In mathematically oriented research we attempt to crystallise clear and appliable definitions of a system being complex, in the sense of being more than the direct combination of its components.

The notion of Emergent behaviour is a key focus of our attention, and connnects to the question of forecastability vs chaos in complex systems and more mathematically to non-uniqueness of Gibbs phases.

Specifically identifying the emerging behaviour is crucial in real examples: we are researching general methodologies for variable reduction on networks, the identification of continuum limits in particle systems, and of coherent phenomena in turbulent systems.

 Application areas:

• theory of complex systems
• weather & climate
  
• understanding jet and resonant wave formation in atmospheric and ocean flows
• contributing to controlling stability of fusion plasmas.

People:

• Robin Ball
• Robert MacKay