Summer Graduate School
| Parent Program: | -- |
|---|---|
| Location: | UC Berkeley |
Show List of Lecturers
- Otis Chodosh (Stanford University)
- Giada Franz (Centre National de la Recherche Scientifique (CNRS))
- Daniel Ketover (Rutgers University)
- Yevgeny Liokumovich (University of Toronto)
Show List of Teaching Assistants
- Bruno Staffa (Rice University)
- Douglas Stryker (Stanford University; ETH Zürich)
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
Elliptic PDE (any standard graduate first course) and basic Riemannian geometry (at the level of Do Carmo’s graduate text).
Application Procedure
For eligibility and how to apply, see the Summer Graduate Schools homepage.
minimal surfaces
min-max theory
Allen-Cahn
interfaces
Almgren- Pitts
variational methods