## 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.

### Gauss lecture

Welcome to the 35th Gauss lecture of the German Mathematical Society (DMV). It will be hosted by the University of Augsburg (online) on Tuesday July…

## Latest publications

#### The positive mass theorem and distance estimates in the spin setting

Simone Cecchini, Rudolf Zeidler

Let \(\mathcal{E}\) be an asymptotically Euclidean end in an otherwise arbitrary complete and connected Riemannian spin manifold \((M,g)\). We show…

#### Complete families of embedded high genus CMC surfaces in the 3-sphere

Lynn Heller, Sebastian Heller, Martin Traizet

For every $g \gg 1$, we show the existence of a complete and smooth family of closed constant mean curvature surfaces $f_\varphi^g,$ $ \varphi \in…

#### Holomorphic sl(2,C)-systems with Fuchsian monodromy (with an appendix by Takuro Mochizuki)

Indranil Biswas, Sorin Dumitrescu, Lynn Heller, Sebastian Heller

For every integer $g \,\geq\, 2$ we show the existence of a compact Riemann surface $\Sigma$ of genus $g$ such that the rank two trivial holomorphic…

#### Geometry of the space of sections of twistor spaces with circle action

Florian Beck, Indranil Biswas, Sebastian Heller, Markus Röser

We study the holomorphic symplectic geometry of (the smooth locus of) the space of holomorphic sections of a twistor space with rotating circle…

## Latest Blog posts

**PSC obstructions via infinite width and index theory**In a recent preprint (arXiv:2108.08506), Yosuke Kubota proved an intriguing new result on the relation of largeness properties of spin manifolds and index-theoretic obstructions to positive scalar curvature (psc): Let \(M\) be a closed spin \(n\)-manifold. If \(M\) has infinite \(\mathcal{KO}\)-width, then its Rosenberg index \(\alpha(M) \in \mathrm{KO}_n(\mathrm{C}^\ast_{\max} \pi_1 M)\) does not vanish. Let us … Continue reading "PSC obstructions via infinite width and index theory"

**(Non-)Vanishing results for Lp-cohomology of semisimple Lie groups**For a locally compact, second countable group \(G\) one can define the continuous \(L^p\)-cohomology \(H^*_{ct}(G,L^p(G))\) of \(G\) and the reduced version \(\overline{H}^*_{ct}(G,L^p(G))\) for all \(p > 1\). In his influential paper “Asymptotic invariants of infinite groups” Gromov asked if \[H^j(G,L^p(G)) = 0 \] when \(G\) is a connected semisimple Lie group and \(j < \mathrm{rk}_{\mathbb{R}}(G)\). … Continue reading "(Non-)Vanishing results for Lp-cohomology of semisimple Lie groups"

**New book about Freedman’s proof**Today I learnt from an article in the QuantaMagazine (link to article) that there is finally a new book trying to explain Freedman’s proof of the 4-dimensional Poincaré conjecture (link to book). The article is fun to read since it contains statements of the involved people about how the whole ‘situation’ about the non-understandable write-up … Continue reading "New book about Freedman’s proof"