Research/projects

I specialize in mathematical physics. I am motivated by the information-theoretic aspects of nature.

At IHES, I am focusing mainly on applying category-theory to quantum information theory, more specifically Bayesian inference and functorial entropy. Although this may sound fancy, I spend most of my time doing (finite-dimensional!) linear algebra. I am very excited about this research direction, and I think a good part of it is approachable. Videos on a categorical introduction to Bayes’ theorem, which provides a nice background for the work on disintegrations below, can be watched here: https://www.youtube.com/playlist?list=PLSx1kJDjrLRQksb7H9fqRE8GVMJdkX-4A.

I have also spent some time thinking about higher gauge theory, and more generally 2-dimensional algebra. This describes a way of associating algebraic data to 2-dimensional surfaces that is compatible with the way that 2-dimensional surfaces can be glued (i.e. “sewn”) together.

Even earlier, I worked on condensed matter and periodic potentials using functional analysis and measure theory.

I’m generally interested in many, many, many things. It would be obnoxious to list all the subjects/topics. But some of my favorites to think about from time to time include: the information paradox, operator algebras, quantum measurement, life, homotopy theory, algebraic topology, non-commutative geometry, higher category theory, geometric quantization, etc.

Below, I include some preprints and publications, organized first by category and then from most recent to older works.

Analysis

Algebraic quantum theory

Higher gauge theory

Condensed matter