Title: Synthetic notions of Ricci flow for metric measure spaces
Abstract: We develop different synthetic notions of Ricci flow in the
setting of time-dependent metric measure spaces based on ideas from
optimal transport. They are formulated in terms of dynamic convexity and
local concavity of the entropy along Wasserstein geodesics on the one
hand and in terms of global and short-time asymptotic transport cost
estimates for the heat flow on the other hand.
In this talk we will recall the Lott-Sturm-Villani theory on the
synthetic lower Ricci bound and its generalisations. For the notions of
synthetic Ricci flow, we show that they both characterise smooth
(weighted) Ricci flows and will discuss their relations by providing
examples.
The talk is based on joint work with Matthias Erbar and Timo Schultz.
