Speaker: Emil Have

Affiliation:
University of Edinburgh

Title:
Newton-Cartan Submanifolds and Fluid Membranes

Abstract:
Originally developed to provide a geometric foundation for Newtonian gravity, Newton-Cartan geometry and its torsionful generalization have recently experienced a revival of interest, particularly in the contexts of non-AdS holography and various condensed matter problems — notably the quantum Hall effect. In this talk, I will describe a general theory of Newton-Cartan submanifolds. A covariant description of non-relativistic fluids on surfaces is an important open problem with a wide range of applications in for example soft matter systems. Recasting `elastic’ models, such as the Canham-Helfrich bending energy, in a Newton-Cartan setting allows for a covariant notion of non-relativistic time and provides the ideal starting point for a treatment of Galilean invariant fluids on extremal submanifolds using the technology of hydrostatic partition functions.