Linkage for the start of another academic year

Shift networks (\(\mathbb{M}\)). Jeremy Kun asks how to permute vectors using few vector additions, elementwise multiplications, and rotation operations, for an application involving homomorphic encryption.

Our fractional universe (\(\mathbb{M}\)). Jim Propp and his guest columnist Jeff Glibb parody those breathless but vague pop-sci expositions of new mathematical discoveries.

Byrne’s Euclid (\(\mathbb{M}\)), the one with colored diagrams replacing all the symbols, newly digitized and available online from the Harvard library.

Noted algorithmic bias researcher Timnit Gebru had a recent application for a grant to study the risks of AI turned down because she wouldn’t put it under the thumb of the big corporate players.

The call for papers for the 41st International Symposium on Computational Geometry (SoCG 2025) in Kanazawa, Japan next June is now live (\(\mathbb{M}\)). Abstracts are due November 26, with full submissions due December 3.

Small volume bodies of constant width (\(\mathbb{M}\)). Here “small” means exponentially small, as a function of dimension, relative to the unit ball. See also breathless but vague pop-sci exposition in Quanta.

How not to prove the four color theorem (\(\mathbb{M}\)). Why a failed 2022 proof based on finding a large fraction of planar triangulations that are 4-colorable could never have worked: any large fraction of these graphs contains all planar graphs as subgraphs, and cannot be easier to prove 4-colorable than all planar graphs.

I spent an afternoon at the local beach instead of just staying online all day (\(\mathbb{M}\)). We saw an osprey, hovering low over the shallow water near some skin divers, but I didn’t bring the long lens needed for a good photo of it. Instead, here’s a wide shot of the beach in late afternoon. More photos.

Incidentally this photo totally confused Adobe Lightroom’s level function. It was about \(0.5^\circ\) off-level but I had to correct it manually despite the obvious visible horizon line. The level function wanted to level the sand ripples in the foreground.

Ryan Williams attempts to refute the orthogonal vectors conjecture (\(\mathbb{M}\)), and with it the strong exponential time hypothesis, by proving that if we could find orthogonal vectors (or disjoint sets) quickly, we could prove strong lower bounds in circuit complexity on the simulation of read-once 2-DNFs. He also uses SAT solvers to develop new algorithms for disjointness with interesting time bounds (but not strong enough bounds to refute these conjectures).

See-through illustration of a 38-sided space-filling polyhedron (\(\mathbb{M}\)), with some of its neighbors. This is the most sides known but the best upper bound proven so far is 92.

Innovations in Graph Theory publishes its first issue (\(\mathbb{M}\)). This is a diamond-model open-access journal published by the Centre Mersenne in Grenoble; see also the journal’s home page.

A method from one of my older papers, “Algorithms for coloring quadtrees”, 3-colors the binary tiling of the hyperbolic plane (\(\mathbb{M}\)). The tiles of each color form three interwoven infinite binary trees under corner-to-corner adjacencies.

Tired: publishers shortcutting academic peer-review to profit from open-access publication fees. Wired: publishers shortcutting academic peer-review to generate AI training data as quickly as possible (\(\mathbb{M}\)). Their authors get no say in whether their content is taken for this purpose. The linked story targets Taylor & Francis / Routledge, but Wiley and the Oxford University Press are also complicit in similar deals. The “feed the beast” illustration below is stolen from John Baez’s Mastodon post, where he writes “Yes, this image is AI-generated. I thought that was appropriate, in a darkly humorous way.”