Cartan geometries in soft matter

This project will study the applications of Cartan geometries to soft matter physics. Cartan geometries provide a more general framework than Riemannian geometries admitting, in particular, the notion of the torsion of a space. The latter is essentially in describing topological defects in phases with broken translational symmetries. The project will focus on gauge theories of defects in ordered phases, the dynamics of submanifolds of Euclidean spaces, and the geometry of irreversibility in stochastic dynamics.