## 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.

### Evaluation colloquium

The evaluation colloquium for the second funding period 2020-2023 will take place in Bad Honnef on 5 March 2020.

## Next Activities

## Latest publications

#### Plateau's problem for singular curves

Paul Creutz

We give a solution of Plateau's problem for singular curves possibly having self-intersections. The proof is based on the solution of Plateau's…

#### Equivariant coarse (co-)homology theories

Christopher Wulff

We present an Eilenberg--Steenrod-like axiomatic framework for equivariant coarse homology and cohomology theories. We also discuss a general…

#### Moduli space of nonnegatively curved metrics on manifolds of dimension $4k+1$

Anand Dessai

In each dimension $4k+1\geq 9$, we exhibit infinite families of closed manifolds with fundamental group $\mathbb Z_2$ for which the moduli space of…

#### Space of minimal discs and its compactification

Paul Creutz

We investigate the class of geodesic metric discs satisfying a uniform quadratic isoperimetric inequality and uniform bounds on the length of the…

## Latest Blog posts

**Validity of results**Can you vouch for the validity of the results in papers that you cite and use in your own articles? In April this year Blagojević, Cohen, Crabb, Lück and Ziegler posted a preprint on the arXiv (arXiv:2004.12350) writing in the abstract “This invalidates a paper by three of the present authors […] who used a … Continue reading "Validity of results"

**Conjugation Curvature**Recently I saw some papers on the arXiv on conjugation curvature of finitely generated groups (also called medium-scale curvature, transportation curvature, metric Ricci curvature or comparison curvature for Cayley graphs). I got a bit interested in it and so decided to write up a short post about it. Let \(G\) be a finitely generated group … Continue reading "Conjugation Curvature"

**Collatz conjecture**Given a natural number n, the Collatz sequence it generates is the following: if n is even, then divide it by 2, if n is odd, then multiply it by 3 and add 1; and now iterate this procedure. The Collatz conjecture states that you will always end up with the number 1 after finitely … Continue reading "Collatz conjecture"