Planning on getting back to writing some longer postings, but for today, here’s a collection of quick news and links:
There is a standard conjecture, originating in work of Goldfeld, that states that the average rank of all elliptic curves should be 1/2; however, it has not previously been known that the average rank is even finite! In this lecture, we describe recent work that shows that the average rank is finite (in fact, we show that the average rank is bounded by 1.5).
Is there a mathematical formula for love without death? The film ‘Rites of Love and Math’ is a sprawling allegory about Truth and Beauty, Love and Death, Mathematics and Tattoo, set on the stage of Japanese Noh theater. About the directors: Edward Frenkel is Professor of Mathematics at University of California at Berkeley and one of the leading mathematical physicists in the world. Reine Graves is a talented French filmmaker who has directed a number of original and controversial films that have won prestigious awards. Having met in Paris, Frenkel and Graves decided to create a film showing the beauty of mathematics. But how to do this without getting bogged down in technical details of the subject that could scare away non-specialists? Looking for the right metaphor, they came across the idea of making the tattoo of a mathematical formula. What better way to show the beauty of the formula than by letting it merge – literally – with beautiful female body! They found the aesthetic language for expressing this allegory in the enigmatic film ‘Rites of Love and Death’ (a.k.a. ‘Patriotism’) by the great Japanese writer Yukio Mishima, which had a very unusual and mysterious history of its own (banned for over 40 years, it came out on DVD in the Criterion Collection in 2008). The exquisite imagery of Mishima’s film and the original idea of Frenkel and Graves have led to the creation of ‘Rites of Love and Math.’
Update: One more. See here for Jester’s summary of what particle theory came up with during the noughties, which has to have been the most depressing decade for the subject in a very, very long time.
Update: There are two new papers (see here and here) on the arXiv this evening that address Sabine Hossenfelder’s arguments about DSR (she also has a new paper summarizing her argument, here). In one of these, Lee Smolin argues that, at least in some cases, the paradoxes pointed out by Hossenfelder can be eliminated if one studies wave-packet propagation instead of classical propagation.
Update: There’s another unusual paper on the arXiv this evening, by Longo and Witten, entitled An Algebraic Construction of Boundary Quantum Field Theory. It’s an algebraic QFT paper, written in a rigorous mathematical style, quite out of character with typical papers from Witten.