### 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”.

### Hyperbolicity of one-relator groups

Recall that a one-relator group is a group $$G$$ admitting a presentation of the form $$G = \langle x_1, \ldots, x_n \ | \ r = 1\rangle$$, where $$r$$ is a (cyclically reduced) word in the letters $$\{x_1, \ldots, x_n\}$$. One-relator groups form an interesting class of groups studied by many people in geometric group … Continue reading "Hyperbolicity of one-relator groups"

### ICM 2022 takes place as a fully virtual event

The International Mathematical Union announced that the International Congress of Mathematicians 2022 will not be held in Saint Petersburg but will take place as a fully virtual event instead. The participation will be free of charge. The full statement can be found here.

### 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"

### Lehmer’s conjecture and the Fuglede-Kadison determinant

Lehmer’s conjecture is one of the most striking open problems in number theory. It roughly postulates that the complex roots $$a$$ with $$|a| > 1$$ of a polynomial with integral coefficients cannot simultaneously be close to the unit circle (unless all non-zero roots lie on the unit circle). More precisely, the Mahler measure of a … Continue reading "Lehmer’s conjecture and the Fuglede-Kadison determinant"

### 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"