Mathematical Physics
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Group Members
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Projects
Applied Matrix Positivity
01/03/2021 → 30/06/2021
Research
The Alliance Hubert Curien Programme 2021: Noncummuatative Probabilty, Matrix Analysis and Quantum Groups (NP, MA & Q Groups)
01/01/2021 → 31/12/2022
Research
Algebraic Quantum Field Theory in the UK
01/10/2020 → 30/11/2020
Research
Permutation Patterns as Noncommutative Central Limits
01/10/2020 → 30/09/2021
Research
Mathematical Theory of Symbiosis
01/08/2020 → 31/07/2021
Research
Support of Collaborative Research with Prof E. Steingrimmson at Hrísey, Iceland
01/08/2020 → 31/07/2021
Research
Combinatorial and Geometric Methods in Representation Theory
20/01/2020 → 19/01/2022
Research
Algebraic Quantum Field Theory in the UK
01/10/2019 → 30/09/2021
Research
An introduction to quantum filtering
24/06/2019 → 13/09/2019
Research
Undergraduate Mathematics Society Meetings Grant
03/03/2019 → 03/03/2019
Research
Supplementary Issue of Glasgow Mathematical Journal on Non-Associative Algebras
01/12/2018 → 30/11/2020
Research
Quantum Random Walks and Quasi-Free Quantum Stochastic Calculus
05/01/2015 → 04/01/2017
Research
Reconstructing Broken Symmetry
28/11/2014 → 27/03/2016
Research
KTP:Industrial Mathematics shorter KTP with BT Research: TV Whitespace Interference Modelling
20/02/2013 → 19/07/2013
Research
Spectral Properties of Magnetic Operators (Funded Project)
01/07/2007 → 30/06/2010
Research
Research Activity
Mathematical physics encompasses a wide variety of topics that interface with disciplines in pure mathematics. What they have in common is that they are motivated by a desire to contribute to the understanding of phenomena arising in physics using mathematics - algebra, analysis, geometry, topology, probability, the theory of differential equations and more.
Research in our group focusses, in particular, on the following areas
- Quantum theory and partial differential equations. Spectral and other mathematical properties of differential operators arising in quantum mechanics, in particular, Schrodinger and Dirac type operators.
- Algebraic and geometric structures. Noncommutative algebraic and geometric structures, such as quantum analogues of classical Lie-theoretic objects, for founding new theories.
- Conformal Field Theory. Mathematically rigorous conformal quantum field theory, in particular, the operator algebraic frameworks of algebraic quantum field theory, and vertex operator algebras.
- Quantum theory of open systems. The mathematics of irreversible quantum dynamics, in particular dilation to reversible dynamics via operator algebraic and quantum stochastic means. Open systems arise in quantum computing, decoherence and control theory.
- Quantum probability and quantum symmetry. Quantum stochastic processes, in particular, Levy processes on (locally) compact quantum groups.
Members of the group are also affiliated with the LMS network Algebraic Quantum Field Theory in the UK.