Timo Schultz — Neckpinchhttps://neckpinch.com/authors/timo-schultz/New arXiv papers by Timo Schultz, from Neckpinch Tue, 03 Nov 2026 07:43:57 GMT Synthetic approaches to Ricci flowshttps://neckpinch.com/papers/2511.11477/arxiv:2511.11477Fri, 14 Nov 2025 00:00:00 GMTMatthias Erbar, Marco Flaim, Eric Hupp, Zhenhao Li, Timo Schultz, Karl-Theodor Sturm — We review different notions of synthetic Ricci flow that apply to time-dependent families of metric measure spaces and which are based on properties of the heat flow, ideas from optimal transport, and the asymptotic behaviour of volumes. Each notion equivalently characterises (weighted) Ricci flow for smooth families of weighted Riemannian manifolds. We discuss the features of the different notions on various examples.Ricci flowWeak & singular flowsLimit spaces & RCD Synthetic notions of Ricci flow for metric measure spaceshttps://neckpinch.com/papers/2501.07175/arxiv:2501.07175Mon, 13 Jan 2025 00:00:00 GMTMatthias Erbar, Zhenhao Li, Timo Schultz — 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. We show that these properties characterise smooth (weighted) Ricci flows. Further, we investigate the relation between the different notions in the non-smooth setting of time-dependent metric measure spaces.Ricci flowWeak & singular flowsLimit spaces & RCD