Author: Alexander Engel

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"

Abel Prize 2022

The Abel Prize 2022 was awarded to Dennis Sullivan “for his groundbreaking contributions to topology in its broadest sense, and in particular its algebraic, geometric and dynamical aspects”.

Mathematikleistungen von Schüler*innen der gymnasialen Oberstufe

Im Journal für Mathematik-Didaktik ist letztes Jahr ein Artikel von Rolfes-Lindmeier-Heinze erschienen (DOI:10.1007/s13138-020-00180-1), welcher die seit 1995 durchgeführten Schulleistungsuntersuchungen zu Mathematikleistungen in der Oberstufe einer Sekundäranalyse unterzieht, d.h. auf vergleichbare Skalen transformiert und vergleicht. Viele Dozierende in den MINT-Fächern klagen bei Studienanfänger*innen über schlechte Mathematikkenntnisse und es wird auch ein Verfall dieser über die letzten … Continue reading "Mathematikleistungen von Schüler*innen der gymnasialen Oberstufe"

Wolf Prize 2022

The Wolf Prize in Mathematics 2022 is awarded to George Lusztig for “groundbreaking contributions to representation theory and related areas.” The Wolf Prize is an international award granted in Israel for “achievements in the interest of mankind and friendly relations among people …”. Wikipedia writes further: “Until the establishment of the Abel Prize, the Wolf Prize was probably the closest equivalent of … Continue reading "Wolf Prize 2022"

Positive scalar curvature and the conjugate radius

A classical result in Riemannian geometry is the theorem of P. O. Bonnet and S. B. Myers stating that a complete Riemannian \(n\)-manifold \(M\) with Ricci curvature bounded from below by \(n-1\) has diameter at most \(\pi\). In the introduction of Bo Zhu’s recent preprint arXiv:2201.12668 the following ‘analogue’ of the Bonnet-Myers Theorem for scalar … Continue reading "Positive scalar curvature and the conjugate radius"

Properly positive scalar curvature

An interesting (at least to me) research theme in the geometry of manifolds is the question about the existence of positive scalar curvature metrics on closed manifolds. Since I also like to do coarse geometry, I therefore also consider the corresponding question on non-compact manifolds. But what is the ‘corresponding’ question on non-compact manifolds? Currently, … Continue reading "Properly positive scalar curvature"