Online Talk

 In the 1980s Frederick J. Almgren and Bill Browder started a program aimed at studying the regularity of minimal surfaces with tools and techniques from differential topology and homotopy theory. This led them to announce the solution to basic questions in geometric measure theory and, in particular, in the Federer-Fleming theory of integral currents; however, the project was never finished and no proof of the announced results ever appeared. In this seminar I will describe a joint study with Bill and Camillo De Lellis in which we complete the program started with Almgren, providing a full answer to the question of how closely one can approximate an integral current representing an integral homology class by a smooth submanifold.