Cartan geometries in soft matter

这个项目将研究Cartan几何在软物质物理中的应用。Cartan几何提供了比黎曼几何更一般的框架，特别是承认了空间挠率的概念。后者本质上是用来描述平移对称性被破坏的相中的拓扑缺陷。这个项目将集中在有序相中缺陷的规范理论，欧几里德空间的子流形的动力学，以及随机动力学中的不可逆几何。

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.