Our research

The results of the Research Excellence Framework (REF 2014) showed that 59.6% of our research outputs were regarded as world leading (4*) or internationally excellent (3*).

Our research was highlighted in the International Review of Mathematical Sciences 2010 as making an important contribution to the UK’s world-leading position in stochastic analysis.

Algebra and Topology Group

Hairy Ball Theorem (pic off Web/Wikipedia)

We are a diverse and active research group with a number of PhD students, an active weekly seminar, and many international connections and collaborations.

Our research group's areas of interest include:

  • Algebras of operations and cooperations for cohomology and K-theory
  • Categorical methods in algebra and topology
  • Homotopy theory and homological algebra
  • Hopf algebras, coalgebras and corings
  • K-theory
  • Noncommutative geometry
  • Ring and module theory
  • Topology of moduli spaces, operads and low-dimensional topology
  • Topological field theory
  • Triangulated categories
  • Tropical geometry

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Stochastic Analysis Group

Pressure exerted by collision (pic off web/Wikipedia)

In the International Review Mathematics U.K. 2010 this group was flagged up (as in 2004) to contribute significantly to the U.K.'s world leader status in Stochastic Analysis.

Our group's research interests include:

  • Functional inequalities and applications
  • Infinite dimensional stochastic analysis
  • Information theory
  • Lévy-type processes
  • Mathematical biology and epidemiology
  • Non-commutative (quantum) probability
  • Numerical simulation of stochastic processes
  • (Quantum) statistical mechanics
  • Stochastic modelling of fractal, multifractal and multiscale systems
  • Stochastic partial differential equations and applications to fluid mechanics

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Research in Mathematics Education


The education research group was formed between the Education Department in UWTSD and the Mathematics Department in Swansea University in 2014. It was initiated as part of the Mathematics Department’s growing interest in and influence over school mathematics education in Wales. The Department has been running the Further Mathematics Support Programme Wales since 2010 which positively impacted on participation and attainment in Further Mathematics in Wales. 

The research undertaken by the group aims to:

  • Inform the policies and practices of FMSP Wales,
  • influence positive change in the mathematics teaching community,
  • deliver positive changes to the mathematics curriculum and school provision through liaising with policymakers.

The group is led by Sofya Lyakhova and Andrew Neate and is supported by the School of Education in Swansea University.

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Mathematical Methods in Biology and Life Sciences Group

Brain Image2

Our group applies cutting edge mathematical and computational techniques to solve research problems from across the biosciences and medicine. Our expertise includes mathematical modelling and scientific computing, and our interdisciplinary work involves collaboration with scientists from academia, healthcare and industry.

Our research groups areas of interest include:

  • Mathematical pharmacology
  • Heat and mass transfer models for plant cooling 
  • Modelling cellular signal transduction dynamics 
  • Mathematical Oncology: Multiscale modelling of cancer growth, progression and therapies, and modelling-optimized delivery of multi-modality therapies
  • Multi-scale Analysis of Individual-Based Models
  • Spreading speeds and travelling waves in ecology
  • High Performance Computing

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Centre for Biomathematics

The Centre for Biomathematics provides a cross-community, interdisciplinary focus for experts from across the College of Science and beyond with interests on the interface between mathematics and biology or medicine.

Analysis and Nonlinear Partial Differential Equations Group

Lorenz Attractor (pic off web/wikipedia)

We combine skill in analysis and the theory of nonlinear PDE with computation expertise.

Our research group's areas of interest include:

  • Calculus of variations and critical points theory
  • Morse Theory in nonlinear PDEs
  • Reaction-diffusion equations and systems
  • Nonlinear Schrödinger equations
  • Pseudo-differential operators generating semi-groups
  • Numerical solution of PDEs

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