The Wolf Prize in one of the most prestigious prizes in mathematics (Wikipedia entry). This year’s laureates are Prof. Gregory Lawler (Wikipedia, Homepage) and Prof. Jean Francois le Gall (Wikipedia, Homepage). The corresponding press release of the EMS may be found here.
Recall that the Whitehead manifold is a contractible 3-manifold which is not homeomorphic to Euclidean 3-space (Wikipedia entry). It was proven by Chang-Weinberger-Yu (link) that the Whitehead manifold can not admit a complete metric of uniformly positive scalar curvature. Last year their result was strengthened by Jian Wang in arXiv:1805.03544 to the statement that the Whitehead manifold can … Continue reading "The Whitehead manifold and positive scalar curvature"
Sir Michael Atiyah died three days ago on January 11th, 2019 (news of The Royal Society). A nice obituary (together with one for Jean Bourgain) may be found on this blog: link. Here is another obituary by the New York Times.
Let \((X,d)\) be a complete, geodesic metric space. \((X,d)\) is called an Alexandrov space of global non-positive curvature if for every quadruple of points \(x,y,z,w\) such that \(w\) is a metric midpoint of \(x\) and \(y\), i.e., \(d(w,x) = d(w,y) = d(x,y)/2\), we have \[d(z,w)^2 + d(x,y)^2/4 \le d(z,x)^2/2 + d(z,y)^2/2.\] If the reverse inequality … Continue reading "Coarse embeddings and non-positive curvature"