New connections in mathematical physics
Project ID: 2228cd1409 (You will need this ID for your application)
Research Theme: Mathematical Sciences
UCL Lead department: Mathematics
Lead Supervisor: Rod Halburd
Project Summary:
The aim of this project is to pursue new developments within the fields of general relativity, integrable systems, and continuum mechanics, and especially to develop new links between the three.
Within general relativity, research will focus on (i) modifications of the Einstein-Hilbert action, and (ii) the use of dynamical systems in cosmology. The latter allows the study of very generic cosmological models which can then be tested against observational data.
In continuum mechanics, we will investigate Cosserat elasticity or micropolar elasticity, which shows some surprising similarities with general relativity.
Integrable systems are described by non-linear ordinary differential equations or partial differential equations for which it is possible to find exact solutions - two well-known examples are the Korteweg–de Vries equation and the Sine-Gordon equation. Understanding under which conditions a system of equations is integrable is an important line of research.