The Kervaire Conjecture

Think about your favourite non-trivial group. Now add a generator to it and then add any relation. Is the resulting group still non-trivial? The above question is known as the Kervaire conjecture. Phrased more concretely, if \(G\) is any non-trivial group and \(r \in G \ast \mathbb{Z}\), is \((G \ast \mathbb{Z})/\langle\!\langle r\rangle\!\rangle\) again non-trivial? This … Continue reading "The Kervaire Conjecture"

Hilbert spaces and C*-algebras without Choice

Today a paper was posted on the arXiv by Blackadar, Farah and Karagila (arXiv:2304.09602) that examines Hilbert spaces and C*-algebras in ZF set theory without the assumption of any Axiom of Choice (not even with Countable Choice). Since many standard tools from functional analysis like the Hahn-Banach theorem or the Baire category theorem fail without … Continue reading "Hilbert spaces and C*-algebras without Choice"

An aperiodic monotile

It is finally done – the long standing question whether there exists a single tile that can cover the entire plane, but only aperiodically, is answered! Here is the answer (arXiv:2303.10798): Many other people have already written blog posts, etc. about this, hence I will refrain from repeating everything and just refer to those other … Continue reading "An aperiodic monotile"

Illustrating the Impact of the Mathematical Sciences

A series of posters and some other related media were produced by the National Academy of Sciences of the USA to showcase mathematics of the twenty-first century and its applications in the real world: link. If you still don’t know what to put on your office walls, have a look at those posters!

Status-Bias im Peer-Review

In der aktuellen Forschung & Lehre ist ein Beitrag mit dem Titel Status-Bias im Peer-Review-Verfahren, den ich sehr interessant fand. Der Beitrag beginnt mit folgenden Worten: Forschungsarbeiten von renommierten Wissenschaftlerinnen und Wissenschaftlern werden trotz gleicher Qualität im Peer-Review-Verfahren deutlich besser bewertet als Arbeiten weniger bekannter Forschender. Zu diesem Ergebnis kommt ein Wissenschaftlerteam um Professor Jürgen … Continue reading "Status-Bias im Peer-Review"