About

The underlying theme of the group is the application of rigorous mathematical models to quantitatively analyse and understand in depth problems in science and engineering. We have a wide range of mathematical expertise and techniques in modelling, from partial differential equations, to agent modelling, dynamical systems, or topological methods. Often, the research take place in close interdisciplinary collaborations. As an example, we have developed a very successful model of lithium-ion batteries by combining classical differential equation modelling with asymptotic analysis and state of the art coding to produce a software package that is both fast and comprehensive.  Other examples are the application of asymptotic analysis in controlling aircraft sounds, stochastic methods in modelling gene expression and agent-based techniques in healthcare.  We apply topological data analysis to model phase transitions of mesoscopic physical systems, and to enhance and up-scale optical imaging in medical applications, as precursors to efficient machine learning and data analysis.

Droplets of water falling on water along with their concentric wave patterns

Applicable Resurgent Asymptotics: towards a universal theory. An Isaac Newton Institute Programme

An innovative Southampton initiative, that brought together mathematicians and theoretical physicists from around the world, is helping shed light on complex challenges in mathematics and physics.

Read more
  • Image of graphene

    Disorder is Good – Taming disorder in self-assembled materials with topology

    Instead of fighting disorder, we should identify structures that are ordered enough to perform the required function.
    We have combined cutting edge experiments with breakthrough methods from topological data analysis to quantify emerging structure in apparently disordered nano-assemblies and classify their response to light. We aim to design a new generation of controllable nanosystems at a fraction of the cost of the current methods.

    Read more

People, projects, publications and PhDs

People

Giampaolo D'Alessandro
View profile
Mathematical modelling allows you to see the world as an interconnected whole, with causes and effects, so that we can fulfil knowledgeably our responsibility to sustain it.

Related research institutes, centres and groups