Notes

I like to solidify my understanding of various topics by typing up notes. I'll put some of my nicer notes here. Please note that I do not claim originality for any of this content, and some of these sets of notes may be incomplete or works in progress.

Course Notes:

C*-Algebraic Foundations of Quantum Spin Systems (Notes for my course at the 2024 Boulder summer school)

Normal States and Quasi-Equivalence (A series of 16 lectures I gave at UC Davis to teach about von Neumann algebras. I was aiming to get to the split property but didn't quite get there. Maybe I'll complete them later.)

Functional Analysis (My lecture notes for a quarter-long graduate course in functional analysis at UC Davis.)

Miscellaneous Functional Analysis and C*-Algebras:

A Hahn-Banach Theorem for Normed Spaces (I proved a variation of the Hahn-Banach theorem I hadn't seen before. Surely someone has done this already but I don't know a reference with this exact statement.)

The Principle of Local Reflexivity

The Category of Banach Spaces

The Category of C*-Algebras

Tensor Products of C*-Algebras

Completely Positive Maps

Primitive Ideals, Full Sets of States, and Fell's Theorem 

Real Rank Zero C*-Algebras

Stinespring's Theorem  (A lecture note from a pedagogical talk I gave about Stinespring's theorem)

Topological Groups and Haar Measure