## 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

#### Hitchin components for orbifolds

Daniele Alessandrini, Gye-Seon Lee, Florent Schaffhauser

We extend the notion of Hitchin component from surface groups to orbifold groups and prove that this gives new examples of Higher Teichmüller...

#### Higgs bundles and geometric structures on manifolds

Daniele Alessandrini

Geometric structures on manifolds became popular when Thurston used them in his work on the Geometrization Conjecture. They were studied by many...

#### On orientations for gauge-theoretic moduli spaces

Dominic Joyce, Yuuji Tanaka and Markus Upmeier

Let X be a compact manifold, D a real elliptic operator on X, G a Lie group, P a principal G-bundle on X, and B_P the infinite-dimensional moduli...

#### Canonical orientations for moduli spaces of G_2-instantons with gauge group SU(m) or U(m)

Dominic Joyce and Markus Upmeier

Suppose (X, g) is a compact, spin Riemannian 7-manifold, with Dirac operator D. Let G be SU(m) or U(m), and E be a rank m complex bundle with...

## Latest Blog posts

**Selberg’s lemma and negatively curved Hadamard manifolds**Selberg’s lemma is a fundamental result about linear groups. It states that every finitely generated subgroup of \(\mathrm{GL}(n,K)\), where \(K\) is a field of characteristic zero, is virtually torsion-free (i.e., contains a torsion-free subgroup of finite index). Recently, Michael Kapovich proved that the conclusion of Selberg’s lemma can fail for finitely generated, discrete subgroups of isometry groups … Continue reading "Selberg’s lemma and negatively curved Hadamard manifolds"

**Breakthrough Prize 2019**Ten days ago the winners of the Breakthrough Prize 2019 were announced (press release, AMS Blog). In mathematics the award goes to Vincent Lafforgue for “ground-breaking contributions to several areas of mathematics, in particular to the Langlands program in the function field case”. Further, the New Horizons Prize in mathematics goes to Chenyang Xu for “major … Continue reading "Breakthrough Prize 2019"

**Classification of static vacuum black holes**In a series of two papers ( arXiv:1806.00818 and arXiv:1806.00819 ) Martin Reiris Ithurralde classifies all metrically complete solutions of the static vacuum Einstein equations with compact (but not necessarily connected) horizon. Main Theorem Any static vacuum black hole is either a Schwarzschild black hole, a Boost, or of Myers/Korotkin-Nicolai type. Basic definition A static vacuum … Continue reading "Classification of static vacuum black holes"