# Geometry at Infinity

Priority programme of the DFG

## 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.

## Latest publications

#### Metrisability of projective surfaces and pseudo-holomorphic curvesThomas 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 splittingsThomas 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 bundlesLaura 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-foldsDominic 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...

#### Maximal metric surfaces and the Sobolev-to-Lipschitz propertyPaul Creutz and Elefterios Soultanis

We find maximal representatives within equivalence classes of metric discs. For Ahlfors regular ones these are uniquely characterized by satisfying...