Here are some notes I have written up. They are all works in progress.

NOTES:

Representation Theory of Categorified Quantum sl2: This is my dissertation for my Ph. D. and this is the presentation I gave in defense.

A Mathematical Approach to Menger's Theory of Goods (pdf): This is my attempt to formalize some of the economic theory for ordinal marginal utility of goods as explained by Carl Menger, founder of the Austrian school of economics.

Khovanov Homology (pdf): Notes on the definition of Khovanov homology including proof of invariance.

Quantum Invariants of Knots (pdf): In order to study for my orals, I am preparing notes on subjects related to knot theory. This piece deals with some category theory which is applied to quantum invariants such as the Kauffman and Jones invariants.

Categories (pdf): A little category theory.

2-Categories (pdf): The definition of 2-category.

Tangles (pdf): The category of tangles and the Kauffman bracket.

Axiomatic Introduction to the Riemann Integral (pdf): Wrote this up for my own edification.

Introduction to the Fundamental Group (pdf): Again for my own edification. So far it's got paths, homotopies, path-homotopies and the fundamental groupoid. More to come.

Rigid Body Mechanics and SO(3) (pdf): I wrote this up based on a talk I gave to SPS. I discussed an interesting application of Lie groups to classical mechanics.

Elliptic Functions (pdf): Notes for a talk i gave for a seminar class.

Differential Forms (pdf): It's got alternating and differential forms, wedge products, exterior derivatives, but as yet no De Rham cohomology.

Commutative Algebra (pdf): Notes I wrote up to study for a commutative algebra test.

Dirichlet's Theorem (pdf): Wrote this for a talk for my seminar class. It's on Dirichlet's theorem on primes in arithmetic progressions. Yay, L-functions.

Snake Lemma (pdf): Part of the proof of the snake lemma from homological algebra.

Fourier Analysis (pdf): Some very rough notes about some Fourier analysis.

Fundamental Theorem of Riemannian Geometry (pdf): A proof.