Quantum mathematics
The study of the mathematics underpinning quantum physics, quantum computing and quantum information theory: the algebraic structure of transformations in infinite dimensions, deformations of classical geometry, new tools in topology and dynamics, and the deep mysteries of quantum field theory.
Quantum mathematics is the essential mathematical framework of quantum mechanics. It uses tools like linear algebra, spectral theory and complex variables to describe the behaviour of subatomic particles, model quantum systems like quantum computers, and untangle the riddles of quantum information and communication. Quantum mathematics represents phenomena like wave-particle duality and quantization through the abstract concepts of spectral theory for linear operators on infinite-dimensional vector spaces, abstract algebras and operator algebras, topological dynamics, and probability distributions. It provides a precise and predictive mathematical language for the behaviour of our universe at the scale of individual subatomic particles, which utterly defies our macroscopic intuition.
Group members
Research interests
Anna Duwenig works in noncommutative topology and noncommutative geometry. Her focus is on C*-algebras built from topological groupoids and the reconstruction of these groupoids from functional analytic data such as Cartan subalgebras. She is further interested in self-similarity and Zappa-Szép products, for example of groupoids, k-graphs, and Fell bundles.
Aidan Sims' work lies in functional analysis, operator algebras, noncommutative geometry, and their interactions with dynamics, graph theory, groupoids, and quantum mathematics.