### Nobel Prize for Sir Roger Penrose

Sir Roger Penrose won the Nobel Prize in Physics for the discovery that black hole formation is a robust prediction of the general theory of relativity. I have to admit that I connected him up to now only with aperiodic tilings of the plane (Wikipedia link). If you want to know more about him you … Continue reading "Nobel Prize for Sir Roger Penrose"

### Positive scalar curvature metrics on manifolds with boundary

Usually when I blog here about positive scalar curvature, the manifolds I consider are assumed to have no boundary. In this post I want to explain the basics of what happens when the manifolds actually do have a boundary. So first of all, one has to mention that any compact manifold with boundary admits a … Continue reading "Positive scalar curvature metrics on manifolds with boundary"

Das braucht man doch nie in der Schule! ist ein oft gehörtes Argument, wenn sich Studierende des gymnasialen Lehramts der Mathematik über die Inhalte ihrer Fachvorlesungen beschweren. Sie hören in den ersten Semestern oft dieselben Vorlesungen wie ihre Kommilitonen, welche die Mathematik auf einen Bachelor studieren, und in der Tat ist ein Teil des erlernten … Continue reading "Akademisches und schulbezogenes Fachwissen"

### Preise auf der DMV-Jahrestagung 2020

Die Jahrestagung 2020 der DMV fand vor zwei Wochen statt. Hier könnt ihr einen Kurzbericht dazu lesen: link. An dieser Stelle möchte ich kurz von den zwei auf dieser Jahrestagung verliehenen Preisen berichten: Anlässlich ihres 130-jährigen Bestehens hat die DMV die Minkowski-Medaille für besondere mathematische Forschungsleistungen geschaffen. Mit der Minkowski-Medaille will die DMV Mathematikerinnen und Mathematiker … Continue reading "Preise auf der DMV-Jahrestagung 2020"

### Can one hear orientability?

Mark Kac asked in a paper from 1966 the following question: Can one hear the shape of a drum? The mathematically precise question is the following: Assume that $$(M,g)$$ and $$(N,h)$$ are two compact Riemannian surfaces (thought of as the heads of two drums). If the Laplace operators of $$(M,g)$$ and of $$(N,h)$$ have the … Continue reading "Can one hear orientability?"

### Breakthrough Prizes 2021

Three days ago the Breakthrough Prize Foundation announced the recipients of the 2021 Breakthrough Prizes. I focus in this post only on the prizes in mathematics (there are also prizes in life sciences and physics). Martin Hairer is the recipient of the 2021 Breakthrough Prize in Mathematics for transformative contributions to the theory of stochastic … Continue reading "Breakthrough Prizes 2021"

### Contractible 3-manifolds and positive scalar curvature, II

Let $$(M,g)$$ be a complete, contractible Riemannian $$3$$-manifold (without boundary). Chang-Weinberger-Yu (link) proved that if $$(M,g)$$ has uniformly positive scalar curvature, then $$M$$ must be homeomorphic to $$\mathbb{R}^3$$. Recently (arXiv:1906.04128), Wang proved that if $$(M,g)$$ has positive scalar curvature and $$M$$ has trivial fundamental group at infinity, then $$M$$ must be homeomorphic to $$\mathbb{R}^3$$. Jiang … Continue reading "Contractible 3-manifolds and positive scalar curvature, II"

### Isometry groups of hyperbolic surfaces

A month ago Aougab, Patel and Vlamis posted a preprint on the arXiv (arXiv:2007.01982) about the question which groups, for a fixed orientable surface of infinite genus, can be realized as the full isometry group of a Riemannian metric of constant negative curvature on that surface. To my surprise, they stated in the introduction that … Continue reading "Isometry groups of hyperbolic surfaces"