Summer Graduate School

The course will introduce graduate students to the many modern methods to construct minimal surfaces from a variational or min-max principle as well as applications to problems in geometry and topology. Topics include Almgren-Pitts min max theory, Allen-Cahn construction and PDE methods, the proof of the Willmore conjecture, the resolution of Yau’s conjecture on the infinitude of minimal hypersurfaces in general Riemannnian manifolds and corresponding Weyl law and equidistribution results.

School Structure

The program will feature two mini-courses:  

Week 1: Minimal surfaces and min-max theory: basic constructions, techniques and applications (lectures by Daniel Ketover and Giada Franz)

Week 2: Further techniques and applications (lectures by Yevgeny Liokumovich and Otis Chodosh)

The problem and research discussions will be informal, interactive and focus on exercises from the lectures, examples, as well as expanding on any material only cursorily covered.

Prerequisites

PDE:
Partial Differential Equations by L. C. Evans   (Chapter 2, 5, 6, 8)
Elliptic PDE by Q. Han and F. Lin (Chapter 1 - 4)  (includes more advanced material)

Geometry:  (Either one of the following would be useful, which cover the same material)
Introduction to Riemannian geometry by J. Lee. (Chapter 1 -8)
Riemannian Geometry by M. do Carmo (Chapter 1 - 6)

Application Procedure

For eligibility and how to apply, see the Summer Graduate Schools homepage.