Min-max Techniques in Geometry

The length of the largest leaf of a one-dimensional foliation of a two-dimensional disk is not less than the diameter of the disk. The generalization of this fact to higher (co-)dimension requires beautiful and deep geometric insights. The relevant min-max techniques have been crucial in the recent proof of the Willmore conjecture and in the solutions of many other open problems.

In this course we will familiarize ourselves with these techniques using growth bounds on min-max volumes of families of cycles in an n-dimensional ball by Gromov and Guth as a guideline.

The lectures will link topology, geometry and metric properties of spaces.

Date and time info
Thursday 13:30 - 15:00

Keywords
Almgren-Pitts min-max theory, Gromov-Guth families, Willmore conjecture

Prerequisites
Basic Geometry and Topology

Audience
MSc students, PhD students, Postdocs

Language
English