Research

My research lies at the intersection of category theory, quantum theory, mathematics, and theoretical computer science.

I am particularly interested in categorical structures that provide mathematical frameworks for describing quantum systems, and which may be used to extend categorical quantum mechanics to settings involving infinite-dimensional systems.

PhD Research¶

Infinite-Dimensional Categorical Quantum Mechanics¶

My doctoral research investigates mathematical structures for developing infinite-dimensional categorical quantum mechanics.

The project explores how categorical models of quantum theory can be extended beyond the finite-dimensional setting.

Some relevant topics for this research are the following:

• $*$-autonomous categories

• Linearly distributive categories (LDCs)

• Operator spaces

• Matrix regular operator spaces

• Differential categorical structures

• Quantum harmonic oscillator

• Domain theory

The project is being developed jointly at Université Paris-Saclay (LMF, QuaCS) and Macquarie University.

(The website is still under construction, so there isn’t a lot of information yet, but I will update it regularly!)