Research (Mathematics)

Dr Matthew Daws

Dr Daws is interested in the interactions between algebra and analysis, typically looking at algebraic structures which have a good notion of distance, or a topology, and studying how these two structures interact.  Recently, he has been principally interested in:

– The study of locally compact groups (including countably infinite discrete groups), their actions, and algebras, such as group C* and von Neumann algebras, and the Fourier algebra.

– Operator Algebraic approaches to Quantum Groups, which grew out of efforts to extend Pontryagin Duality beyond abelian groups, but which also have many links with the more algebraic theory of Quantum Groups, and the study of symmetries of Operator Algebras.  Recent work has looked at actions of quantum groups, approximation properties, and “categorical” aspects.

– Older work looked at the abstract theory of classes of Banach algebras, drawing analogies with the smaller but richer class of Operator Algebras.

Dr Daws has also worked in the Financial Industry as a Java Developer, and most recently, as an inter-disciplinary researcher and Python programmer, interacting with Geographers and Criminologists.  He remains interested in Software Development (Object-Oriented Designed, Test Driven Development) and in Reproducible Research: the use of Open Data, Open Source software, and especially, in the use of such data, software, and related tools, to allow the entire lifecycle of computational research to the reproduced.  He is interested in inter-disciplinary research which involved Mathematical Model and the novel use of computational tools.

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Dr Davide Penazzi

Dr Davide Penazzi is interested in Model Theory and Applications. Applied Model Theory is the study of mathematical structures with a viewpoint informed by Logic. In particular, he studies real closed fields (whose axiomatic structure is equivalent to that of the real numbers) with particular attention to Nash groups definable in them. He is also interested in topological dynamics: the actions of groups on a compact space, in particular the action of a definable group on the space of its types.

He is also interested in Mathematical education, especially on the use of experiential learning and facilitation to increase motivation of studying mathematics in schools, developing mathematical resilience and helping with transition to HE.

Dr Christopher Powles

Dr Powles’s research interests lie mainly in the field of mathematical acoustics. To date, his work has involved the application of analytical techniques to problems related to aeroacoustics (specifically to the noise problems of modern aeroengines), and to problems in underwater acoustics and in loudspeaker design.


  • Propagation of fan tones from the bypass duct using the extended Munt method (Wiener-Hopf solution).


  • Propagation of sound through sheared steady mean flows, for applications to jet blockage.
  • Propagation of sound through unsteady (turbulent) sheared flows, for application to the prediction of spectral broadening of turbine tones.


  • Prediction of jet noise generated in mixer-ejector nozzles, for supersonic business jets.


  • Propagation of sound through sheared steady mean flows, for applications to engine installation effects.


Scattering of noise by rotating blade rows. Additional work carried out, not linked to any large-scale projects and with funding from a variety of sources including EPSRC, the Nuffield foundation, Rolls-Royce and uclan include

  • The behaviour of energy paths in sound fields.
  • Generation of noise by blade-vortex interaction.
  • Scattering of sound in non-uniform ducts.
  • Noise generation and propagation from open-rotor engines.
  • The use of Green’s function techniques in Computational Aeroacoustics.
  • Remote monitoring of sperm-whale populations.
  • The design of transmission-line loudspeaker cabinets.

Dr Jonathan Wilson

Dr Wilson’s research focuses on the interplay between combinatorics, geometry, and representation theory. Specifically, he aims at using cluster algebras (and related structures) to unearth deep connections between these subjects. Recently, he has primarily been interested in:

  • Cluster algebras from surfaces;
  • Quiver representations;
  • Teichmüller theory of non-orientable surfaces, and related cluster structures.

Please see for more details.