## 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.

## Next Activities

## Latest publications

#### Perelman's Entropies for Manifolds with conical Singularities

Klaus Kröncke, Boris Vertman

In this paper we discuss Perelman's Lambda-functional, Perelman's Ricci shrinker entropy as well as the Ricci expander entropy on a class of manifolds...

#### A categorified excision principle for elliptic symbol families

Markus Upmeier

We develop a categorical index calculus for elliptic symbol families. The categorified index problems we consider are a secondary version of the...

#### The fundamental solution of a class of ultra-hyperbolic operators on Pseudo H-type groups

W. Bauer, A. Froehly, I. Markina

Pseudo H-type Lie groups \(G_{r,s}\) of signature (r,s) are defined via a module action of the Clifford algebra \(C\ell_{r,s}\) on a vector space V≅\(...

#### Profinite invariants of arithmetic groups

Holger Kammeyer, Steffen Kionke, Jean Raimbault, Roman Sauer

We prove that the sign of the Euler characteristic of arithmetic groups with CSP is determined by the profinite completion. In contrast, we construct...

## Latest Blog posts

**Global existence for non-linear wave equations**Non-linear wave equations (in 3+1 dimensions) are ubiquitous in physics, playing a vital role in many subfields of it. There are many methods available to show short-time existence of solutions for such equations, but global-in-time existence is a much more subtle problem. In the 1980s Klainermann introduced a so-called null condition on the nonlinearities of … Continue reading "Global existence for non-linear wave equations"

**Ten Years of Polymath**Ten years ago the first Polymath project was launched (link to the original proposal of Timothy Gowers). Polymath can be described as massively collaborative mathematics, i.e., a large groups of mathematicians works on a predefined problem and each member posts his or her (partial) ideas, so that the collective makes progress from each small step … Continue reading "Ten Years of Polymath"