Research/projects

I am driven by the information-theoretic aspects of nature. I am especially curious about the nature of space and time and their relationship to quantum information theory. Although motivated largely by questions stemming from physics, I generally adhere to strict mathematical logic in formulating definitions, making statements, and proving theorems. Category theory provides me with the structure to do this, and it appears heavily in my thinking.

More specifically, my research program primarily focuses on extending inference, retrodiction, Bayes’ rule, entropy, and causality to quantum systems and dynamics.

Videos on a categorical introduction to (classical) Bayes’ theorem can be watched here: https://www.youtube.com/playlist?list=PLSx1kJDjrLRQksb7H9fqRE8GVMJdkX-4A.

I have also spent some time thinking about K-theory, higher gauge theory, and 2-dimensional algebra. The latter 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.

During the summer of 2009, while still an undergraduate in Queens College (CUNY), I visited Steven G. Johnson at MIT. There, we worked on a project in condensed matter to prove the existence of bound states for certain periodic potentials using tools from functional analysis and measure theory. The summer internship resulted in a publication in Phys. Rev. B.

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

Quantum Bayes, Probability, and Retrodiction

Entropy

  • “A functorial characterization of von Neumann entropy” Cah. Topol. Géom. Différ. Catég. LXIII, 1 (2022), 89–128, arXiv: 2009.07125 [quant-ph]
  • (with James Fullwood) “The information loss of a stochastic map,” Entropy 23, no. 8 (2021). DOI: 10.3390/e23081021, arXiv: 2107.01975 [cs.IT]
  • “Towards a functorial description of quantum relative entropy,” in: Nielsen F., Barbaresco F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science, vol 12829. Springer, Cham. (2021). DOI: 10.1007/978-3-030-80209-7_60, arXiv: 2105.04059 [quant-ph]

Algebraic quantum theory and operator algebras

K-theory

Analysis

Higher gauge theory

Condensed matter

"You can never verify a theory, you can only verify its predictions." – Venkataraman Balakrishnan