Yuansi Chen's preprint, "An Almost Constant Lower Bound of the Isoperimetric Coefficient in the KLS Conjecture", https://arxiv.org/abs/2011.13661, is described less technically by Gil Kalai (https://gilkalai.wordpress.com/2020/12/21/to-cheer-you-up-in-difficult-times-15-yuansi-chen-achieved-a-major-breakthrough-on-bourgains-slicing-problem-and-the-kannan-lovasz-and-simonovits-conjecture/) and now Quanta (https://www.quantamagazine.org/statistics-postdoc-tames-decades-old-geometry-problem-20210301/)

It doesn't quite solve the Bourgain slicing conjecture, that high-dimensional convex bodies of unit volume have cross-sections of constant volume, but it reduces the dependence on dimension from a power of d to something smaller.

Tensioned suspension: https://www.bldgblog.com/2013/08/tensioned-suspension/

Sculptures by Dan Grayber in which the weight of mechanical linkages causes them to push out against the sides of their glass enclosures, seemingly causing them to hang suspended in air.

Via https://news.ycombinator.com/item?id=9093187; more at Grayber's web site, http://www.dangrayber.com/

Applications of the no-3-in-line problem and cap-sets to complexity theory: https://rjlipton.wordpress.com/2021/02/27/new-old-ancient-results/

"What is most curious to us is that for matrix multiplication, the cap-set related technique frustrates a better complexity upper bound, whereas [for linear algebraic circuits] it frustrates a better lower bound."

For some reason, I just like watching Lloyd's algorithm (https://en.wikipedia.org/wiki/Lloyd%27s_algorithm) in animated form.

Today's LaTeX formatting tip: You know that bug where amsthm + hyperref, with one numbering for theorems and lemmas and corollaries and whatever, causes \autoref to call them theorems even when they're really lemmas and corollaries and whatever? If you don't, you're lucky. Anyway, there's a very simple workaround: after loading amsthm and hyperref, add one more package:

\usepackage[capitalize,nameinlink]{cleveref}

Then, just use \cref everywhere you were using \autoref

Problem solved!

Gender Trends in Computer Science Authorship: https://cacm.acm.org/magazines/2021/3/250708-gender-trends-in-computer-science-authorship

Takeaways for me (mostly from the barely-readable Fig. 4) are:

- Roughly one in four coauthors of CS research publications are currently female, up from a big dip of one in seven in the 1970s to 1990s

- Mathematics started lower and is currently more or less the same

- We are not on track to gender parity

Fun with shapes: draw an iceberg and see which way up and how deep it would float, https://joshdata.me/iceberger.html, inspired by a twitter thread by Megan Thompson-Munson, https://mobile.twitter.com/GlacialMeg/status/1362557149147058178, pointing out that many supposed photos or illustrations of icebergs are fake and wrong.

Via https://news.ycombinator.com/item?id=26201160, https://www.metafilter.com/190533/Iceberger, and https://boingboing.net/2021/02/20/make-your-own-iceberg-with-iceberger.html

New blog post: Loops, degrees, and matchings, https://11011110.github.io/blog/2021/02/19/loops-degrees-matchings.html

What happens when you allow self-loops to be included in graph matchings? Not much different, it turns out.

Arranging invisible icons in quadratic time: https://randomascii.wordpress.com/2021/02/16/arranging-invisible-icons-in-quadratic-time/, via https://news.ycombinator.com/item?id=26152335

Yet another instance where using a too-slow algorithm causes a UI hang, with the twist that the better solution would not be to replace it with a faster algorithm, but instead to not do the useless thing that the bad algorithm does at all.

Computational Geometry YouTube channel: https://www.youtube.com/channel/UC8bRNi3tJX-tfR_RMtyWR7w

This has been set up by @sarielhp and Sándor Fekete, and is recording talks from the New York Geometry Seminar. So far there are eleven, of roughly an hour length each.

A new contribution of Hypatia to mathematics: http://jdh.hamkins.org/ode-to-hippasus/

Not the ancient Hypatia, but Hypatia Hamkins, and her parents, philosopher Barbara Gail Montero and logician Joel David Hamkins; the contribution is a verse proof of the irrationality of √2.

Accepted papers for the Symp. on Computational Geometry (SoCG 2021): https://cse.buffalo.edu/socg21/accepted.html

Decisions are out for the Symp. on Theory of Computing (STOC) but I haven't seen a public list yet.

Upcoming submission deadlines include the Algorithms and Data Structures Symp. (WADS, Feb. 20, https://projects.cs.dal.ca/wads2021/), Graph-Theoretic Concepts in CS (WG, Mar. 3, https://wg2021.mimuw.edu.pl/), and the new SIAM Conf. on Applied and Computational Discrete Algorithms (ACDA21, Mar. 1), https://www.siam.org/conferences/cm/conference/acda21

Self-organizing textures: https://distill.pub/selforg/2021/textures/

A small input image + "neural cellular automata" magic leads to organic-looking image textures. Via https://news.ycombinator.com/item?id=26112959

The compound of an 11-simplex in an 11-hypercube (as a subset of its vertices) has the Mathieu group M11 as its symmetries: https://mathoverflow.net/q/382940/440, via https://cp4space.hatsya.com/2021/02/08/a-curious-construction-of-the-mathieu-group-m11/

The cp4space post goes on to describe how to find two dual 11-simplices in the same hypercube from the perfect ternary Golay code, much like the two simplices in a 3-cube that form the stella octangula.

- Home page
- https://www.ics.uci.edu/~eppstein/

I'm a computer scientist at the University of California, Irvine, interested in algorithms, data structures, discrete geometry, and graph theory.

Joined Apr 2017