06.06.2023, 15 Uhr
Phenomena in High Dimensions
Pierre Youssef (New York University, Abu Dhabi)
Ulrich Pinkall (Berlin), Max Wardetzky (Göttingen)
Ulrich Pinkall (Berlin): Schrödinger Smoke
In Physics, the motion of "super fluids" or "quantum fluids" is described by a nonlinear Schrodinger
equation. These fluids have no viscosity and all the vorticity is concentrated in one-dimensional
filaments of uniform strength. The vortex filaments are the zero-set of the complex-valued wave
function on the fluid domain. Therefore, they are of a topological nature and thus extremely stable.
In this talk we propose to use the quantum fluid equations to overcome problems arising from fluid simulations in Computer Graphics. The resulting numerical algorithm is extremely simple and
Max Wardetzky (Göttingen): Variational convergence of minimal surfaces
Minimal surfaces in Geometry are surfaces which locally minimize the surface area, i.e. they are
critical points of the area functional with respect to local variations. Minimal surfaces also appear
in physics and everyday life e.g. as soap films. The theory of minimal surfaces has become one of
the corner stones of modern geometric analysis.
Discrete minimal surfaces are one of the most widely studied examples of discrete surfaces in
Discrete Differential Geometry. However their convergence to smooth minimal surfaces has only
been proven for special cases, such as for disk-like and cylinder-like topologies. Using tools from
variational analysis, I will present a convergence result for triangulated area-minimizing surfaces
that deals with the general case of arbitrary topology.