## 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.

### Not Only Scalar Curvature Seminar

Virtual seminar on scalar curvature geometry and related topics

## Latest publications

#### Hyperkähler metrics on the moduli space of weakly parabolic Higgs bundles

Maximilian Holdt

We use the theory of Gaiotto, Moore and Neitzke to construct a set of Darboux coordinates on the moduli space \(\mathcal{M}\) of weakly parabolic \(SL…

#### On the existence of holomorphic curves in compact quotients of SL$(2,\mathbb C)$

Indranil Biswas, Sorin Dumitrescu, Lynn Heller, Sebastian Heller

We prove the existence of a pair $(\Sigma ,\, \Gamma)$, where $\Sigma$ is a compact Riemann surface with $\text{genus}(\Sigma)\, \geq\, 2$, and…

#### 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…

## Latest Blog posts

**Properly positive scalar curvature**An interesting (at least to me) research theme in the geometry of manifolds is the question about the existence of positive scalar curvature metrics on closed manifolds. Since I also like to do coarse geometry, I therefore also consider the corresponding question on non-compact manifolds. But what is the ‘corresponding’ question on non-compact manifolds? Currently, … Continue reading "Properly positive scalar curvature"

**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"