## 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.

### Gauss lecture

Welcome to the 35th Gauss lecture of the German Mathematical Society (DMV). It will be hosted by the University of Augsburg (online) on Tuesday July…

## Latest publications

#### Constructing electrically charged Riemannian manifolds with minimal boundary, prescribed asymptotics, and controlled mass

Armando J. Cabrera Pacheco, Carla Cederbaum, Penelope Gehring, Alejandro Penuela Diaz

In 2015, Mantoulidis and Schoen constructed 3-dimensional asymptotically Euclidean manifolds with non-negative scalar curvature whose ADM mass can be…

#### Paschke duality and assembly maps

U. Bunke, A. Engel, M. Land

We construct a natural transformation between two versions of G-equivariant K-homology with coefficients in a G-C*-category for a countable discrete…

#### Ricci flow starting from an embedded closed convex surface in $\mathbb{R}^3$

Jiuzhou Huang, Jiawei Liu

In this paper, we establish the existence and uniqueness of Ricci flow that admits an embedded closed convex surface in $\mathbb{R}^3$ as metric…

#### Amenability and profinite completions of finitely generated groups

Steffen Kionke, Eduard Schesler

This article explores the interplay between the finite quotients of finitely generated residually finite groups and the concept of amenability.

We…

## 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"