Michael Bradford Williams

Quick! What's the spectrum of a self-adjoint compact linear operator on a Hilbert Space? If you have to think for more than 3 seconds before answering, then you should check out my worksheet (pdf) on such operators.

Even better, what's the universal cover of this topological space? Click for the answer.

Here's some stuff on cellular automata that I've been working on for my own amusement. If this doesn't immediately pique your interest, here's a picture:

Finally! Your chance to learn all about super linear algebra! I prepared a few background notes for a paper I was reading recently. Also included is info on vector bundles. These are in no way comprehensive.

I wrote a short note that proves a few interesting facts about the Fibonacci sequence. It should be understandable to anyone who knows anything about calculus and basic linear algebra.

What is infinity? How many infinities are there? Infinitely many! I wrote another short note that introduces the concept of cardinality and proves a few facts about it. It is written at a basic level, and does not assume much knowledge of mathematics beyond basic facts about sets and functions.

Also for my own amusement, I wrote a program to visualize certain complex mappings. This page contains the Java applet and various pretty pictures.

For my own benefit, I have compiled a reference for many topics needed in Differential Topology and Geometry. Pretty much all of the basic facts about structures on smooth manifolds, as well as the background algebra, are here in some form or another.

Richard P. Feynman is approximately the man. Here's an amazing speech given to the National Academy of Sciences in 1955.

Also the man: Paul Erdos, the Kevin Bacon of Mathematics. Here is perhaps the first published reference to the Erdos number, appearing in the American Mathematical Monthly in 1969. Erdos himself replied to the short article by, unsuprisingly, doing real mathematics with the Erdos number. Sadly, my own Erdos number is still undefined.

Here are notes from my recent oral candidacy exam. I presented the main ideas from this paper, which uses the Ricci flow to classify certain types of manifolds.

I recently participated in transcribing a series of lectures on Topological Quantum Field Theory and the Cobordism Hypothesis, give by Jacob Lurie. Videos of the lectures, which were part of the Persepctive in Geometry lecture series, are also available.