Eight years after Shinichi Mochizuki first posted his proof of the ABC Conjecture on his website it has been announced that it has been accepted for publication in Publications of the Research Institute for Mathematical Sciences (RIMS).
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Here’s a quick round-up of some news stories from the tail end of 2012 that we characteristically failed to write up!
According to this post on phys.org, which reports on this paper in science journal Nature, there’s some beautiful physics which results from tying knots in light. It opens, “New research published today seeks to push the discovery that light can be tied in knots to the next level.” Between us, I wasn’t actually aware of the discovery that light can be tied in knots (and I’ve done a fair amount of knot theory, and observed a decent quantity of light) – but apparently it’s something scientists have been exploring for years.
A spinning optical soliton (wave pulse) can spontaneously create knotted and linked structures, as the soliton curves around in space, and while previously it’s been observed after engineering them to happen, now the knots are forming spontaneously, like ” those annoying knots that you always get in electrical cables.” (see: here). The paper suggests similar behaviour might be seen in other types of wavefronts, such as superfluids and trapped matter waves. For anyone who got lost around ‘soliton’, rest assured it involves the use of lasers. Obviously.
Beautiful physics: tying knots in light on phys.org.
Spontaneous knotting of self-trapped waves in Nature
via @haggismaths (retweeting @eusci) on Twitter.
The march of the righteous towards victory over the rent-seeking publishers continues apace, so here’s another Open Access round up. I’m not even going to bother trying to remain impartial any more, for the following reasons: