## 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.

### ERC Starting Grant

We congratulate our SPP member Rudolf Zeidler from the University of Münster on receiving an ERC Starting Grant for his project "Comparison and…

## Next Activities

## Latest publications

#### Gassmann triples with special cycle types and applications

Holger Kammeyer, Steffen Kionke

We show that if one of various cycle types occurs in the permutation action of a finite group on the cosets of a given subgroup, then every almost…

#### K-cowaist of manifolds with boundary

Christian Bär, Bernhard Hanke

We extend the K-cowaist inequality to generalized Dirac operators in the sense of Gromov and Lawson and study applications to manifolds with boundary.

…#### Kac-Moody Symmetric Spaces: An Addendum

Ralf Köhl, Christian Vock

Kac-Moody symmetric spaces have been introduced by Freyn, Hartnick, Horn and the first-named author for centered Kac-Moody groups, that is, Kac-Moody…

#### Fundamental groups of split real Kac-Moody groups and generalized real flag manifolds. With appendices by Tobias Hartnick and Ralf Köhl and by Julius Grüning and Ralf Köhl

Paula Harring, Ralf Köhl

We determine the fundamental groups of symmetrizable algebraically simply connected split real Kac-Moody groups endowed with the Kac-Peterson…

## Latest Blog posts

**2024 Breakthrough Prize in Mathematics**The 2024 Breakthrough Prize in Mathematics goes to Simon Brendle for transformative contributions to differential geometry, including sharp geometric inequalities, many results on Ricci flow and mean curvature flow and the Lawson conjecture on minimal tori in the 3-sphere. The 2024 New Horizons in Mathematics Prize goes to Roland Bauerschmidt for outstanding contributions to probability … Continue reading "2024 Breakthrough Prize in Mathematics"

**Metric spaces and C*-algebras II**In the previous post about metric spaces and C*-algebras we saw the definition of the uniform Roe algebra \(C^*_u(X)\) of a metric space \(X\) and discussed its remarkable property that two metric spaces (of bounded geometry) \(X\) and \(Y\) are coarsely equivalent if and only if their uniform Roe algebras \(C^*_u(X)\) and \(C^*_u(Y)\) are Morita … Continue reading "Metric spaces and C*-algebras II"

**The Kervaire Conjecture**Think about your favourite non-trivial group. Now add a generator to it and then add any relation. Is the resulting group still non-trivial? The above question is known as the Kervaire conjecture. Phrased more concretely, if \(G\) is any non-trivial group and \(r \in G \ast \mathbb{Z}\), is \((G \ast \mathbb{Z})/\langle\!\langle r\rangle\!\rangle\) again non-trivial? This … Continue reading "The Kervaire Conjecture"