Effective Theories for the Dynamics of Surfaces: From Biophysical Fluid Membranes to Black Holes

Course description

The course will take place in the second half of the fall semester 2018 (27.11-06.12) in room B1. Dates for the meetings are:
Tuesdays from 9-12 on 27.11 and 04.12,
Wednesdays from 9-11 on 28.11 and 05.12 and
Thursdays from 10-12 on 29.11 and 06.12.

For small deformations or for slow time scales, the physics of interfaces can be modelled by long-wavelength effective theories. These theories are theories of continuous media and can be purely hydrodynamic, purely elastic or contain elements of both. Using a covariant formulation, this general class of theories can be put into a single framework, allowing to describe the dynamics of (fluid) membranes, soap bubbles, space-filling fluids with or without boundaries and also confined fluids. Starting with simple examples, such as the Canham-Helfrich model for lipid vesicles and space-filling fluids, two different approaches will be highlighted, namely, a phenomenological approach to hydrodynamics and an approach based on an effective action (or equilibrium partition function). The mathematics of embedded (minimal) surfaces, which has a variety of applications in physics, will be dwelt with. As an example of such applications, a connection with gravity will be highlighted, in particular, in the effective description of black holes. In addition, using basic elements of Newton-Cartan geometry, it will be shown how gravity has led to new insights into the equilibrium states of soft condensed matter systems.

Lecturer

Dr. J. Armas