## 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 Giles Gardam from the University of Münster on receiving an ERC Starting Grant for his project "Satisfiability and…

## Next Activities

## Latest publications

#### Bounded cohomology is not a profinite invariant

Daniel Echtler, Holger Kammeyer

We construct pairs of residually finite groups with isomorphic profinite completions such that one has non-vanishing and the other has vanishing real…

#### Boundary conditions for scalar curvature

Christian Bär and Bernhard Hanke

Based on the Atiyah-Patodi-Singer index formula, we construct an obstruction to positive scalar curvature metrics with mean convex boundaries on spin…

#### Realisations of elliptic operators on compact manifolds with boundary

Lashi Bandara, Magnus Goffeng, Hemanth Saratchandran

This paper investigates realisations of elliptic differential operators of general order on manifolds with boundary following the approach of…

#### Fourier expansions of vector-valued automorphic functions with non-unitary twists

Ksenia Fedosova, Anke Pohl, Julie Rowlett

We provide Fourier expansions of vector-valued eigenfunctions of the hyperbolic Laplacian that are twist-periodic in a horocycle direction. The twist…

## Latest Blog posts

**The invariant subspace problem in Hilbert spaces**I was a bit surprised today to see a preprint by Per Enflo on the arXiv (arXiv:2305.15442). He is already 79 years old (Wikipedia)! Per Enflo is famous for several fundamental results in functional analysis (see the English Wikipedia article linked above for an overview). The one related to this post is his counter-example (the … Continue reading "The invariant subspace problem in Hilbert spaces"

**Metric spaces and C*-algebras**Let \(X\) be a metric space of bounded geometry. The latter means that for all \(r > 0\) exists an \(n_r \in \mathbb{N}\) such that every ball in \(X\) of radius \(r\) has at most \(n_r\) elements. This especially implies that \(X\) is discrete. It might seem a bit strange for some to consider discrete … Continue reading "Metric spaces and C*-algebras"