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!

Progress on the union-closed sets conjecture

The union-closed sets conjecture is the following extremely easy to state conjecture about subsets of finite sets: Assume that \(\mathcal{F}\) is a family of subsets of \(\{1, 2, \ldots, n\}\) which is union-closed; this means that for any two sets \(A,B\) in \(\mathcal{F}\) their union \(A \cup B\) is also a member of \(\mathcal{F}\). Then … Continue reading "Progress on the union-closed sets conjecture"

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"

Non-positive immersions

In a blog post about hyperbolicity of one-relator groups I mentioned the following property that a 2-dimensional complex \(X\) might have: \(X\) is said to have non-positive immersions if for every immersion of a finite, connected 2-complex \(Y\) into \(X\), we either have \(\chi(Y) \le 0\) or \(Y\) is contractible. For example, this property rules … Continue reading "Non-positive immersions"