We invite applications for a Postdoctoral Research Associate (PDRA) to join the EPSRC Hub on the Mathematical and Computational Foundations of Artificial Intelligence. One PDRA will be recruited to work within one of, or across, the four research themes: Learning with Structured & Geometric Models, Low Effective-dimensional Learning Models, Implicit Regularization, and Reinforcement Learning through Stochastic Control (a brief description of each these is as follows (additional details are in the further particulars):
Flowing to Free Boundary Minimal Surfaces
Abstract
In this talk, I will discuss an approach to free boundary minimal surfaces which comes out of recent work by Struwe on a non-local energy, called the half-energy. I will introduce the gradient flow of this functional and its theory in the already studied case of disc type domains, covering existence, uniqueness, regularity and singularity analysis and highlighting the striking parallels with the theory of the classical harmonic map flow. Then I will go on to present new work, joint with Melanie Rupflin and Michael Struwe, which extends this theory to all compact surfaces with boundary. This relies upon combining the above ideas with those of the Teichmüller harmonic map flow introduced by Rupflin and Topping.