Monday, November 15, 2010

Atiyah on the Magic Square

The Geometry and Topology of
the Freudenthal Magic Square

Sir Michael Atiyah
Edinburgh University
HKUST Institute for Advanced Study

(click images below to view videos)


Kea said...

Oh Cool! I was hoping this would show up online!!

Kea said...

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!

kneemo said...

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.

Kea said...

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).

Alejandro Rivero said...

Hey, we are looking for the 12th November lecture all across the web! :-DDD

Anyone can ask for the slides?

kneemo said...

Indeed. Has anyone asked?

Alejandro Rivero said...

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.

Alejandro Rivero said...

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.