Lecture Notes

• Sheaves and Motivic Homotopy Theory (PDF) (TeX)
  Lecture notes (in progress) for a topics course in algebraic topology, Fall 2026.

Short Notes

• Presentations of Burnside Rings (PDF)
  In this note, I want to present the basic ideas and techniques for computing (presentations of) Burnside rings and formulae for their restriction, transfer, and norm maps.
• Hall Matching via Krein-Milman (PDF)
  Every finite regular bipartite graph with at least one edge has a perfect matching. The Krein-Milman theorem provides a very slick proof of this fact.
• A Linear Map with No Adjoint (PDF)
  A quick example of a linear map between inner-product spaces which does not admit an adjoint.
• Classification of Finite-Dimensional Composition-Closed Vector Spaces of Functions (PDF)
  We show that all finite-dimensional vector spaces of differentiable functions \(\mathbb{R} \to \mathbb{R}\) which are closed under composition must consist entirely of affine-linear functions.