Non-positive immersions

In a blog post about hyperbolicity of one-relator groups I mentioned the following property that a 2-dimensional complex \(X\) might have: \(X\) is said to have non-positive immersions if for every immersion of a finite, connected 2-complex \(Y\) into \(X\), we either have \(\chi(Y) \le 0\) or \(Y\) is contractible. For example, this property rules … Continue reading "Non-positive immersions"

Fields medalists 2022

Recently the Fields medalists 2022 (and all the other prizes given out by the IMU) were announced: official page. You can read about some of the achievements of these people on the blog of Gil Kalai (and of course also in the official laudationes).

Shaw Prize 2022

The Shaw Prize in Mathematical Sciences 2022 (link) is awarded to Noga Alon and to Ehud Hrushovski for their remarkable contributions to discrete mathematics and model theory with interaction notably with algebraic geometry, topology and computer sciences.

A quantitative coarse obstruction to psc-metrics

Recently, Guo and Yu pushed the following result to the arXiv (math.KT/2203.15003): For any \(R > 0\) and positive integer \(m\), there exists a constant \(k(R,m)\) such that the following holds. If \((M,g)\) is a Riemannian spin manifold that admits a uniformly bounded, good open cover with Lebesgue number \(R\) and \(R\)-multiplicity \(m\), then \[\inf_{x \in M} \kappa_g(x) \le … Continue reading "A quantitative coarse obstruction to psc-metrics"