Linkage

Famous people’s bookshelves, visible as they teleconference from home (\(\mathbb{M}\), via). The story calls this inadvertent, but that seems dubious. Much of my teleconferencing has books behind me, deliberately, mostly as a clean background in a part of the house where it’s convenient to sit and lighting is good, but also because very few views in my house avoid books. On the other hand, at least one colleague has substituted a fake background from a library…

Susan Goldstine paints numbers onto the scales of pinecones (\(\mathbb{M}\)) to show how phyllotaxis causes the Fibonacci numbers to line up.

In a post on the Quine–McCluskey algorithm for minimizing Boolean functions (\(\mathbb{M}\)), Colin Beveridge suggests that all mathematical Q-eponyms are named for Dan Quillen or Willard Quine. But even if you discount Quasi-abelian categories, Quasi-Hopf algebras, and Quasi-Newton methods (named after Quasi-Abel, Quasi-Hopf, and Quasi-Newton) there’s also Qvist’s theorem in finite geometry, from Bertil Qvist.

Why the Szpiro conjecture is still a conjecture (\(\mathbb{M}\)). See especially the linked collection of comments from the preceding post (with significant contributions from Fields medalist Peter Scholze) for details of why Scholze thinks Mochizuki’s claimed proof not only doesn’t work, but can’t work.

Colin (not to be confused with Colin, above) asks for self-intersecting polyhedra with only hexagonal faces. I described a non-self-intersecting toroidal polyhedron with L-shaped hexagonal faces in an earlier post, but I think the small triambic icosahedron (conjectured by Grünbaum to be the only face-symmetric polyhedron with more than five sides per face) is closer to what he is asking for.

Bill Gasarch asks: why is there no grid for Hilbert’s 10th? (\(\mathbb{M}\)). What he wants to know is, for which pairs \((d,n)\) can we algorithmically find integer solutions to degree-\(d\) \(n\)-variable polynomial equations, and for which pairs is it undecidable? The answer seems to be: we can solve them when \(d\le 2\), we can’t solve them for some pairs of larger numbers, and there’s a big gap of unknown pairs.

EMS Prize, Klein Prize, and Neugebauer Prize (\(\mathbb{M}\)). Winners: Karim Adiprasito, Ana Caraiani, Alexander Efimov, Simion Filip, Aleksandr Logunov, Kaisa Matomäki, Phan Thành Nam, Joaquim Serra, Jack Thorne, and Maryna Viazovska; Arnulf Jentzen; Karine Chemla.

On the complexity of a “list” datastructure in the RAM model (\(\mathbb{M}\)). Linked lists can insert and delete at arbitrary positions. Arrays can find the value at position \(i\). Binary trees can do both, but with log time per operation. Combining methods for maintaining order in a list and integer ranking/unranking instead gives \(O(\log n/\log\log n)\). This showed up just in time for me to add some of the ideas to the syllabus for my ongoing online graduate data structures class.

Some reading on “git pull –rebase”: Gabeau/medium, Hasiński/coderwall, Shved & Mortensen/stackoverflow (\(\mathbb{M}\)). I have been using this in situations with multiple authors simultaneously working on a paper, to keep my contributions to the edit history linear (avoiding edit conflicts and merge bubbles in the history). It’s been working well for me but I realize it might be controversial…

Klaus Roth (1925–2015), Fields medalist who made important contributions to Diophantine approximation, arithmetic combinatorics, and discrepancy theory (\(\mathbb{M}\)). Now a Good Article on Wikipedia.

Scott Aaronson discusses four new preprints in quantum computing (\(\mathbb{M}\)).

Call for nominations for new editor-in-chief of ACM Transactions on Algorithms (\(\mathbb{M}\)). Nominations are due June 8.

My campus computing support people have decided that the middle of a very work-intensive term is the time to make me choose between stopping making illustrations or giving up access to the scientific literature (\(\mathbb{M}\)). The connection is the VPN I use to access campus journal and database subscriptions. They want to upgrade to a version incompatible with OS X 10.12. Upgrading OS X would be incompatible with my purchased Adobe software and make me pay money I don’t have for a subscription instead.