Gradient Flows in Metric Spaces

What it is about

You will learn the analytical and geometric foundations of the metric theory of gradient flows. In the end you will be able to investigate existence, regularity and long-term behavior of such flows and qualitatively analyze solutions of the associated class of partial differential equations.

What you will be able to do

• Analytical fundamental concepts of metric gradient flows
• Geometric fundamental concepts of metric gradient flows
• Techniques for existence proofs of gradient flows
• Methods for regularity analysis
• Analysis of the long-term behavior of gradient flows
• Qualitative analysis of the associated partial differential equations

What the module consists of

• VorlesungConveying the material with a focus on linking geometric ideas and functional-analytic techniques
• ÜbungIn-depth discussion of the lecture material and solving exercises

Teaching method

• VortragLinking visually-geometric ideas with functional-analytic techniques, also for non-smooth infinite-dimensional situations
• ÜbungDiscussion of the current material and solving exercises