## 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.

### Research projects for second funding period

DFG granted 45 research proposals for the second funding period of SPP 2026 (2020-2023).

## 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…

#### Long-time estimates for heat flows on ALE manifolds

Klaus Kröncke, Oliver Lindblad Petersen

We consider the heat equation associated to Schrödinger operators acting on vector bundles on asymptotically locally Euclidean (ALE) manifolds. Novel *…*

#### 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…

## Latest Blog posts

**Spaces of positively curved Riemannian metrics**It is by now a classical topic in index theory to study on a (closed) Riemannian (spin) manifold the space of all Riemannian metrics of positive scalar curvature. We have several results showing that this space is usually highly complicated from a homotopy theoretic point of view (provided it is non-empty). Instead of studying positivity … Continue reading "Spaces of positively curved Riemannian metrics"

**Quasi-local operators**In the first post of this series we asked at the end two questions – in this post we start working towards the answers in the general setup of the third post of this series. Our setup from the third post is the following: We have a metric space \((X,d)\) and we consider a bounded, … Continue reading "Quasi-local operators"