## 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

#### The Baum--Connes conjecture localised at the unit element of a discrete group

Paolo Antonini, Sara Azzali, Georges Skandalis

We construct a Baum--Connes assembly map localised at the unit element of a discrete group $\Gamma$.

This morphism, called $\mu_\tau$, is defined in...

#### Conic manifolds under the Yamabe flow

Nikolaos Roidos

We consider the unnormalized Yamabe flow on manifolds with conical singularities. Under certain geometric assumption on the initial cross-section we...

#### S-arithmetic spinor groups with the same finite quotients and distinct ℓ²-cohomology

Holger Kammeyer, Roman Sauer

In this note we refine examples by Aka from arithmetic to S-arithmetic groups to show that the vanishing of the *i*-th ℓ²-Betti number is not a...

#### Profinite commensurability of S-arithmetic groups

Holger Kammeyer

Given an S-arithmetic group, we ask how much information on the ambient algebraic group, number field of definition, and set of places S is encoded in...

## Latest Blog posts

**Strong cosmic censorship conjecture**The cosmic censorship conjectures concern the singularities arising in general relativity. In May the QuantaMagazine published an article (link) about a potential disproof of a strong version of the cosmic censorship conjecture. This article is nicely written and I recommend everybody interested in general relativity reading it. The preprint the QuantaMagazine refers to is arXiv:1710.01722 … Continue reading "Strong cosmic censorship conjecture"

**News around the ICM 2018**The ICM 2018 is currently taking place in Rio de Janeiro. Here are the prize winners of the IMU prizes and of the K-theory foundation, and the new IMU Executive Committee. The Fields medallists 2018 are Caucher Birkar, Alessio Figalli, Peter Scholze, and Akshay Venkatesh. There are also many more prizes and medals that are … Continue reading "News around the ICM 2018"

**Contractible 3-manifolds and positive scalar curvature**It is known that \(\mathbb{R}^3\) admits a complete metric of uniformly positive scalar curvature. In fact, for any closed manifold \(X\) and any \(k \ge 3\) the manifold \(X \times \mathbb{R}^k\) admits a complete metric of uniformly positive scalar curvature by a result of Rosenberg and Stolz (link). Now there exist contractible, open 3-manifolds which are not … Continue reading "Contractible 3-manifolds and positive scalar curvature"