Expository Notes
- On Generalized Fourier Series This note was my solution to a question I had when taking functional analysis last winter, showing how Fourier series can be defined for any complex Banach space with a continuous action of the circle, and how they ``converge’’ in some sense.
- Fun with Traces In this note, we answer a question of Maxime Ramzi about the image of the Hattori-Stallings trace.
- Cyclotomic Idempotents, a brief note proving that the idempotent algebras in (genuine) cyclotomic spectra are in bijection with the idempotent algebras of spectra, giving the smashing spectrum of cyclotomic spectra. We also discuss the smashing spectra of modules over an E_{infty} algebra in cyclotomic spectra.
- Pro-etale stacks, notes to accompany a talk I gave on how to use pro-etale descent to classify certain algebraic groups over an arbitrary field, such as 1-dimensional tori.
Final Projects
The following is some collection of final projects written for various classes, written to various levels of completeness.
- A PBW Theorem in the Verlinde Category, written for Math 229A (Spring 2022).
- Fukaya Categories and Hochschild Homology, written for Math 226B (Fall 2023).
- L-Functions and Geometry, written for Math 246A (Fall 2023).
- Modular Forms, Manifolds, and More, written for Math 207A (Fall 2023).
- Overconvergent Modular Forms and Modular Forms at Infinite Level, written for Math 207B (Winter 2024).
- A Dedekind Approach to Eisenstein Cocyles in Motivic Cohomology, written for Math 207C (Spring 2024).
- D-modules and Crystalline D-modules, brief notes to accompany a talk for Math 216A (Spring 2024).