the Freudenthal Magic Square
Sir Michael Atiyah
Edinburgh University
HKUST Institute for Advanced Study
(click images below to view videos)
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8 comments:
Oh Cool! I was hoping this would show up online!!
Oh, now I see that this is not a new set of lectures from IAS about quantum gravity, but I enjoyed them anyway.
It certainly makes the Freudenthal square look a lot more interesting, even for those not particularly interested in postcard proofs of Hopkins' fancy theorem. Presumably this is what got Atiyah a whole lot more interested in quantum gravity!
Yeah, these are earlier lectures. I'm thinking a few topics were carried over and expanded in his recent Princeton lecture.
The Hopf fibrations have been used before to classify the types of branes that can end on 9-branes in type IIA string theory. However, the bundle homotopy groups did not agree with the D-brane charges.
The Hopf fibrations also appear in the classification of D=6 magic supergravity black holes. There, the relevant spheres are the spaces of projective black hole charge vectors.
I always liked the Hopf fibrations, ever since I found out that pi_7(S^4) had a Z_4 piece.
At the end, Atiyah talks about self intersection numbers being Euler numbers, and he draws a little piece of the Freudenthal square, given by the triple (n, 2n, 4n). This reminds me of the integer tribimaximal construction, where the first row is (1,1,2); the second row being (2,2,4).
Hey, we are looking for the 12th November lecture all across the web! :-DDD
Anyone can ask for the slides?
Indeed. Has anyone asked?
I did, but I have not a lot of hopes. It could be better to ask the secretary of the theory groups at IAS and/or Edimbourgh.
Got a feedback: that there was no record of the talk. And the ideas were labeled by the speaker as "still very fluid", so no preprint, slides or paper yet.
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