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"

Fields medalists 2022

Recently the Fields medalists 2022 (and all the other prizes given out by the IMU) were announced: official page. You can read about some of the achievements of these people on the blog of Gil Kalai (and of course also in the official laudationes).