数学所周五学术报告—Metric measure spaces and synthetic Ricci bounds – from optimal transport to Ricci flow
主 题: 数学所周五学术报告—Metric measure spaces and synthetic Ricci bounds – from optimal transport to Ricci flow
报告人: Professor Karl-Theodor Sturm (University of Bonn, Germany)
时 间: 2017-06-02 15:00-16:00
地 点: 理科1号楼1114
Abstract: We give a brief introduction to the theory of metric measure spaces with synthetic Ricci bounds as introduced by Lott-Villani and the author and to the analysis on these spaces as developed by Ambrosio-Gigli-Savare. A key observation is the equivalence of the entropic curvature-dimension condition in the sense of Lott-Sturm-Villani and the energetic curvature-dimension condition in the sense of Bakry-Emery. Based on these concepts, in recent years a powerful analysis on singular spaces has been developed with deep results and far reaching applications (heat kernel comparison, Li-Yau estimates, splitting theorem, maximal diameter theorem, coupled Brownian motions).
Of particular interest are extensions of these results to a time-depending setting which
provides new insights for (super)Ricci flows of metric measure spaces.