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

A question about the first \(L^2\)-Betti number In a recent arXiv preprint (arxiv:2106.15750) J. A. Hillman discusses a new homological approach towards some old results on 3-manifold groups due to Elkalla. In his article he runs into an interesting question concerning the first \(L^2\)-Betti number of finitely generated groups: Assume that a finitely generated group G has infinite subgroups \(N\leq U\) such … Continue reading "A question about the first \(L^2\)-Betti number"
Computer assisted verification of contemporary mathematics Half a year ago Steffen Kionke wrote a blog post on condensed mathematics wherein he mentioned that Peter Scholze put up a challenge to formally verify a key fundamental result of a joint paper with Clausen: a result Scholze terms his most important theorem to date. Today I want to inform you that the mentioned … Continue reading "Computer assisted verification of contemporary mathematics"
A hyperbolic 5-manifold which fibres over the circle and subgroups of hyperbolic groups Recently appeared a highly interesting paper by Italiano, Martelli, Migliorini on the arXiv (2105.14795) (Okay, this was already three weeks ago – I don’t follow the “geometric topology” – and someone had to point me there). The paper solves at least two longstanding open problems by studying an explicit 5-dimensional hyperbolic manifold. It is well-known … Continue reading "A hyperbolic 5-manifold which fibres over the circle and subgroups of hyperbolic groups"

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