## Welcome to SPP 2026

This is the platform of a coordinated research programme in mathematics, funded by the German Research Foundation (DFG). It comprises 79 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.

### Kick-off meeting

The Kick-Off Meeting for the second SPP funding period will take place on 4 and 5 November 2021.

## Latest publications

#### 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…

#### The Calderón Projector for fibred cusp operators

K. Fritzsch, D. Grieser, E. Schrohe

A Calder\'on projector for an elliptic operator $P$ on a manifold with boundary $X$ is a projection from general boundary data to the set of boundary…

#### Resolvent at low energy]{Spectral geometry on manifolds with fibred boundary metrics I: Low energy resolvent

D. Grieser, M. Talebi, B. Vertman

We study the low energy resolvent of the Hodge Laplacian on a manifold equipped with a fibred boundary metric. We determine the precise asymptotic…

#### Secondary cup and cap products in coarse geometry

Christopher Wulff

We construct secondary cup and cap products on coarse (co-)homology theories from given cross and slant products. They are defined for coarse spaces…

## Latest Blog posts

**Tetrahedra**Consider the following three basic questions about tetrahedra: Does a given tetrahedron tile space? Which tetrahedra are scissors-congruent to a cube? Can one describe the tetrahedra all of whose six dihedral angles are a rational number of degrees? The first question goes back to Aristotle, the second is from Hilbert’s list of problems, and the … Continue reading "Tetrahedra"

**The commutator subgroups of surface groups**Every subgroup of infinite index in a surface group is a free group. There are many ways to see this, for instance, using a bit of topology. An infinite index subgroup corresponds to a covering space with infinitely many sheets and this covering space is a non-compact surface. By a result of Whitehead it deformation … Continue reading "The commutator subgroups of surface groups"

**Condensed mathematics**This post is inspired by Alex Engel’s post “Validity of results II” on incorrect results and computer proof checking. Before I get there, let me start with some background first and reveal the connection later. Dustin Clausen and Peter Scholze have put forward the idea of “condensed mathematics” which aims at replacing topological spaces by … Continue reading "Condensed mathematics"