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.
Algebraic quantum theory
- “A non-commutative Bayes’ theorem,” with Benjamin P Russo (2020) Available as
- “Inverses, disintegrations, and Bayesian inversion in quantum Markov categories,” (2020) Available as
- “Non-commutative disintegrations: existence and uniqueness in finite dimensions,” with Benjamin P Russo (2019) Available as
- “Stinespring’s construction as an adjunction,” Accepted in Compositionality on 2019-07-24
- “From observables and states to Hilbert space and back: a 2-categorical adjunction,” Applied Categorical Structures, Vol. 26, Issue 6, pp 1123-1157 (2018). Available as https://link.springer.com/article/10.1007/s10485-018-9522-6 and
- “Discrete probabilistic and algebraic dynamics: a stochastic Gelfand-Naimark Theorem,”
Higher gauge theory
- “Two-dimensional algebra in lattice gauge theory,” Journal of Mathematical Physics 60, 043506 (2019); https://doi.org/10.1063/1.5078532. Also available as
- “Gauge invariant surface holonomy and monopoles,” Theory and Applications of Categories, Vol. 30, No. 42, pp 1319-1428 (2015)
- “Sufficient conditions for two-dimensional localization by arbitrarily weak defects in periodic potentials with band gaps” with Karen K. Y. Lee, Yehuda Avniel, and Steven G. Johnson, Phys. Rev. B 81, 155324 (2010)