## 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.

### Gauss lecture

Welcome to the 36th Gauss lecture of the German Mathematical Society (DMV). It is organized by the University of Bremen and will take place on Monday…

## Latest publications

#### Logarithmic connections, WZNW action, and moduli of parabolic bundles on the sphere

Claudio Meneses, Leon A. Takhtajan

Moduli spaces of stable parabolic bundles of parabolic degree \(0\) over the Riemann sphere are stratified according to the Harder-Narasimhan…

#### Thin homotopy and the holonomy approach to gauge theories

Claudio Meneses

We survey several mathematical developments in the holonomy approach to gauge theory. A cornerstone of such approach is the introduction of group…

#### 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…

## Latest Blog posts

**An implication of the Farrell-Jones conjecture**A ‘well-known’ implication of the Farrell-Jones conjecture (for a given group G) is that the map \[\widetilde{K_0(\mathbb{Z}G)} \to \widetilde{K_0(\mathbb{Q}G)}\] in reduced algebraic K-theory is rationally trivial. What at first might seem as a technical statement about algebraic K-theory turns out to have an interesting geometric consequence. It implies the Bass conjecture, which is equivalent to … Continue reading "An implication of the Farrell-Jones conjecture"

**Kaplansky’s direct finiteness conjecture**Not too long ago I blogged about the first counter-example to Kaplansky’s unit conjecture (link) stating that there are no non-trivial units in the group ring K[G] for K a field and G a torsion-free group. A related conjecture of Kaplansky (one that I was not aware of until recently) is that K[G] is directly … Continue reading "Kaplansky’s direct finiteness conjecture"

**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"