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 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. 


Latest Blog posts

Optimality of Gerver’s Sofa The moving sofa problem is one of those deceptively simple yet incredibly difficult “real-world” math problems. Despite its straightforward formulation, it has remained unsolved for roughly 60 years—until recently, when Jineon Baek announced a complete solution (arXiv:2411.19826; hopefully, this time the topic I’m blogging about won’t turn out to be incorrect in the end). In … Continue reading "Optimality of Gerver’s Sofa"
The \(S^1\)-Stability Conjecture for psc-Metrics Jonathan Rosenberg introduced the following conjecture: A closed manifold \(M\) admits a Riemannian metric of positive scalar curvature if and only if the product \(M \times S^1\) admits one. One direction of the conjecture is trivial: If \(M\) admits a psc-metric, then the product metric on \(M \times S^1\) will also have psc. The other … Continue reading "The \(S^1\)-Stability Conjecture for psc-Metrics"
K-homology class of the Euler characteristic operator When studying the Atiyah-Singer index theorem one usually sees four main examples. Atiyah-Singer operator: Its topological index is the \(\hat{A}\)-genus and its analytical index can be related to scalar curvature. This shows that the \(\hat{A}\)-genus of a manifold is an obstruction to the existence of a Riemannian metric of positive scalar curvature on it. Signature … Continue reading "K-homology class of the Euler characteristic operator"

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