Aspherical manifolds and positive scalar curvature

Recall the following conjecture about aspherical manifolds (i.e., manifolds whose universal cover is contractible): If M is a closed, aspherical manifold, then M does not admit any Riemannian metric of positive scalar curvature. In January I saw a preprint being posted on the arXiv (2001.02644) claiming to have resolved this conjecture. If it turns out … Continue reading "Aspherical manifolds and positive scalar curvature"

Lindelöf hypothesis

Today I stumbled across a news article ( link ) written about someone (actually, Athanassios Fokas – a known mathematician) having announced progress on the Lindelöf hypothesis ( wikipedia ). The Lindelöf hypothesis is related to the Riemannian hypothesis and actually also follows from it – progress on the Lindelöf hypothesis would also mean progress … Continue reading "Lindelöf hypothesis"