Talks

Here are some selected past talks I have given:

• A Disc Embedding Starter Kit: a starter on Freedman's Disc Embedding Theorem following the Disc Embedding Theorem book, discussing some main motivations and objects, as well as the definition of a skyscraper. The talk was given at the Top Secret Seminar.
• Optimal Paper Mobius Bands: a quick account of Schwartz' amazing proof determining how stout a paper Mobius band can be. The talk was given at the Princeton First Year Seminar.

Expository Writing

Here is some more selected expository writing:

• Skein Lasagna Modules Detect Exotic 4-Manifolds: a very accessible guide on Ren and Willis' 2024 proof that Khovanov homology (via Skein Lasagna modules) can detect exotic pairs of compact manifolds. There are a lot of diagrams, and only a general topological background is assumed. Written as my Part III Essay.
• Morse Theory on Path Spaces: an expository account of Bott's proof that the second and third fundamental groups of a compact simply connected Lie group are respectively trivial and free abelian. The beginning requires a bit of knowledge of homotopy groups, but afterwards we build the necessary Morse theory results from the ground up. Written as a final paper for an advanced Algebraic Topology class taught by Andy Senger.