## 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.

### SPP 2026 kick-off meeting in Potsdam

The kick-off meeting took place in the Audimax of the University of Potsdam, Campus am Neuen Palais, November 9-10, 2017.

## Next Activities

## Latest publications

#### The Bieri-Neumann-Strebel invariants via Newton polytopes

Dawid Kielak

We study the Newton polytopes of determinants of square matrices defined over rings of twisted Laurent polynomials. We prove that such Newton...

#### Stability of Ricci de Turck flow on Singular Spaces

Klaus Kröncke, Boris Vertman

In this paper we establish stability of the Ricci de Turck flow near Ricci-flat metrics with isolated conical singularities. More precisely, we...

#### Nonconnected moduli spaces of nonnegative sectional curvature metrics on simply connected manifolds

Anand DESSAI, Stephan KLAUS, Wilderich TUSCHMANN

We show that in each dimension 4n+3, n>1, there exist infinite sequences of closed smooth simply connected manifolds M of pairwise distinct homotopy...

#### Appendix to `Warped cones, (non-)rigidity, and piecewise properties' by Damian Sawicki

Dawid Kielak and Damian Sawicki

We prove that if a quasi-isometry of warped cones is induced by a map between the base spaces of the cones, the actions must be conjugate by this map....

## Latest Blog posts

**Snowflakes at infinity**The countless shapes of snowflakes have long raised the curiosity of many scientists, among others the famous Kepler. They have by now been classified by empirical observation into 80 different shapes, but a mathematical explanation for this classification seems to be missing. A striking point about them is that, even though two snowflakes are almost … Continue reading "Snowflakes at infinity"

**What’s new on the ArXiv: Ricci flow and diffeomorphism groups of 3-manifolds**A new paper proves the contractibility of the space of constant curvature metrics on all 3-manifolds except possibly real projective space. Bamler, Kleiner: Ricci flow and diffeomorphism groups of 3-manifolds, https://arxiv.org/pdf/1712.06197.pdf The Smale conjecture in its original form asserted that the diffeomorphism group of the 3-sphere deformation retracts onto O(3), the isometry group of its … Continue reading "What’s new on the ArXiv: Ricci flow and diffeomorphism groups of 3-manifolds"

**What’s new on the ArXiv: A locally hyperbolic 3-manifold that is not hyperbolic**A preprint with a new example shows that the understanding of infinitely generated Kleinian groups will be more complicated than for the finitely generated ones. Cremaschi: A locally hyperbolic 3-manifold that is not hyperbolic, https://arxiv.org/pdf/1711.11568 By the proofs of hyperbolization and tameness, one knows precisely which irreducible 3-manifolds with finitely generated fundamental groups admit hyperbolic … Continue reading "What’s new on the ArXiv: A locally hyperbolic 3-manifold that is not hyperbolic"