11011110

11011110, 23 hours ago to random

Recent salary increases for graduate-student teaching assistants at the University of California have left lecturers behind, causing situations where the Ph.D.-holding instructor of a course gets less pay than the master's student hired to be their assistant, leading to hurt feelings and badwill: https://www.chronicle.com/article/after-learning-her-ta-would-be-paid-more-than-her-this-lecturer-quit, https://archive.is/JW8lM

Both the graduate students and the lecturers are represented by unions, but these inversions happened after the students struck for a new contract, while the current lecturer contract extends until 2026. It doesn't look like local administrators can do much to work around the problem, and a higher-level university spokesperson issued only a bland statement saying essentially that they think they pay lecturers well already (obviously not) and that this would be on the table the next time negotiations roll around.

11011110, 9 days ago to random

My university has gone online-only today, after an anti-Israel protest encampment was shut down by and cleared by police, resulting in 50 arrests: https://www.latimes.com/california/story/2024-05-15/police-converge-on-pro-palestinian-protest-at-uc-irvine-students-are-told-to-shelter-in-place

Negotiations between the protesters and the university administration had broken down a week earlier, with some protesting students getting suspended and banned from campus, after what our chancellor and the rumor mill tell us were unreasonable demands from the protest negotiators: calling for the campus to forbid all researchers from contact with Israelis, censor all faculty and students from expressing opinions out of line with the protesters, shut down the campus support groups for Jewish students and Jewish studies, and close the campus police department (maybe the least impossible of the requests, but also the most nonsensical to me as it would predictably lead to less-friendly policing from less-local departments, as in fact happened when the shutdown brought in many police from nearby towns).

Despite all that, the administration had been prepared to let them continue their protest indefinitely as long as it remained peaceful and did not impede other university activities. The trigger to yesterday's police action was the protesters taking over and barricading one of the main campus lecture halls.

gregeganSF, 11 days ago to random

Wow, Thomas Hales and Koundinya Vajjha have proved Mahler’s First Conjecture! (That’s Kurt Mahler, not Gustave.)

https://arxiv.org/abs/2405.04331

Mahler’s First Conjecture says that the centrally symmetric convex shape with the worst possible packing ratio is made up of straight lines and arcs of hyperbolas, like the smoothed octagons shown in the animation below (demonstrating a 1-parameter family of slightly different packings all with the same density).

Whether these smoothed octagons are, as Karl Reinhardt conjectured, the actual worst case is still an open problem.

A bit more detail on Reinhardt’s conjecture in this article by @johncarlosbaez :

https://blogs.ams.org/visualinsight/2014/11/01/packing-smoothed-octagons/

and this thread by Koundinya Vajjha on Twitter:

https://twitter.com/KodyVajjha/status/1790211313618362848

A 1-parameter family of packings of smoothed octagons.

11011110, 14 days ago to random

Gasarch on what counts as "closed form" and what does not, using the Ordered Bell numbers as an example: https://blog.computationalcomplexity.org/2024/05/what-is-closed-form-horse-numbers-are.html

He asks, in the form of a Platonic dialogue: is (\tbinom{n}{i}) or (\tfrac{n!}{i!(n-i)!}) closed form? What, if anything, makes that sort of formula different from the formula (H(n)), denoting the (n)th ordered Bell number?

11011110, 15 days ago to random

After seeing several recent student presentations on quantum algorithms, it occurs to me (as I'm sure it has occurred to others) that we desperately need some way of communicating these concepts at a higher and more intuitive level than slide after slide of tensor algebra equations. If we tried to describe classical algorithms but our language was limited to circuit diagrams, how far would we get?

peterrowlett, 23 days ago to random

My son: “I’ve spotted a little typo in Kyle’s book. He says natural logarithm, or L N for short, not N L.” #tmwyk

christianp, 29 days ago to random

Another entry in the annals of the Tyne and Wear Metro's difficulties with communicating statistics.
The current iteration of their stats poster has two statements about the number of trains arriving on time: "77% of trains arriving on time", and "on average, four out of five trains arrive on time".

I'd say 77% is more like three out of four than four out of five, wouldn't you? Is there any wiggle room with the phrase "on average"?

#TWMetro

11011110, 1 month ago to random

The dumbest election recount ever (Chris Staecker, Youtube, https://www.youtube.com/watch?v=TfwQkFam_ww) or, why instant runoff voting makes it very hard to test whether an election result was so close that a recount is worthwhile. (But not in this real-world instance, where it definitely was not worthwhile.)

