NotesI like to write notes for talks and self-study. Most aren't fit for public consumption, but a few that are have been linked below. Some notes are based closely on a single source, others multiple sources, and none of the ideas are my own. Please let me know if I have omitted an important reference. I hope there aren't too many mistakes.
Low-Dimensional Geometry and Topology
Teichmuller's Theorems and the Nielsen-Thurston Classification
The 3-Dimensional Margulis Lemma from Matsuzaki and Taniguchi.
Gromov's Proof of Mostow Rigidity.
Notes on the Skinning Map I wrote for a talk at the joint Brown-Yale GATSBY seminar.
The Spectral Geometry of Riemann Surfaces from Buser's wonderful book.
Teichmuller Theory and the Statistics of Shape, a presentation from my talk at Brown's Math Slam 2016.
General Geometry and Topology
Some notes on connections.
Some notes on curvature.
The basics of symplectic geometry, Noether's theorem, and Lagrangian/Hamiltonian mechanics.
The basics of Galois Cohomology.
An overview and proof of the Hilbert Syzygy Theorem.
An introduction to Non-Standard Analysis.