Melchior Wirth - Gradient flows in Euclidean, Hilbert, and metric spaces

Flows of gradient vector fields in Euclidean space or on Riemannian manifolds are a classical object in several field of mathematics. Recent years have seen an uprise of interest in generalizations of the concept of gradient flows to metric spaces, in particular in the study of evolution equations and Ricci curvature bounds of non-smooth spaces. In this talk I want to give a gentle introduction to the theory of gradient flows and show how the definitions in Hilbert and metric spaces can be viewed as natural extensions of the Euclidean case. If time permits, I will finish the talk by giving a primer on Otto calculus, which concerns the identification of the heat flow with the gradient flow of the Boltzmann entropy.