# My Math

I was in graduate school for a number of years, and this is a collection of the notes/papers I wrote.

## Homotopy Theory

Homotopy Theory is the most important field in all of mathematics, physics and computer science. So, these are some of my notes on it.

## Low Dimensional Topology

Notes I made while preparing for my oral exam.

## Classifying Spaces and Representability Theorems

The foundations and statement of the Brown Representability Theorem, a very general result on representing functors as morphisms into a single object. There is a far more general result known as the Yoneda Lemma that is very applicable to computer science.

## Computations in Khovanov Homology

Just some examples of how to compute an object known as Khovanov Homology.

## Gauge Theory

I spent one summer trying to learn some physics and this is the resulting notes.

## Lee's Variant of Khovanov Homology

Notes on Lee's variant of Khovanov homology, which leads to a spectral sequence.

## Knot Theory

Very rough and incomplete notes on some basic knot theory.

## Oral Exam Syllabus

Syllabus for my oral exam in graduate school.

## Spectral Sequences

An incredibly complicated object arising often in algebra and topology.

## State Sum Invariants of Links and Manifolds

Very rough and incomplete notes on some basic state sum invariants of links and manifolds.