Linkage

Rotations of Klein’s quartic. Lieven Le Bruyn uses both geometric and group-theoretic arguments to understand the symmetries of this surface.

Predatory journals that list academics as being on their editorial boards, without asking, and then won’t remove them even when asked. Just in case you were under the impression that taking money to publish bad papers and spamming calls for papers to researchers in unrelated areas were the only annoying things they did.

The “guerrilla” Wikipedia editors who combat conspiracy theories.

Random points on a group (G+). John Baez uses character theory to explain why the even moments of distances between randomly-selected points on a circle or on a 3-sphere form combinatorially-significant integer sequences, but other dimensions give non-integers. It turns out to be closely related to the fact that the spheres of those dimensions are compact Lie groups.

Videos from the workshop in honor of Vijay Vazirani are now up (via). Which gives me an opportunity to ask what’s known about a commutative but non-associative binary operation on pairs \((x,y)\) that takes the \(x\) whose \(y\) is maximum and then adds the \(y\) values, used by Manuel Blum as part of a mathematical model for pain.

Intricate tunnels in garnet crystals (via), thought to be the tracks of microbial growth.

Kill sticky headers. Annoyed by stuck-in-place web site banners that get in the way of reading the content you’re trying to read? This useful little bookmarklet can help.

How to make a rhombic spirallohedron (via). There are lots of convex polyhedra having rhombuses as faces — the zonohedra formed from the Minkowski sum of unit line segments (no three parallel to a single plane, to avoid faces with more than four sides). But I don’t know much about these non-convex rhombohedra.

Merge-insertion sort. New Wikipedia article on a comparison sorting algorithm that for two decades held the record for the fewest number of comparisons known.

New National Academy of Sciences members. Congratulations to Sanjeev Arora, Umesh Vazirani, and Mihalis Yannakakis, who are adding to the representation of theoretical computer science within the National Academy!

Data-dependent hashing via nonlinear spectral gaps (Andoni et al, STOC 2018) and a clickbaity Quanta article about it. “A universal method to sort information”? Really it’s about using embeddability of expander graphs to distinguish metric spaces that have nontrivial approximate nearest-neighbor data structures from those that don’t, and developing such data structures for all normed spaces.

Lenore and Manuel Blum resign from CMU (G+, via) over “professional harassment” and “sexist management”.