The Geometry and Topology of

the Freudenthal Magic Square

Sir Michael Atiyah

Edinburgh University

HKUST Institute for Advanced Study

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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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