Computer assisted verification of contemporary mathematics

Half a year ago Steffen Kionke wrote a blog post on condensed mathematics wherein he mentioned that Peter Scholze put up a challenge to formally verify a key fundamental result of a joint paper with Clausen: a result Scholze terms his most important theorem to date. Today I want to inform you that the mentioned … Continue reading "Computer assisted verification of contemporary mathematics"

Topological complexity

Rummaging in the arXiv I ran across this article and the notion of topological complexity which is really appealing. The idea of topological complexity isn’t quite new, it was developed by M. Farber in a short article published in 2003 in Discrete & Computational Geometry. The article doesn’t even have a proper review on MathSciNet, … Continue reading "Topological complexity"

The group of germs at infinity of line homeomorphisms

Recently, I learned that the group G∞ of germs at +∞ of orientation preserving homeomorphisms of the real line has two remarkable properites: it is simple and left-orderable. I thought it is maybe worth to share some background on left-orderability (and why this might be interesting). Let’s start with a definition: A group G is … Continue reading "The group of germs at infinity of line homeomorphisms"

Ergebnisse der Wissenschaftsbefragung

Gestern sind die Ergebnisse der DZHW-Wissenschaftsbefragung veröffentlicht worden. Die Wissenschaftsbefragung ist eine bundesweite repräsentative Trendstudie. [… Sie] versteht sich als langfristiges Barometer der Wissenschaft. Sie ist ein wichtiges Werkzeug zur Untersuchung der Arbeits- und Forschungsbedingungen an deutschen Universitäten und soll ein umfassendes Meinungsbild zur Lage und Entwicklung des deutschen Wissenschaftssystems liefern. Hier ist die Pressemeldung, … Continue reading "Ergebnisse der Wissenschaftsbefragung"

Catastrophe theory

This term I am teaching a course on catastrophe theory for 2nd year students. When you look up this topic on Wikipedia, you will see words like chaos and singularities mentioned, and you will be shown fancy pictures of the seven elementary catastrophes. But when you try to understand what the actual mathematical content of … Continue reading "Catastrophe theory"