During the 2018-19 academic year, the School will have a special program on Variational Methods in Geometry. Fernando Codá Marques of Princeton University will be the Distinguished Visiting Professor.
Confirmed senior participants for Term I: Richard Schoen and Andre Neves Term II: Tristan Rivière
Geometric variational problems have been studied by mathematicians for more than two centuries. The theory of minimal submanifolds, for instance, was initiated by Lagrange in 1760. Minimization principles have been extremely useful in the solution of various questions in geometry and topology. Most recently, and remarkably, minimax principles and unstable critical points have given us new tools and played a key role in the solution of old problems.
Many basic questions about existence and regularity remain to be solved. Recent advances suggest this is an exciting time for the field. This program will cover a variety of topics, including minimal submanifolds, harmonic maps, Willmore and constant mean curvature surfaces, eigenvalue extremal problems, systolic inequalities, connections with phase transition partial differential equations and others. The goal of the program is to develop further the variational theory of these objects and to find new connections between the themes.