Welcome to SPP 2026
This is the platform of a coordinated research programme in mathematics, funded by the German Research Foundation (DFG). It comprises 33 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.
Next Activities
Latest publications
Scalar positive immersions
Luis A. Florit, Bernhard Hanke
As shown by Gromov-Lawson and Stolz the only obstruction to the existence of positive scalar curvature metrics on closed simply connected manifolds...
Photon surfaces with equipotential time-slices
Carla Cederbaum, Gregory J. Galloway
Photon surfaces are timelike, totally umbilic hypersurfaces of Lorentzian spacetimes. In the first part of this paper, we locally characterize all...
On the regularity of Ricci flows coming out of metric spaces
Alix Deruelle , Felix Schulze and Miles Simon
We consider solutions to Ricci flow defined on manifolds M for a time interval (0,T) whose Ricci curvature is bounded uniformly in time
from below,...
Latest Blog posts
A Prime Breakthrough
It seems that at the beginning of this year a major breakthrough on prime numbers was achieved. I learned about it from this blog: link. Let me summarize the result quickly for you if you don’t want to read the other blog post. Almost a hundred years ago Jensen and Pólya proved that the Riemannian … Continue reading "A Prime Breakthrough"
Laplace operator and covering spaces
Let M be a closed Riemannian manifold and denote by X its universal covering space equipped with the pulled back Riemannian metric. There is an intimate relation between the Laplace operator on X and the fundamental group of M. One example of this is the result of Brooks from 1981: the fundamental group of M … Continue reading "Laplace operator and covering spaces"
Lindelöf hypothesis
Today I stumbled across a news article ( link ) written about someone (actually, Athanassios Fokas – a known mathematician) having announced progress on the Lindelöf hypothesis ( wikipedia ). The Lindelöf hypothesis is related to the Riemannian hypothesis and actually also follows from it – progress on the Lindelöf hypothesis would also mean progress … Continue reading "Lindelöf hypothesis"