## 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.

### ERC Starting Grant

We congratulate our SPP member Giles Gardam from the University of Münster on receiving an ERC Starting Grant for his project "Satisfiability and…

## Next Activities

## Latest publications

#### Galois cohomology and profinitely solitary Chevalley groups

Holger Kammeyer, Ryan Spitler

For every number field and every Cartan Killing type, there is an associated split simple algebraic group. We examine whether the corresponding…

#### Yamabe problem in the presence of singular Riemannian Foliations

Diego Corro, Juan Carlos Fernández and Raquel Perales

Using variational methods together with symmetries given by singular Riemannian foliations with positive dimensional leaves, we prove the existence of…

#### Stability of Einstein metrics and effective hyperbolization in large Hempel distance

Ursula Hamenstädt, Frieder Jäckel

Extending earlier work of Tian, we show that if a manifold admits a metric that is almost hyperbolic in a suitable sense, then there exists an…

#### Gromov-Hausdorff Limits of Closed Surfaces

Tobias Zisgen

We describe the Gromov-Hausdorff closure of the class of length spaces being homeomorphic to a fixed closed surface.

## Latest Blog posts

**Double Soul Conjecture**Recall the Soul Theorem of Cheeger and Gromoll: If \((M,g)\) is a complete and connected Riemannian manifold of non-negative sectional curvature, then there exists a closed, totally convex and totally geodesic embedded submanifold whose normal bundle is diffeomorphic to \(M\). Such a submanifold is called a soul of \((M,g)\) and the Riemannian metric induced on … Continue reading "Double Soul Conjecture"

**Progress on the union-closed sets conjecture**The union-closed sets conjecture is the following extremely easy to state conjecture about subsets of finite sets: Assume that \(\mathcal{F}\) is a family of subsets of \(\{1, 2, \ldots, n\}\) which is union-closed; this means that for any two sets \(A,B\) in \(\mathcal{F}\) their union \(A \cup B\) is also a member of \(\mathcal{F}\). Then … Continue reading "Progress on the union-closed sets conjecture"