An Operad of Operad Algebras
In this talk we present a construction that takes a coloured operad O and produces a new operad who algebras are functors into O-algebras. From the Categories and Companions Symposium 2022.
Research
My research is in mathematical physics: developing ways of making arguments and objects from quantum field theory mathematically rigorous. Currently my focus is on understanding the mathematical underpinnings of correlation functions and scattering amplitudes.
Along the way, the mathematical tools I use introduce me to interesting problems in Lie theory, functional analysis, algebra, and category theory.
Preprints and Publications
- A Lie Correspondence in the Setting of Hopf and Frobenius Algebras, arxiv:2610.04046
- On Diamond-Free Subgroup Lattices, arXiv:2307.06568
- A polar decomposition for quantum channels (with applications to bounding error propagation in quantum circuits) (with A. Carignan-Dugas and J. Emerson), Quantum 3, 173 (2019), arXiv version: arXiv:1904.008897
Theses
PhD Thesis (Mathematical Physics)
A Frobenius and Hopf Algebraic Formulation of Quantum Field Theory (2025)
Masters Thesis (Quantum Information)
A Polar Decomposition for Quantum Channels: Theory and Applications (2019)
Undergraduate Thesis (Condensed Matter)
Entanglement Characterization of Topological Phases of Kitaev's Honeycomb Model (2017)