11011110, 1 month ago to random

US government holds back new grants to an entire university (the University of California, San Diego) because some guy retired in 2022 without finishing his final grant reports:https://www.chronicle.com/article/one-scientist-didnt-turn-in-his-grant-reports-now-federal-agencies-are-withholding-grants-for-an-entire-university, https://archive.is/WXtQa The story says he's doing them now, but what would have happened if he got hit by a bus?

andrejbauer, 1 month ago to random

What is the correct reply to a mathematician, who has never formalized anything, asking how they would go about formalizing a research paper of theirs?

11011110, 1 month ago to random

Somehow I ended up with https://mathstodon.xyz/@foldworks/112240192935752642 by @foldworks (the ceiling of a museum in Uzbekistan, intricately decorated by two sizes of 30-90-120-90 kites) and https://mathstodon.xyz/@curved_ruler/112235975585206140 by @curved_ruler (a tiling by approximate 30-120-30-120 diamonds, distorted to reduce in size as they approach a central limit) next to each other on my Mastodon favorites list. Both remind me of my old work on diamond-kite meshes, https://11011110.github.io/blog/2012/07/23/diamonds-kites-and.html, which combine these two shapes to allow the mesh to vary in scale without distortion.

11011110, 1 month ago to random

Continued attack on the public domain by the Italian court system, ruling that the Florence gallery that owns Michelangelo's David also owns "image rights" to the statue, can require licensing fees for any image depicting it, and can impose additional fines for presenting it in a distorted way: https://news.artnet.com/art-world/florence-gallerie-dellaccademia-wins-david-lawsuit-2313262, https://news.ycombinator.com/item?id=40023471

It is perhaps important to note that the statue, created in 1504, was on outdoor exhibit in a public square in Florence until 1873, and a replica is still visible there.

Via https://news.ycombinator.com/item?id=40023471; see also "A fight to protect the dignity of Michelangelo’s David raises questions about freedom of expression", LA Times, https://www.latimes.com/world-nation/story/2024-04-01/a-fight-to-protect-the-dignity-of-michelangelos-david-raises-questions-about-freedom-of-expression

11011110, 1 month ago to random

New blog post: Mendocino, sakura, and my father, https://11011110.github.io/blog/2024/04/12/mendocino-sakura-father.html

11011110, 1 month ago to random

Fast and simple sorting using partial information: https://arxiv.org/abs/2404.04552,
Bernhard Haeupler, Richard Hladík, John Iacono, Vaclav Rozhon, Robert Tarjan, and Jakub Tětek.

Tarjan gave a distinguished seminar on this at my department last Friday. The result is that if you are given the outcomes of some comparisons on a totally ordered set, as a directed acyclic graph with (n) vertices, (m) edges, and (T) topological orders (linear extensions), you can do more comparisons to complete the sorting proces in time (O(n+m+\log T)) using (O(\log T)) comparisons. The main ideas include:

• Combining a greedy topological ordering algorithm with a priority queue on available items to pick out the smallest available item at each step.

• Using a priority queue with the "working set property": the time to insert or delete an element (x) is logarithmic in the maximum number of other elements, inserted after (x) and active at the same time as each other.

• Proving the working set property for pairing heaps (https://en.wikipedia.org/wiki/Pairing_heap), a simple priority queue

• Using a clique decomposition of an interval graph, formed from the lifetimes of elements in the priority queue, to show that the working set bound on the priority queue almost matches the claimed bound on comparisons in terms of (T)

• Some special case handling of input DAGs with long paths to fix up the cases where the two bounds don't quite match

11011110, 1 month ago to random

Quanta on integer distances: https://www.quantamagazine.org/merging-fields-mathematicians-go-the-distance-on-old-problem-20240401/

The linked article highlights new research of Rachel Greenfeld, Sarah Peluse, and Marina Iliopoulou (https://arxiv.org/abs/2401.10821), on sets of planar points with integer distances.
A paper of Solymosi shows that any such set has size at most linear in the diameter, achieved by evenly spaced points on the line. There also exist arbitrarily large cocircular integer-distance sets. The new preprint shows that everything else must be small: if you remove the largest point or circle from an integer-distance set, the number of points remaining is polylogarithmic in the diameter. Don't be confused (as I initially was) by the restriction that the points lie in ([-N,N]^2): they can have any real coordinate in that range, not just integers. The range limit (N) is just a stand-in for the diameter.

