These are a collection of notes on mathematical topics.
Notes on the homotopy groups of topological modular forms at the prime 3 (for a talk at Juvitop).
Notes on the Browder-Novikov theorem, giving necessary and sufficient conditions for a simply connected 4k-dimensional space to have the homotopy type of a manifold.
Some notes on a theorem of Snaith that constructs complex K-theory.
Notes on simplicial commutative rings (written for a talk at a workshop).
The fundamental group of a smooth projective curve in nonzero characteristic (in particular, the fact that it admits 2g topological generators). .pdf
Notes on Kodaira vanishing (and a few other things, like Chern-Weil theory). .pdf
Verdier duality .pdf
The Dold-Kan correspondence between simplicial abelian groups and chain complexes. .pdf
(Unfinished) notes on the semicontinuity theorem (on the cohomology of a flat family) in algebraic geometry. .pdf
Notes on chapter 1 of "Higher Topos Theory," for a talk. .pdf
Interactive proofs, notes from a talk I gave at an undergraduate mathematics colloquium. .pdf
Zariski's Main Theorem and some of its applications (following mostly EGA and Raynaud's Anneaux locaux henseliens). .pdf
Notes from a talk I gave at HMMT on Sperner's lemma and some of its applications. .pdf
A short expository paper on Arrow's theorem. .pdf
An exposition of the Synge-Weinstein theorem in Riemannian geometry. .pdf
Some notes on divisors and line bundles..pdf