: Presents the model theoretic proof of Hilbert’s 17th Problem.