## 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.

### Evaluation colloquium

The evaluation colloquium for the second funding period 2020-2023 will take place in Bad Honnef on 5 March 2020.

## Next Activities

## Latest publications

#### Metrisability of projective surfaces and pseudo-holomorphic curves

Thomas Mettler

We show that the metrisability of an oriented projective surface is equivalent to the existence of pseudo-holomorphic curves. A projective structure...

#### Vortices over Riemann surfaces and dominated splittings

Thomas Mettler, Gabriel P. Paternain

We associate a flow $\phi$ to a solution of the vortex equations on a closed oriented Riemannian 2-manifold $(M,g)$ of negative Euler characteristic...

#### Asymptotic geometry of the moduli space of parabolic $SL(2,\mathbb{C})$-Higgs bundles

Laura Fredrickson, Rafe Mazzeo, Jan Swoboda, Hartmut Weiß

Given a generic stable strongly parabolic $SL(2,\mathbb{C})$-Higgs bundle

$(\mathcal{E}, \varphi)$, we describe the family of harmonic metrics $h_t$...

#### Orientation data for moduli spaces of coherent sheaves over Calabi-Yau 3-folds

Dominic Joyce, Markus Upmeier

Let X be a compact Calabi-Yau 3-fold, and write \(\mathcal{M}, \overline{\mathcal{M}}\) for the moduli stacks of objects in coh(X) and the derived...

## Latest Blog posts

**A Prime Breakthrough**It seems that at the beginning of this year a major breakthrough on prime numbers was achieved. I learned about it from this blog: link. Let me summarize the result quickly for you if you don’t want to read the other blog post. Almost a hundred years ago Jensen and Pólya proved that the Riemannian … Continue reading "A Prime Breakthrough"

**Laplace operator and covering spaces**Let M be a closed Riemannian manifold and denote by X its universal covering space equipped with the pulled back Riemannian metric. There is an intimate relation between the Laplace operator on X and the fundamental group of M. One example of this is the result of Brooks from 1981: the fundamental group of M … Continue reading "Laplace operator and covering spaces"

**Lindelöf hypothesis**Today I stumbled across a news article ( link ) written about someone (actually, Athanassios Fokas – a known mathematician) having announced progress on the Lindelöf hypothesis ( wikipedia ). The Lindelöf hypothesis is related to the Riemannian hypothesis and actually also follows from it – progress on the Lindelöf hypothesis would also mean progress … Continue reading "Lindelöf hypothesis"