GDM-Monat 2021 – Hauptvortrag zum Mathematischen Beweisen

Die Gesellschaft für Didaktik der Mathematik (GDM) hat wegen der Corona-Pandemie anstatt einer Präsenztagung im Jahre 2021 im März einen Monat lang Vorträge und Veranstaltungen ‘dezentral und online’ durchgeführt (link). In manche der Vorträge hatte ich damals reingehört (hauptsächlich solche, die sich mit der Hochschuldidaktik beschäftigen) und wollte auf diesem Blog kurz über die Inhalte … Continue reading "GDM-Monat 2021 – Hauptvortrag zum Mathematischen Beweisen"

Shaw Prize 2021

The Shaw Prize 2021 in the Mathematical Sciences goes to Jean-Michel Bismut and Jeff Cheeger for their remarkable insights that have transformed, and continue to transform, modern geometry. Bismut […] imported ideas from probability into index theory, reproving all the main theorems and vastly extending them, which enabled him to link index theory to other parts … Continue reading "Shaw Prize 2021"

Characterizing Euclidean 3-space

In my previous post about the recent preprint of Jiang Wang we saw the following characterization of Euclidean 3-space among all contractible 3-manifolds: It is the only one that admits a complete Riemannian metric of non-negative scalar curvature. Today a preprint was posted on the arXiv:2105.09035 by Bargagnati and Frigerio providing another characterization: The only … Continue reading "Characterizing Euclidean 3-space"

Online Fernklausuren in Mathematik

Im letzten Semester mussten aufgrund der Pandemie viele Prüfungen in anderen (oft digitalen) Formaten abgehalten werden. Für das laufende Sommersemester – auch wenn sich die Lage derzeit bessert – scheint es mir wahrscheinlich, dass zumindest Prüfungen mit vielen Teilnehmern weiterhin Einschränkungen unterworfen sind. Daher will ich die Gelegenheit nutzen, um ein paar Überlegungen zu sammeln, … Continue reading "Online Fernklausuren in Mathematik"

Contractible 3-manifolds and positive scalar curvature, III

I have already blogged several times about complete Riemannian metrics of positive scalar curvature on 3-manifolds: here, here and here. Now it seems that finally Jian Wang proved the result that he was working on for quite some time now (arXiv:2105.07095): Any contractible 3-manifold admitting a complete Riemannian metric of non-negative scalar curvature is homeomorphic to Euclidean … Continue reading "Contractible 3-manifolds and positive scalar curvature, III"

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"

Extensions, coarse embeddability and the coarse Baum-Connes conjecture

One of the pinnacle results so far about the (strong) Novikov conjecture is Guoliang Yu’s proof that it holds for groups which are coarsely embeddable into a Hilbert space. In fact, he first proved that under this assumption the coarse Baum-Connes conjecture holds, and then one can invoke the descent principle to get to the … Continue reading "Extensions, coarse embeddability and the coarse Baum-Connes conjecture"