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 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"

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