Title: Metric Measure Spaces with Synthetic Ricci Bounds
Speaker: Karl-Theodor Sturm
Speaker Info: University of Bonn
The talk will provide an introduction to the theory of metric measure spaces with generalized lower Ricci bounds and a survey of the state of the art of this fast developing field. The concept of generalized Ricci bounds can either be based on optimal transportation or on so-called Γ-calculus. 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.Date: Wednesday, February 11, 2015
The list of recent results includes Bakry-Ledoux space-time gradient estimate, Li-Yau differential Harnack inequality, distance monotonicity of coupled Brownian motions, splitting theorem, maximal diameter theorem, and structure of tangent spaces. Of particular interest are extensions of these results to a time-depending setting which provides new insights in (super) Ricci flows of metric measure spaces.