## 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

#### On property (T) for $\mathrm{Aut}(F_n)$ and $\mathrm{SL}_n(\mathbb Z)$

Marek Kaluba, Dawid Kielak, Piotr Nowak

We prove that $\mathrm{Aut}(F_n)$ has Kazhdan's property (T) for every $n \geqslant 6$. Together with a previous result of Kaluba, Nowak, and Ozawa,...

#### Heinz-Kato inequality in Banach spaces

Nikolaos Roidos

We show a Heinz-Kato inequality in Banach spaces for sectorial operators having bounded imaginary powers.

#### Torus orbifolds, slice-maximal torus actions and rational ellipticity

Fernando Galaz-García, Martin Kerin, Marco Radeschi, Michael Wiemeler

In this work, it is shown that a simply-connected, rationally-elliptic torus orbifold is equivariantly rationally homotopy equivalent to the quotient...

#### Semi-free actions with manifold orbit spaces

John Harvey, Martin Kerin, Krishnan Shankar

In this paper, we study smooth, semi-free actions on closed, smooth, simply connected manifolds, such that the orbit space is a smoothable manifold....

## Latest Blog posts

**Non-negative scalar curvature and mean convex boundaries**In a recent preprint ( arXiv:1811.08519 ) E. Barbosa and F. Conrado derive for manifolds with boundary topological obstructions to the existence of non-negative scalar curvature metrics with mean convex boundaries. The boundary of a Riemannian manifold is said to be mean convex, if the mean curvature of it with respect to the outward unit … Continue reading "Non-negative scalar curvature and mean convex boundaries"