51³Ô¹ÏÍø

Abstract: The problem of finding minimal surfaces in general manifolds has been of significant interest to differential geometers for at least 100 years. In broad terms, this can be construed as the problem of finding critical points of the area functional defined on some appropriate space of surfaces. Making sense of this is not easy, for one because it is not clear what the appropriate space should be. All available options come with significant technical challenges.

In the 1970s, the school of de Giorgi proposed a different approach whereby the area functional is ‘regularised’ to a family of functionals depending on some small parameter. This family has the benefit of being defined on a standard function space and of having critical points described by a nice PDE. The hope is that, after sending the parameter to zero, one can recover minimal surfaces from critical points of the regularised family. In this talk, I will tell this story and time-permitting explain some recent developments in higher codimension. I will take care to define things from the ground up, so the talk should be accessible to people without a background in this area.