Let M be a closed Riemannian manifold and denote by X its universal covering space equipped with the pulled back Riemannian metric. There is an intimate relation between the Laplace operator on X and the fundamental group of M. One example of this is the result of Brooks from 1981: the fundamental group of M … Continue reading "Laplace operator and covering spaces"
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"
This is actually already old news (it is from September 2018), but since then it was on my list of things to blog about and only now I found the time to actually do it. There was a meta-study published in Nature Communications (doi:10.1038/s41467-018-06292-0) about the performance of girls and boys in STEM fields. I … Continue reading "Girls and boys performing in STEM fields"
This year’s Shaw Prize in Mathematical Sciences goes to Michel Talagrand (link to the press release, link to his Wikipedia page).
Recently a preprint was posted on the arXiv ( arXiv:1904.12720 ) claiming to have constructed the first examples of compact orientable hyperbolic non-spin manifolds (in every dimension at least 4). I was a bit surprised by this, since I thought that such examples should be already known. Apparently not … One reason why constructing such … Continue reading "Compact hyperbolic non-spin manifolds"
Some pictures from the SPP Conference in April 2019 in Münster. Let me start with a picture of the speaker of the SPP, Bernhard Hanke, explaining at the beginning of the conference the next steps leading to the second funding period of the SPP. (I unfortunately forgot to take a picture of Carsten Balleier from … Continue reading "Impressions from the SPP Conference"
A week ago the EMS posted links to reports on the impact of mathematical research on society and economy. You can access these reports here: link. Though probably for many too long to read in detail, reading just the introductions is already interesting.
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"
In the last few weeks were two quite different prizes awarded, on which I want to report. In March 14th, 2019, the L’Oréal-UNESCO For Women in Science International Awards (homepage, UNESCO webpage, wikipedia) were presented to five women. One of the five laureates is Claire Voisin (wikipedia) who is “rewarded for her outstanding work in algebraic geometry. Her pioneering … Continue reading "Two quite different prizes"
There was a Special Session on Coarse Geometry, Index Theory, and Operator Algebras: Around the Mathematics of John Roe at the Spring Central and Western Joint Sectional Meeting of the AMS last weekend to which Christopher and I were invited to give talks. John Roe passed away last year. His personal webpage is still online … Continue reading "AMS Special Session on the Mathematics of John Roe"