## 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.

### Kick-off meeting

The Kick-Off Meeting for the second SPP funding period will take place on 19 and 20 November 2021.

## Next Activities

## Latest publications

#### Manifolds with many Rarita-Schwinger fields

Christian Bär, Rafe Mazzeo

The Rarita-Schwinger operator is the twisted Dirac operator restricted to 3/2-spinors. Rarita-Schwinger fields are solutions of this operator which…

#### Sphericity of kappa-classes and positive curvature via block bundles

Georg Frenck, Jens Reinhold

Given a manifold $M$, we completely determine which rational $\kappa$-classes are non-trivial for (fiber homotopy trivial) $M$-bundles over the…

#### Spaces of positive intermediate curvature metrics

Georg Frenck, Jan-Bernhard Kordaß

In this paper we study spaces of Riemannian metrics with lower bounds on intermedi- ate curvatures. We show that the spaces of metrics of…

#### H-Space structures on spaces of metrics of positive scalar curvature

Georg Frenck

We construct and study an H-space multiplication on \(\mathcal{R}^+(M)\) for manifolds M which are nullcobordant in their own tangential 2-type. This…

## Latest Blog posts

**Message from the EMS president**In the last EMS Magazine (2021/No. 121) Volker Mehrmann reflected in his editorial (link) on the bygone (virtual) European Congress 8ECM. At the end he asked to write to him our opinions about the matters that he addressed, which I did. I want to share here now my e-mail to him with you: Lieber Volker, … Continue reading "Message from the EMS president"

**Lie groups acting on countable sets**Does every connected Lie group act faithfully on a countable set? In other words: is every Lie group a subgroup of \(\mathrm{Sym}(\mathbb{N})\)? This question is sometimes called Ulam’s problem and there is recent progress in a paper of Nicolas Monod. Monod proves that every nilpotent connected Lie group acts faithfully on a countable set. It … Continue reading "Lie groups acting on countable sets"

**Topological CAT(0)-manifolds**It is an interesting and important fact that a contractible manifold (without boundary) is not necessarily homeomorphic to Euclidean space. This makes the classical Cartan-Hadamard theorem, stating that a contractible manifold equipped with a Riemannian metric of non-positive sectional curvature is diffeomorphic to Euclidean space, even more powerful. One can ask now whether one can … Continue reading "Topological CAT(0)-manifolds"