Linkage
Beware the Ides of February.

Holes and their reflections (\(\mathbb{M}\)). (The reflections are in the curved surface of an espresso portafilter.)

The 2019 Bridges mathematical art gallery is online! (\(\mathbb{M}\)). Brian Hayes lists his favorites as being the warped notepaper of Matt Enlow and the Penrose quilt of Douglas G. Burkholder.

Some of my own favorites from this year’s Bridges mathematical art gallery (\(\mathbb{M}\)): Fielding Brown’s 3d Lissajous wood ribbon sculpture, Diana Davis’s periodic pentagonal billiards patterns, Stephen Kenney’s illustration of triangle geometry, Elizabeth Paley’s stoneware Klein bottle, and Anduriel Widmark’s knotted glasswork.

Rod Downey, a New Zealandbased theoretical computer scientist who cofounded the theory of parameterized complexity, has won the Rutherford Medal, New Zealand’s highest science award (\(\mathbb{M}\)). Somehow I missed this when it came around last October.

Hannah Bast’s slides on the European Symposium on Algorithms 2018 Track B experiment (\(\mathbb{M}\)). (two independent program committees decided on the same set of papers and then the conference accepted the union of their acceptances). Some conclusions: the initial scoring is remarkably consistent, and perpaper discussions to reconcile differences of scoring are useful, but the final decision on which “gray zone” papers to keep is random and could be replaced by a simple threshold.

Quanta writes up recent progress on the Erdős–Szemerédi sumproduct problem, that any set of numbers must either have many distinct pairwise sums or many distinct products (\(\mathbb{M}\)). Progress: “many” increased from \(\Omega(n^{4/3+1/1509})\) to \(\Omega(n^{4/3+5/5277})\).

How to handle journal referees who ask authors to add unjustified citations to their own papers? (\(\mathbb{M}\)). Is their misbehavior protected by the anonymity of peer review or can they be publicly named and shamed?

The Cal Poly ag students have started selling these blood oranges at the local farmer’s market, as they do every year around this time, only $1 for five. In the summer they sell sweet corn on the cob. (\(\mathbb{M}\)).

Turing patterns in shark skin (\(\mathbb{M}\), original paper). Researchers at the University of Florida led by Gareth Fraser and his student Rory Cooper used reactiondiffusion patterns (also named Turing patterns after Turing’s early work) to model the distribution of scales on sharks, and performed knockdown experiments to validate their model in vivo.

Did you know that two different graphs with 81 vertices and 20 edges/vertex are famous enough to have Wikipedia articles? (\(\mathbb{M}\)). The strongly regular Brouwer–Haemers graph connects elements of GF(81) that differ by a fourth power. The Sudoku graph connects cells of a Sudoku grid that should be unequal. Sudoku puzzles are instances of precoloring extension on this graph. Unfortunately the natural graphs on the 81 cards of Set have degree ≠ 20…

Josh “cortex” Millard describes how he made a stained glass Menger sponge (\(\mathbb{M}\)).

Jacob Siehler labels cubic graphs with binary strings of length 5 so that all labels appear once and each vertex is the xor of its neighbors (\(\mathbb{M}\)). He can do three vertextransitive 32vertex graphs: the Dyck graph, an expansion of the vertices of \(K_{4,4}\) into four cycles, and another one I don’t know.

Four of Conway’s five $1000prize problems remain unsolved (\(\mathbb{M}\)): the dead fly problem on spacing of point sets that touch all large convex sets, existence of a 99vertex graph with each edge in a unique triangle and each nonedge the diagonal of a unique quadrilateral, the thrackle conjecture, on graphs drawn so all edges cross once, and who wins Sylver coinage after move 16?

The list of accepted papers from this year’s Symposium on Computational Geometry just came out (\(\mathbb{M}\)).