Metric analysis

In recent years, the development of analytic tools to study geometric questions in metric spaces beyond Riemannian manifolds has seen tremendous progress and led to many structural results which shed a new light even on classical questions. The goal of this HIM program is to further refine such tools and explore their applications, like the study of filling invariants, norms, volumes, energies, in various concrete geometric frameworks.

The program aims at bringing together researchers in analysis on metric spaces, geometric group theory, differential geometry, higher Teichmüller theory and low dimensional topology to isolate and enhance common core ideas and tie these strands to a more global theory, geared at making progress towards some well established open problems.

The trimester will includ

• an Introductory Winter School "Analysis and geometry on groups and spaces" (January, 27-31),
• the Felix Klein Lectures,
• and an International Conference "Differential geometry beyond Riemannian manifolds” (March, 24-28).