## 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

#### A counterexample to the unit conjecture for group rings

Giles Gardam

The unit conjecture, commonly attributed to Kaplansky, predicts that if *\(K\)* is a field and \(G\) is a torsion-free group then the only units of the…

#### A stable ∞-category for equivariant KK-theory

U. Bunke, A. Engel, M. Land

For a countable group G we construct a small, idempotent complete, symmetric monoidal, stable ∞-category KK^G_sep whose homotopy category recovers the…

#### Triangulating metric surfaces

Paul Creutz and Matthew Romney

We prove that any length metric space homeomorphic to a surface may be decomposed into non-overlapping convex triangles of arbitrarily small diameter.…

#### Bott-Thom isomorphism, Hopf bundles and Morse theory

Jost-Hinrich Eschenburg and Bernhard Hanke

Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups.…

## Latest Blog posts

**Unit conjecture disproved!**There are three conjectures about group rings of torsion-free groups that are attributed to Kaplansky. To state them, let \(K\) be a field, \(G\) be a torsion-free group and denote by \(K[G]\) the corresponding group ring. The unit conjecture states that every unit in \(K[G]\) is of the form \(kg\) for \(k \in K\setminus\{0\}\) and … Continue reading "Unit conjecture disproved!"

**Database of online seminar talks**Due to the current situation there are numerous online seminar talks organized all over the world. I was quite happy to discover this week that the website researchseminars.org maintains a useful database of online seminars and conferences, focusing on mathematics and related fields. The website is supported by the American Mathematical Society, the MIT and … Continue reading "Database of online seminar talks"

**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"