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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.