Research

My research interests sit within three major areas of modern functional analysis and mathematical physics: operator algebras, quantum information theory, and quantum groups/quantum symmetries. I am interested in the theoretical development of these areas independently, as well as the (many) interactions between them.

Pre-prints

1. A. Gow and R. Hernández Palomares, Property (SP) and Inclusions of C*-algebras, (2026) arXiv:2608.30057 (submitted - under review).
2. A. Gow, On the Quasitrace Problem and a Characterization of W*-algebras, (2026) arXiv:2601.04431 (submitted - under review).

In progress

1. M. Brannan, J. Crann, and A. Gow, Mixed Quantum Unitary Channels and Bi-Unitary Dilations, ongoing project.

Dissertation

My PhD thesis is currently in progress; the two overarching topics of my dissertation are "C*-algebras with lots of projections" and "quantum logic(s)". These topics are tied together by the fact that a quantum logic is (modeled by) a complete orthomodular lattice of projections.

Mathematically, a quantum system can be described by a C*-algebra. In (operator algebraic) quantum theory, it is common to impose a strong topological condition on the C*-algebra of interest, by requiring it to be a von Neumann algebra (or a W*-algebra); from the perspective of a C*-algebraist, this is very restrictive. It turns out that AW*-algebras ("algebraic W*-algebras") capture much of the needed structure for the development of quantum theory, without the topological requirements.

An AW*-algebra is a unital C*-algebra with lots of projections (they have Property (SP)) and the projections form a complete lattice (a quantum logic). Unsurprisingly, these have become central objects of interest in my studies (see above).