## 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.

### SPP Conference 2025

The SPP Main Conference will take place from March 31 to April 4, 2025, at the MPI for Mathematics in the Sciences in Leipzig.

## Latest News

## Next Activities

## Latest publications

#### Period functions for vector-valued Maass cusp forms of real weight, with an application to Jacobi Maass cusp forms

Roelof Bruggeman, YoungJu Choie, Anke Pohl

For vector-valued Maass cusp forms for* SL*(2,Z) with real weight* k*∈R and spectral parameter *s*∈C, Re*s*∈(0,1), *s*≢±*k*/2 mod 1, we propose a notion of…

#### Dirac eigenvalues and the hyperspherical radius

Christian Bär

For closed connected Riemannian spin manifolds an upper estimate of the smallest eigenvalue of the Dirac operator in terms of the hyperspherical…

#### Groups acting amenably on their Higson corona

A. Engel

We investigate groups that act amenably on their Higson corona (also known as bi-exact groups) and we provide reformulations of this in relation to…

#### Hereditarily just-infinite torsion groups with positive first L2-Betti number

Steffen Kionke, Eduard Schesler

We present a new method to construct finitely generated, residually finite, infinite torsion groups. In contrast to known constructions, a profinite…

## Latest Blog posts

**The Probability of the Law of Excluded Middle**This is basically a repost of this blog post by John Carlos Baez: link. I wanted to share it with you since I find the result unexpectedly interesting. The Law of Excluded Middle states that for any statement P we have that either P or not P is true. Almost all of us work under … Continue reading "The Probability of the Law of Excluded Middle"

**AI achieves silver-medal at IMO**Google developed AI models that achieved on this year’s IMO questions a silver-medal (with only one point away from a gold-medal). You can read more about it in this blog post of Google: link. The for me most interesting thing in this news is not that it achieves a silver-medal, but how the system works, … Continue reading "AI achieves silver-medal at IMO"

**All triangulations have a common stellar subdivision**Already in April a paper was put on the arXiv (2404.05930) by Karim Adiprasito and Igor Pak proving the following result: Every two triangulations of a geometric complex in Euclidean space have a common stellar subdivision. At first I was a bit confused, because my mind connected this to the Hauptvermutung, which was disproven a … Continue reading "All triangulations have a common stellar subdivision"