A recent article in the QuantaMagazine (link) discusses a paper of Georgios Moschidis (arXiv:1812.04268) who proved instability of Anti-de Sitter space-time for a certain Einstein-matter system. Recall that the Anti-de Sitter space-time is the maximally symmetric solution of the vacuum Einstein equations in the presence of a negative cosmological constant. One can attach a boundary-at-infinity to Anti-de Sitter … Continue reading "Instability of Anti-de Sitter Space-Time"
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"
The classical algorithm, that everyone knows from elementary school, for multiplying two n-digit integers runs in \(O(n^2)\)-time. Recently, there was a preprint posted on HAL (link) in which the authors provide an algorithm which runs in \(O(n\log(n))\)-time. A nice article about this discovery may be found at the QuantaMagazine: link. Further, it was also recently proven in another preprint … Continue reading "Multiplying integers"
The problem From the usual Euclidean plane we form the following graph: the points of the plane are the vertices of our graph, and two vertices are connected by an edge if they are exactly unit distance apart. The so-called Hadwiger-Nelson problem is to compute the chromatic number of this graph, i.e., the least amount … Continue reading "Chromatic Number of the Plane is at least 5"
The award ceremony is certainly not what mathematicians are used to, and there are certainly many things that one can say for and against such monstrous awards and the ambience around. In any case, if you‘d like to see the ceremony, the math part starts at 1:22:30. The breakthrough prize for 2018 was given to … Continue reading "Breakthrough Prize for higher-dimensional geometry"
Spiegel Online reports today (Escher in 3D) on work of Alexander Gürten from the contest Math Creations. It is about bulls tesselating Euclidean space. Have a look at the linked video:
The New York Times has an article about the untimely death of Marina Ratner and Maryam Mirzakhani: With Snowflakes and Unicorns, Marina Ratner and Maryam Mirzakhani Explored a Universe in Motion