Linkage

A new algorithm for graph crossings, hiding in plain sight (\(\mathbb{M}\)). Dynamic graph planarity testing, in Quanta. The original papers are arXiv:1910.09005, in SODA 2020 and arXiv:1911.03449, in STOC 2020, by Jacob Holm and Eva Rotenberg.

Fun with Algorithms proceedings, now online (\(\mathbb{M}\)). So if you want to read about robot bamboo trimmers, phase transitions in the mine density of minesweeper, applications of the Blaschke–Lebesgue inequality to the game of battleship, multiplication of base-Fibonacci numbers, or trains that can jump gaps in their tracks, you know where to go. The conference itself has been rescheduled to next May. Maybe by then we can actually get a trip to an Italian resort island out of it.

Cantor set kirigami (\(\mathbb{M}\)). One of many many mathy-craft blog posts at Fractal Kitty, which I found via the AMS math blog tour.

Probability theorist Nina Holden, quantum complexity theorist Urmila Mahadev, and knot theorist Lisa Piccirillo win the 2021 Maryam Mirzakhani New Frontiers Prizes (\(\mathbb{M}\)). For more on them their work, see Baez on the Brownian map, Quanta on quantum verification, and Quanta on Conway’s knot problem.

Richard Borcherd’s YouTube channel (\(\mathbb{M}\)), “a trove of mathematical lectures at various levels”.

Perspectiva corporum regularium (1568), by Wenzel Jamnitzer (\(\mathbb{M}\), see also). I don’t know how readable the brief medieval German text connecting the regular polyhedra to Plato’s theory of the four elements is, but the pictures of elaborated variations of the regular polyhedra can be understood in any language.

Two new Wikipedia articles inspired by papers at Graph Drawing 2020 (\(\mathbb{M}\)):

• Geodetic graph, a graph in which all shortest paths are unique, inspired by “Drawing shortest paths in geodetic graphs”

• Kirchberger’s theorem, that if every points in a red-blue point set are linearly separable then all of them are, inspired by “Topological drawings meet classical theorems from convex geometry”

European Women in Mathematics have written an open letter advocating proactive support of temporary employees, applicants, women, and parents in academia (\(\mathbb{M}\), via), to forestall disproportionate losses in diversity in the wake of the covid pandemic. It’s addressed to European authorities but most of the same concerns apply more globally.

China blocks Wikimedia Foundation from being an observer to the World Intellectual Property Organization (\(\mathbb{M}\), via), apparently because it has a chapter in Taiwan.

Royal Society Open Science journal publishes crank quantum paper despite negative referee reports, and has not responded to two-year-old open letter from two of the referees and several other quantum heavy hitters requesting its retraction (\(\mathbb{M}\), via).

Michael Wehar posted a nice algorithms / fine grained complexity question on the CS theory stack exchange: how quickly can we test whether a 2d matrix has a square of four non-zero entries (\(\mathbb{M}\))? The obvious method, looping over nonzeros and testing the squares each might be part of, is cubic when there are many nonzeros. And there can be many nonzeros without forcing a square to exist. Is there a standard hardness assumption under which strongly subcubic is impossible?

The connection between the unexpected appearance of \(\pi\) in counting the bounces of billiard balls of different sizes and Grover’s algorithm for quantum search (\(\mathbb{M}\)): hidden constraints that keep things on a unit circle. Based on a preprint by Adam Brown.

Puzzle reviews by a puzzle writer (\(\mathbb{M}\)). Lipton and Regan look at a few puzzles from the book Bicycles or Unicycles: A Collection of Intriguing Mathematical Puzzles, by Velleman and Wagon, concentrating on one that places a pebble at the origin of the positive quadrant and asks to clear a \(3\times 3\) square by moves that replace a pebble by one above and one to its left. The puzzle writer is Jason Rosenhouse, who reviewed Bicycles or Unicycles in the Notices.

Otto Neugebauer, famous as a historian of mathematics, also championed internationalism and diversity during Nazi times (\(\mathbb{M}\), via).

Nature covers the stories of five international students and postdocs whose plans to join US academia were disrupted by Trumpist visa restrictions (\(\mathbb{M}\), via).