Henrik Schumacher - Repulsive Curves and Surfaces

I am going to report on recent work on the numerical optimization of tangent-point energies of curves and surfaces. After a motivation and brief introduction to the central computational tools (construction of suitable Riemannian metrics on the space of embedded manifolds, a polyhedral discretization of the energies, and fast multipole techniques), I am going to show a couple of numerical results. Not much about the shape of minimizers has been know so far. So, for the first time, we will be able to admire the beauty of the energies' minimizers and gradient flows.

This is based on joint work with Philipp Reiter (Chemnitz University of Technology) and Caleb Brakensiek, Keenan Crane, and Chris Yu (Carnegie Mellon University, Pittsburgh).