Title: From superconductors to minimal submanifolds
Speaker: Daniel Stern
Speaker Info: University of Chicago
Brief Description:
Special Note: Note unusual time
Abstract:
Since Lagrange's time, efforts to prove the existence of minimal submanifolds in various settings have given rise to a lot of beautiful mathematics, including the development of Morse theory and the Lebesgue integral. For minimal submanifolds of dimension one (geodesic curves) and codimension one (minimal hypersurfaces), the existence theory is by now fairly mature; however, the space of minimal submanifolds of higher dimension and codimension remains rather poorly understood, with few major advances since the 1960s. After surveying some of this history, I'll describe a new approach to the existence theory for minimal submanifolds of codimension two, based on connections to a well-studied family of geometric pdes with origins in the study of superconductivity and gauge theory. I'll highlight some initial successes of this approach and point to some open problems. (Based on joint work with Davide Parise and Alessandro Pigati.)Date: Wednesday, January 11, 2023