### Validity of results

Can you vouch for the validity of the results in papers that you cite and use in your own articles? In April this year Blagojević, Cohen, Crabb, Lück and Ziegler posted a preprint on the arXiv (arXiv:2004.12350) writing in the abstract “This invalidates a paper by three of the present authors […] who used a … Continue reading "Validity of results"

### Conjugation Curvature

Recently I saw some papers on the arXiv on conjugation curvature of finitely generated groups (also called medium-scale curvature, transportation curvature, metric Ricci curvature or comparison curvature for Cayley graphs). I got a bit interested in it and so decided to write up a short post about it. Let $$G$$ be a finitely generated group … Continue reading "Conjugation Curvature"

### Collatz conjecture

Given a natural number n, the Collatz sequence it generates is the following: if n is even, then divide it by 2, if n is odd, then multiply it by 3 and add 1; and now iterate this procedure. The Collatz conjecture states that you will always end up with the number 1 after finitely … Continue reading "Collatz conjecture"

### Large scale properties of 3-manifold groups

A week ago there was a preprint posted on the arXiv by Peter Haïssinsky and Cyril Lecuire about Quasi-isometric rigidity of three manifold groups (arXiv:2005.06813). Building on work by many other people, they complete the proof that the class of 3-manifold groups is quasi-isometrically rigid, meaning the following: if a finitely generated group G is quasi-isometric … Continue reading "Large scale properties of 3-manifold groups"

### Banach conjecture

There was a paper today in the arXiv mailing list (arXiv:2006.00336) proving yet another case of the Banach conjecture. I never heard of this conjecture before, but it is easy to state and seems to me to be a foundational recognition principle for those Banach spaces that are actually Hilbert spaces. The conjecture was stated … Continue reading "Banach conjecture"

### Shaw Prize 2020

The Shaw Prize 2020 in the Mathematical Sciences goes to Alexander Beilinson and David Kazhdan “for their huge influence on and profound contributions to representation theory, as well as many other areas of mathematics.” More information can be found here: https://www.shawprize.org/laureates/mathematical-sciences/2020.

### MINTchallenge

Der Club MINT, eine Initiative des Stifterverbands, ruft regelmäßig die MINTchallenges aus in denen “schlaue Ideen zur Lösung aktueller Herausforderungen der MINT-Bildung an Hochschulen” gesucht werden. In der aktuellen MINTchallenge sucht der Stifterverband nach “kreativen, digitalen Alternativen zu Präsenzveranstaltungen an Hochschulen, die das MINT-Studium auch nach der Corona-Pandemie nachhaltig verbessern.” Bewerbungsschluss ist der 13. Juni … Continue reading "MINTchallenge"

### Instability of Anti-de Sitter Space-Time

A recent article in the QuantaMagazine (link) discusses a paper of Georgios Moschidis (arXiv:1812.04268) who proved instability of Anti-de Sitter space-time for a certain Einstein-matter system. Recall that the Anti-de Sitter space-time is the maximally symmetric solution of the vacuum Einstein equations in the presence of a negative cosmological constant. One can attach a boundary-at-infinity to Anti-de Sitter … Continue reading "Instability of Anti-de Sitter Space-Time"

### EMS Prizes 2020

Though the 8th European Congress of Mathematics was postponed to 2021, the recipients of the EMS Prizes 2020 were already announced: https://8ecm.si/news/69.

### Local-to-global principles for the topology of boundaries of hyperbolic groups

Two weeks ago a paper was posted (by Benjamin Barrett) on the arXiv (arXiv:2004.11650) proving the following theorem about Gromov boundaries of word hyperbolic groups: Let $$G$$ be a one-ended hyperbolic group. Then $$\partial G$$ is locally simply-connected if and only if for every point $$\xi\in \partial G$$ the space $$\partial G \setminus \xi$$ is … Continue reading "Local-to-global principles for the topology of boundaries of hyperbolic groups"