Mathematikgebäude, Hörsaal E29

Metric measure spaces with synthetic Ricci bounds have attracted great interest in recent years, accompanied by spectacular breakthroughs and deep new insights. In this survey, I will provide a brief introduction to the concept of lower Ricci bounds as introduced by Lott-Villani and myself, and illustrate some of its geometric, analytic, and probabilistic consequences, among them Li-Yau estimates, coupling properties for Brownian motions, sharp functional and isoperimetric inequalities, rigidity results, and structural properties like rectifiability. In particular, I will explain its crucial interplay with the heat flow and its link to the curvature-dimension condition formulated in functional-analytic terms by Bakry-Émery. This equivalence between the Lagrangian and the Eulerian approach then will be further explored in various recent research directions.

Mathematisches Kolloquium: Einblicke in die Wunder und Schönheit der Mathematik

Im Sommersemester 2025 sind weitere Vorträge im Mathematischen Kolloquium vorgesehen. Sie finden jeweils am Mittwochnachmittag statt.

Karl-Theodor Sturm

Rheinische Friedrich-Wilhelms-Universität Bonn