Interests

My primary interests tend toward the mathematical, even outside of mathematics itself.

Computer Science

I have a strong interest in machine learning and artificial intelligence. I took a course on machine learning using Java and Python, culminating in writing a neural network to guide an agent in a resource gathering competition against other students' agents. I also have an interest in software verification, stemming from an interest in formal proof verification in mathematical logic. Checking programs, like checking proofs, is hard, especially if you're the one who wrote them, so automated computer verification. From the other direction, the last part of my dissertation required performing dimensional reduction on a high-dimensional data set. I had to use Python to get around memory constraints in Maple and Sage.

Linguistics

I am very fond of linguistics, both as a study of communication systems and as a study of human cognition and society. I am a regular reader of the Language Log blog. I also have an interest in computational linguistics and natural language processing, stemming off of my interest in machine learning.

Music

I enjoy making electronic music. I try to do as much as possible from scratch, applying signal processing to shape basic soundwaves into more complicated timbres. I also use signal flow control to guide mixing choices. I also get inspiration on the compositional side from number theory and algebra.

Fun Stuff

Rubik's Cube

While most of us are familiar with the Rubik's cube, one of my interests is in variants of the Rubik's cube and in the mathematics underpinning it. The Rubik's cube is often considered a useful example of a mathematical field called group ttheory, since the twists and turns that you can do to a Rubik's cube forms a group.

What most people, including many mathematicians, don't realize is that there are many variations of the Rubik's cube, for example the myriad available in the museum at Twisty Puzzles. I have played with and learned how to solve a bunch of the ones listed there, including some non-cubical ones and ones that twist into strange shapes, but there are many that I haven't even seen in real life yet.
cubes from tonyfischerpuzzles.net

Another fun site is Magic Tile, which describes a way of looking at Rubik's cubes and twisting puzzles in a more abstract way than physical toys. This abstraction leads to more interesting mathematics about what the notion of twisting puzzle can mean, including connections to topology and combinatorics.
gravitation3d.com/magictile Here is a rough version of a talk I once gave on generalized twisting puzzles to the graduate students of the University of Pennsylvania, based on the ideas behind Magic Tile. I also enjoy origami, folded paper art, both for the aesthetic and the mathematical aspects.



Origami

I like origami, art based on folding paper without cutting or gluing, for both its aesthetics and its mathematical aspects.
There is actually a lot of interesting mathematics in origami. An interesting question is, starting from a flat piece of paper, what kind of constructions can you make? It turns out that while straightedge and compass can solve quadratic equations but not any higher degree, using the Huzita-Justin axioms one can prove that by folding paper one can solve cubic equations, and thus for instance trisect an angle and double a cube as shown by Margharita Beloch.

Here is a video of Dr. Robert J. Lang giving a talk on mathematical origami and the power of using mathematical ideas to design origami.