Linkage
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Keller’s conjecture (\(\mathbb{M}\)), another new Good Article on Wikipedia. The conjecture was falsified in 1992 with all remaining cases solved by 2019, but the name stuck. It’s about tilings of \(n\)-space by unit cubes, and pairs of cubes that share \((n-1)\)-faces. In 2d, all squares share an edge with a neighbor, but a 3d tiling derived from tetrastix has many cubes with no face-to-face neighbor. Up to 7d, some cubes must be face-to-face, but tilings in eight or more dimensions can have no face-to-face pair.
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Italians and bibliometrics (\(\mathbb{M}\)): Luca Trevisan (a leading theorist with 7 SODA papers, 2 FOCS papers, a JACM paper and a SICOMP paper in the last four years) gets dinged for poor productivity as the Italian system only counts journal papers that do not match conference papers. The fact that these are all in top venues is irrelevant, and the conference papers count only negatively against matching journal papers. Comments discuss similar problems in other countries.
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What is the computational complexity of dinosaur train tracks? (\(\mathbb{M}\)). Answer: not very high, because the only usable junction, a Y that remembers which way you came through it and sends you the same way if you come back through the other direction, is just not powerful enough to do much.
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Congratulations to Martín Farach-Colton, Shang-Hua Teng, and all of the other new SIAM Fellows (\(\mathbb{M}\))!
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Stephen Wolfram tries to track down what happened to logician Moses Schönfinkel (\(\mathbb{M}\), via), who worked in Göttingen from 1914 to 1924, returned to Moscow, and then “basically vanished”. Wikipedia has more detail about what happened after (mental health issues, death around 1942), but Wolfram says the evidence for all that is weak. He doesn’t make direct progress on Schönfinkel himself but does find some relatives.
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How Christian Lawson-Perfect got a pen plotter to draw mathematical notation using TeX (\(\mathbb{M}\)).
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Aaronson on politicization of research prizes (\(\mathbb{M}\)). Jeff Ullman won the Turing Award despite deplorable (some say racist) treatment of grad applicants for the crime of being Iranian, and Oded Goldreich was blocked from the Israel Prize for anti-settlement politics. Politicization is two-edged. I’d rather see Ullman awarded for his worthy contributions, and use the opportunity to decry his abhorrent actions and statements, than subject prizes to litmus tests from all sides.
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Circles, polygons and the Kepler-Bouwkamp constant (\(\mathbb{M}\)). On the limiting behavior of infinitely-nested shapes alternating between circles and polygons with increasing numbers of sides.
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Continuing gender bias in who sees job-opening ads on Facebook (\(\mathbb{M}\), via): if an employer or industry has historically skewed male or female, Facebook replicates that bias, even for pairs of ads with identical qualifications. This is illegal, but Facebook appears unable to find a technical fix and unwilling to apply the obvious fix of not targeting its ads even when that targeting is illegal. As usual for Hacker News via links on topics related to social justice, don’t read the comments there.
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Amusing quote from McLarty’s 2003 “Grothendieck on simplicity and generality” (\(\mathbb{M}\), via): “Serre created a series of concise elegant tools which Grothendieck and coworkers simplified into thousands of pages of category theory.” Nowadays I guess the people doing this sort of simplification are the ones formulating machine-verifiable proofs…
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WADS 2021 accepted papers (\(\mathbb{M}\)). The biennial Algorithms and Data Structures Symposium is usually in Canada, and this time was supposed to be in Halifax, but is looking very likely to be completely online, this August. I have one paper on the list; I’ll write more about it later when I have a preprint version ready to share.
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A “confounding topological curiosity” (\(\mathbb{M}\), via): a double torus with a line through one of its holes can be continuously transformed so that the line instead goes through both holes.
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Strange inverses in the group rings of torsion-free groups (\(\mathbb{M}\), via, see also). This result of Giles Gardam disproves the strongest of the three Kaplansky conjectures on group rings. It’s just an isolated example at this point but it does show that group rings are less well-behaved than had been hoped.