Notes:
Some various notes from talks, teaching, seminars, etc. There are likely errors, please email me if you have any comments, suggestions, corrections, etc. A few of these have public GitHub repositories attached to them, so you're also welcome to submit a pull request.
Course notes:
Expository talk notes, etc.
- Galois groups in enumerative geometry (in progress), notes from a mini-reading seminar, spring 2025
-
Homotopical Galois theory, talk notes from MIT Babyyop seminar on chromatic homotopy theory, spring 2025.
- Hermitian $K$-theory, talk notes from the AMTRraK seminar in spring 2025
- A motivic crash course, talk notes from the Harvard Thursday seminar, fall 2024. The goal of these notes is to work from the ground up to present Voevodsky's proof that Eilenberg-MacLane spaces for motivic cohomology are split proper Tate.
- Diagonalizing symmetric bilinear forms, includes some tips and tricks for diagonalizing forms from their Gram matrices.
- Algebraic vector bundles, Penn grad geometry/topology seminar, 2022.
- Ambidexterity, Talbot 2021
- Euler characteristics of real algebraic manifolds, Penn grad geometry/topology seminar, 2021.
- Hopf algebroids, Penn chromatic homotopy seminar, 2021.
- Complex orientations, Penn chromatic homotopy seminar, 2021.
- Dwyer-Kan localization, Penn infinity-categories seminar, 2020.
- Homotopy coherent nerve, Penn topology proseminar, 2020.
- Bundles, for quals, 2019.
- Constructing the Unstable Motivic Homotopy Category using $(\infty,1)$-Categories, arXiv:1810.00094.
- The Generalized Poincaré Conjecture Using $s$-Cobordism, for the Penn Grad Student Seminar, Fall 2018.
Conference and course notes:
Disclaimer: Any errors found in these notes should be attributed to me, not the original lecturer. If you find any typos or have suggestions, please feel free to contact me.
- School on Motives and Stacks, September 2019, minicourses by Hoskins, Østvæer, Rydh. Notes available upon request.
- European Autumn School in Topology, September 2019, minicourses by Barthel, Salvatore. Notes available upon request.
- PIMS Workshop on Arithmetic Topology, June 2019, minicourses by Ellenberg, Farb, Galatius, Ho, Vakil/Landesman, Wickelgren.
- An Introduction to $\textbf{A}^1$-homotopy theory from an infinity-categorical viewpoint, June 2018, (notes from lectures of Strunk and and Tamme, Homotopy Theory Summer Berlin 2018).