Welcome to SPP 2026
This is the platform of a coordinated research programme in mathematics, funded by the German Research Foundation (DFG). It comprises 80 research projects in the fields of differential geometry, geometric topology, and global analysis. More than 80 researchers from doctoral to professorial level and based at more than 20 German and Swiss universities are represented in this programme.
Latest publications
Non-collapsing, non-inflating and convergence results for solutions to Ricci flow with $L^{p}$ bounded scalar curvature
Jiawei Liu and Miles Simon
In this paper we study n-dimensional Ricci flows (M,g(t)), t in [0,T), where T is finite, and potentially a singular time, and for which the…
Integral curvature estimates for solutions to Ricci flow with $L^p$ bounded scalar curvature
Jiawei Liu and Miles Simon
In this paper we prove localised weighted curvature integral estimates for solutions to the Ricci flow in the setting of a smooth four…
K-cowaist of manifolds with boundary
Christian Bär, Bernhard Hanke
We extend the K-cowaist inequality to generalized Dirac operators in the sense of Gromov and Lawson and study applications to manifolds with boundary.
…Uniqueness of static vacuum asymptotically flat black holes and equipotential photon surfaces in n+1 dimensions à la Robinson
Carla Cederbaum, Albachiara Cogo, Benedito Leandro, João Paulo dos Santos
In this paper, we combine and generalize to higher dimensions the approaches to proving the uniqueness of connected (3+1)-dimensional static vacuum…
Latest Blog posts
K-homology class of the Euler characteristic operator
When studying the Atiyah-Singer index theorem one usually sees four main examples. Atiyah-Singer operator: Its topological index is the \(\hat{A}\)-genus and its analytical index can be related to scalar curvature. This shows that the \(\hat{A}\)-genus of a manifold is an obstruction to the existence of a Riemannian metric of positive scalar curvature on it. Signature … Continue reading "K-homology class of the Euler characteristic operator"
Polynomial and metallic manifolds
I recently came across the notion of a polynomial, resp. metallic manifold. Since I have never heard of it before and I assume that the same applies to most of you, I wanted to share its definition with you. Let \(M\) be a (smooth) manifold. A polynomial structure on \(M\) is a \((1,1)\)-tensor field \(\Phi\) … Continue reading "Polynomial and metallic manifolds"