Linkage with glass viruses and a Cheeto sphere

FOCS 2023 introduces a new “conjectures track” (\(\mathbb{M}\)), seeking papers like the one by Khot that introduced the Unique Games Conjecture.

Intersecting ellipses induced by a max-sum matching (\(\mathbb{M}\)). Any matching on \(2n\) plane points is shorter than any star with them as leaves, by the triangle inequality. But sometimes not much shorter: there is a matching and star center from which all matched edges have angles \(\ge 2\pi/3\), so the length ratio is \(\le 2/\sqrt3\). This preprint by Barabanshchikova & Polyanskii proves more: the max length matching itself has a star that approximates each edge individually with the same ratio.

Three computer scientists have discovered a fast algorithm for finding shortest paths between points on graphs with negative weights (\(\mathbb{M}\)), Quanta summary of a recent breakthrough on a long-standing optimization problem. The original paper by Aaron Bernstein, Danupon Nanongkai, and Christian Wulff-Nilsen is in FOCS 2022 and online at arXiv:2203.03456.

The release of works into the public domain in Canada goes into a 20-year hiatus (\(\mathbb{M}\)) after its North American partners forced Canada into using Life+70 instead of Life+50 protection terms.

ICML banned ChatGPT for writing submissions (\(\mathbb{M}\)) and then walked it back.

The difficulty of of making machines to make machines to make the things you want (\(\mathbb{M}\)); in this case, tiny star-shaped pasta.

Bounds on the tensor rank of the determinant over various fields (\(\mathbb{M}\)). I’m intrigued by the connection between tensor ranks, tilings of space by orthogonal polyhedra, and flip graphs of ordered partitions of subsets alluded to in this blog post on a new preprint.

“CNET’s AI-written articles aren’t just riddled with errors. They also appear to be substantially plagiarized” (\(\mathbb{M}\), via). “The bot’s misbehavior ranges from verbatim copying to moderate edits to significant rephrasings, all without properly crediting the original. In at least some of its articles, it appears that virtually every sentence maps directly onto something previously published elsewhere.”

Quanta interview with Shang-Hua Teng (\(\mathbb{M}\)). “Teng discusses his upbringing in China and the math that good board games have in common.”

Nice explainer on the continuum hypothesis and how the idea that its independence makes the problem intractable “misses the actual nuance of the mathematical terrain”: for any “natural”-enough set, the dichotomy between the cardinalities of \(\mathbb{N}\) and \(\mathbb{R}\) is valid and provable.

I have no mathematical point to share here (\(\mathbb{M}\)), just a recoloring of an old image I made of the Folkman graph that I thought came out interesting-looking. It is something like one of Escher’s impossible figures: Locally it looks like it could be made from overlapping translucent sheets of blue material, cut out in this pattern, but globally it doesn’t all fit together.

You’ve probably heard about the glass flowers at Harvard, but have you seen Luke Jerram’s glass viruses and bacteria (\(\mathbb{M}\), via)?

Jullien Models for Descriptive Geometry (\(\mathbb{M}\)). Fold-out paper-and-thread models of 3d geometric constructions, from the mid-1870s, in the collection of the Smithsonian.

“To afford historic labor contract, UC considers cutting TAs, graduate student admissions” (\(\mathbb{M}\)). Apparently the administration is treating this as a zero-sum game: they’ve agreed to pay teaching assistants significantly more per person, but they won’t give us any larger budget for them, apparently intending that there be fewer slots to make it all balance.

Sam Keller’s Cheetosphere (\(\mathbb{M}\)), an artwork constructed much like a geodesic dome, but out of Cheetos.