Here is an expository paper that I wrote for a Lie Groups class, concerning groupoids.

Here is another expository paper that I wrote for a Geometry class, this time concerning collapse in Riemannian geometry.

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

I 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.

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.

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

I taught an undergraduate real analysis course, which covered the basics of converegent sequences, continuity, differentiability, and integrability. I created a flow chart that shows how the main definitions and theorems depend on each other.

I wrote another short note that explains one of my favorite numbers, Khinchin's constant. This number is the geometric mean of the denominators in the continued fraction representation of almost every real number!

I taught a course in discrete mathematics, and we proved that the famous Petersen graph is not planar. Here is the proof.

I created some animations to help visualize certain complex mappings. (See also this demo.)

What is the universal cover of this topological space?

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. My own Erdos number is 4.