Expository Articles
My senior thesis, advised by Weimin Chen. A 20-years-later update on Terry Lawson's wonderful survey (and with a somewhat different perspective than this survey).It serves as an introduction to a decent swath of topics in 3- and 4-dimensional topology, aimed at someone with a semester of algebraic topology and a semester of smooth manifolds (up to de Rham cohomology). Also contains some minor new results!
A project I did for a class in 2021. This is a short introduction to Higgs bundles and their moduli space. It's constructed using gauge theory and infinite-dimensional symplectic reduction. Aimed at someone with a semester of smooth manifolds and a bit of knowledge of affine connections, it's a good taste of some of the techniques used in this area of physics-y differential geometry.