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Research group

Mathematical Modelling

Textures in a mesoscopic system made of a nematic liquid crystal doped with nanoparticles.

The modelling group focuses on mathematical modelling across science and engineering, including physics (from the physics of quanta and strings to that of liquid crystals), chemistry (modelling lithium-ion batteries and solar cells), engineering (controlling sound direction), biology, medicine and healthcare (from stem cell population dynamics to medical imaging and healthcare models).

Part of the Applied Mathematics and Theoretical Physics, Mathematical sciences

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.

Research highlights

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

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

Future societies and communities
AI, big data and analytics
Engineering
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.

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

AI, big data and analytics
Environment, sustainability and clean growth
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.
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People, projects, publications and PhDs

People

Dr Itamar Yaakov

Lecturer

Research interests

  • Quantum Field Theory
  • String Theory
  • Mathematical Physics
Connect with Itamar

Email: I.Yaakov@soton.ac.uk

Tel: +44 23 8059 4622

ORCID

Dr Ivan Korotkin

Senior Research Fellow

Research interests

  • Lithium-ion batteries
  • Numerical methods
  • High-performance computing
Connect with Ivan

Email: I.Korotkin@soton.ac.uk

Tel: +000

Google Scholar
ORCID
LinkedIn

Mr Javier Carballo

Research interests

  • Gravity
  • Holography
  • CFTs
Connect with Javier

Email: J.Carballo@soton.ac.uk

Mr Jishu Dey

Research interests

  • Dynamic Pattern Recognition
  • Predictive Analysis in Heath Science
  • Application of Advance Machine learning in Finance
Connect with Jishu

Email: J.Dey@soton.ac.uk

Tel: +447440178378

ORCID

Professor Kostas Skenderis

Chair in Mathematical Physics

Accepting applications from PhD students

Connect with Kostas

Email: K.Skenderis@soton.ac.uk

Tel: +44 23 8059 2332

Google Scholar
ORCID

Professor Leor Barack

Professor of Mathematical Physics

Research interests

  • Classical General Relativity
  • Gravitational waves
  • Black Holes

Accepting applications from PhD students

Connect with Leor

Email: L.Barack@soton.ac.uk

Tel: +44 23 8059 5134

ORCID

Dr Lu Heng Sunny Yu

Teaching Fellow

Research interests

  • Quantum gravity, Quantum field theory, Relativity, Gravity and Cosmology
  • Mathematics and Physics Education
Connect with Lu Heng Sunny

Email: LHS.Yu@soton.ac.uk

Tel: +44 7563113124

ORCID
LinkedIn

Dr Michael Kenna-Allison PhD

Teaching Fellow

Research interests

  • Modified Gravity & Cosmology.
  • Dark Energy Theories.
Connect with Michael

Email: M.Kenna-Allison@soton.ac.uk

Dr Mozhdeh Shiranirad

Research Fellow in Machine Learning

Research interests

  • AI for life science and health-care
  • Programming and Development
  • Data Science
Connect with Mozhdeh

Email: M.Shiranirad@soton.ac.uk

Tel: +44 23 8059 7546

ORCID

Professor Nils Andersson

Professor of Applied Maths

Research interests

  • General relativistic astrosphysics
  • Black holes
  • Neutron stars

Accepting applications from PhD students

Connect with Nils

Email: N.A.Andersson@southampton.ac.uk

Tel: +44 23 8059 4551

ORCID
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.
Emeritus Professor Giampaolo D'Alessandro

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