Here are some notes, generally from various math talks. Be aware the quality of the note may experience exponential decay as you scroll back in time. If you find any typos or have any comments or suggestions please send me an email!

Course notes

• Unstable motivic homotopy theory - topics class on motivic homotopy theory - 2024.
• Sets, groups, geometry - course notes from MATH101 - Spring 2024.

Other notes

• An introduction to the norm residue isomorphism theorem - talk notes from Juvitop - Fall 2025.
• Galois groups in enumerative geometry - - 2025.
• Homotopical Galois theory - talk from Babytop seminar on chromatic homotopy theory - Spring 2025.
• Hermitian $K$-theory - AMTRaK seminar talk notes - Spring 2025.
• A motivic crash course - Thursday seminar talk notes - Fall 2024.
• Diagonalizing symmetric bilinear forms - tips and tricks for diagonalizing forms from their Gram matrices - 2023.
• Algebraic vector bundles - Penn graduate geometry/topology seminar talk - Spring 2022.
• Ambidexterity - Talbot talk - Winter 2021.
• Euler characteristics of real algebraic manifolds - Penn graduate geometry/topology seminar talk - Fall 2021.
• Hopf algebroids - Penn chromatic homotopy theory seminar - Spring 2021.
• Complex orientations - Penn chromatic homotopy theory seminar - Spring 2021.
• Dwyer-Kan localization - Penn infinity-categories seminar - Fall 2020.
• $K$-theory of infinity categories - Penn algebraic $K$-theory seminar - Spring 2020.
• Homotopy coherent nerve - Penn topology proseminar - Spring 2020.
• Bundles - quals prep - Summer 2019.
• The generalized Poincaré conjecture via $s$-cobordism - Penn pizza seminar - Fall 2018.