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"
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"
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"
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"
A few days ago I was reading with Rudolf Zeidler the recent preprint by Zhizhang Xie (arXiv:2103.14498). We were especially focusing on the proof of the relative index theorem therein and the global analytic lemmas leading to it. While doing this, we realized that we can not come up on the spot with a counter-example … Continue reading "A relative index theorem too good to be true?"
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"
Two years ago I blogged about recent developments about multiplying integers. The next most important operation in (applied) mathematics is multiplying matrices. The usual way of doing this requires \(n^3\) multiplications (and some additions) for multiplying two \((n\times n)\)-matrices. But there is actually a way of doing it with less than this: the current record … Continue reading "Multiplying matrices"
The Abel Prize Laureates 2021 were announced today. They are László Lovász and Avi Wigderson for … their foundational contributions to theoretical computer science and discrete mathematics, and their leading role in shaping them into central fields of modern mathematics.