SPP 2026 – Geometry at Infinity

The \(S^1\)-Stability Conjecture for psc-Metrics

Jonathan Rosenberg introduced the following conjecture: A closed manifold \(M\) admits a Riemannian metric of positive scalar curvature if and only if the product \(M \times S^1\) admits one. One direction of the conjecture is trivial: If \(M\) admits a psc-metric, then the product metric on \(M \times S^1\) will also have psc. The other … Continue reading

K-homology class of the Euler characteristic operator

When studying the Atiyah-Singer index theorem one usually sees four main examples. Atiyah-Singer operator: Its topological index is the \(\hat{A}\)-genus and its analytical index can be related to scalar curvature. This shows that the \(\hat{A}\)-genus of a manifold is an obstruction to the existence of a Riemannian metric of positive scalar curvature on it. Signature … Continue reading

Polynomial and metallic manifolds

I recently came across the notion of a polynomial, resp. metallic manifold. Since I have never heard of it before and I assume that the same applies to most of you, I wanted to share its definition with you. Let \(M\) be a (smooth) manifold. A polynomial structure on \(M\) is a \((1,1)\)-tensor field \(\Phi\) … Continue reading

Hausdorff medal 2024

The Hausdorff medal is awarded biennially by the European Set Theory Society for the most influential work in set theory in the last five years. This years recipient is Gabriel Goldberg.

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

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

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

Cantor-Medaille 2024 für Felix Otto

Felix Otto bekommt die Cantor-Medaille der Deutschen Mathematiker-Vereinigung (DMV) für herausragende wissenschaftliche Leistungen […] von außergewöhnlicher Tiefe und höchstem Einfluss für das Gebiet der Analysis und die Partiellen Differentialgleichungen (Pressemitteilung).