This is all motivated by the Erdős-Anning theorem (https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Anning_theorem): if an integer-distance set does not lie entirely on one line, it must be finite.

See also my own recent work extending the Erdős-Anning theorem and Solymosi's diameter bounds in a different direction to various non-Euclidean but two-dimensional spaces: https://11011110.github.io/blog/2024/01/14/integer-distances-floppy.html, https://arxiv.org/abs/2401.06328
A paragraph of the Greenfeld-Peluse-Iliopoulou preprint at the end of section 1.1, claiming that all prior work uses low degree algebraic geometry and because of that could not improve on Solymosi's work, is somewhat inaccurate. My preprint is prior to theirs, does move beyond Solymosi (in a different direction), and explicitly avoids any algebraic geometry in favor of a topological analysis of Voronoi diagrams that works in other spaces.

11011110, 1 month ago to random

West Virginia University, the main public university in its state, shuts down pure mathematics as a research topic: https://cameroncounts.wordpress.com/2024/04/03/west-virginia-university/ See also Inside Higher Education, "A Flagship Research University… Without Language Degrees or Math Ph.D.s?", https://www.insidehighered.com/news/institutions/research-universities/2023/08/31/wvu-r-1-flagshipwithout-language-degrees-or-math, https://archive.is/Xg22j and The New Yorker, "An 'academic transformation' takes on the math department", https://www.newyorker.com/news/us-journal/an-academic-transformation-takes-on-the-math-department

I'm not in a mathematics department, but I completely agree with the sentiment of an operations researcher quoted by Peter Cameron in the comments of his post: "I could not hold up my head if I were in a university with no mathematics department".

11011110, 1 month ago to random

Here's an example of why it's important to base Wikipedia's mathematics content on published sources rather than going by your intuition. Wikipedia has an article on the classification of manifolds, topological spaces that look "locally" like Euclidean spaces, in the sense that each point has a neighborhood within which the topology is the same as a Euclidean space: https://en.wikipedia.org/w/index.php?title=Classification_of_manifolds&oldid=169151396

From 2007 until very recently this article has said that there are only two connected 1-dimensional manifolds: the circle and the line. You can draw other curves, of course, but they will be topologically equivalent to one or the other of these two spaces.

But this is wrong! There are two more possibilities, the long line (https://en.wikipedia.org/wiki/Long_line_(topology)) obtained by gluing together an uncountable number of copies of a unit interval, and a line-like space obtained by gluing together an ordinary real ray and a long ray. See Frolík (1962), "On the classification of 1-dimensional manifolds", https://hdl.handle.net/10338.dmlcz/142137

You might think that just as there is more than one line, there might be more than one long line, obtained by gluing together sets of intervals of different cardinalities. But no, it stops here: apparently only the smallest uncountable ordinal works as a gluing pattern. Anything else would have a limit point where more than countably many unit intervals appear in every neighborhood, and that limit point is not locally Euclidean.

11011110, 1 month ago to random

Michael Mitzenmacher is making an unusual request for publicity for his NON-participation in a conference. It calls itself ICAIM, the International Conference on Artificial Intelligence and Mathematics, to be held in Nanjing in September, and it falsely lists Mitzenmacher as a conference chair, Mike Goodrich as program chair, and Jelani Nelson as a program committee member, among others. None of Michael, Mike, and Jelani have agreed to allow their names to be used in this way. The conference contact email goes to a known spam/phishing site. It appears to be a scam. Be aware!

11011110, 1 month ago to random

My colleague Sandy Irani is giving the Richard M. Karp Distinguished Lecture at the Simons Institute in Berkeley next Tuesday afternoon, on "Quantum Constraint Satisfaction": https://simons.berkeley.edu/events/quantum-constraint-satisfaction-richard-m-karp-distinguished-lecture

A livestream is available on a registration basis. A talk recording will also be made available, eventually, but if you don't want to wait you need to register.

fractalkitty, 1 month ago to random

Anyone else procrastinating the saving/migration of hundreds of jamboards?

johncarlosbaez, 2 months ago to random

The citrus harvest is here! Now we have to eat - or give away - a lot of blood oranges and satsumas.