Earlier this month there was a workshop on twisted K-theory held at Oberwolfach. Here is a report, also slides from a talk there by Greg Landweber about the Freed-Hopkins-Teleman theorem. Freed is giving a course on the subject this fall, and Hopkins is giving a series of lectures about TQFT in Gottingen this week. Urs Schreiber has reports on the lectures here and here. Also at the n-category cafe is an advertisement by John Baez for the work of my new Columbia colleague Aaron Lauda on TQFT, which I’ll second here. For yet more on TQFT, see notes by Kevin Walker here, and the book by Bakalov and Kirillov, an early version of which is on-line.

Last week in Paris there was a conference dedicated to Joel Scherk, celebrating 30 years of supergravity.

There’s an interesting interview with Alain Connes on the French TV network ARTE here. For his recent work on non-commutative geometry and the standard model, see this preprint, and talks here from the on-going workshop at the Newton Institute in Cambridge.

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Great. The first chance I had to see Alain Connes and it’s in Real Audio.

Anybody ever heard of youtube?

Nice Alain Connes interview.

Somehow, Connes’ way of talking, maybe it’s the gestures, reminds me of Feynman. Relaxed, confident, playful, enjoying the questions…

My god, I must say the interviewer is very charming!

There is audio (in English) for talk II and III in the Newton Institute website. I strongly recommend to download them into your MP3 machine so you can heard them while in the tube. Every talk recapitulates the previous one, so if you ony can allow for one, start with III. In England, the series will continue November the 9th, plus some another “one-short” talks around. I do not know if there is some similar, or even more gossip-rich, presentations in France. Hints anyone?

There is detailed coverage in the October posts of the n-category cafe, and some more sparse coverage in Motl’s.

“Nice Alain Connes interview”

this is indeed a very enjoyable style, remarkably different from that of those car-salesmen which we often are exposed to.

As a physicist one notes that all mathematicians (perhaps with the exception of Vaughn Jones and some others who entered QFT from subfactor theory) continue to have that lighthearted attitude with respect to the Euclidean—Lorentzian relation (and the related issue of localization) which for the mature quantum field theorists are among the conceptually most subtle and delicate (and even not generally valid) issues of particle physics.

Sorry for the somewhat off topic post, but here is a concrete sign that the opinion of string theory is changing in the public’s collective unconscious. I was reading an article on realclearpolitics about a controversial interpretation of the polling data:

http://time-blog.com/real_clear_politics/2006/10/a_republican_meltdown_part_ii.html

Ouch!

Thanks for the links Peter! I’ve been meaning to catch up on TQFT for some time, finally my schedule will allow me to do this.

I read the articlle of Connes and like Bert Schroer I was astonished that he mentioned only in brackets that the spacetime metric has Euclidian signature and made no further comments about the significance of this. As a physicist having at least second foot in this world I find it very difficult to understand how a physicist proposing a unification of all known interactions can have such a light-hearted attitude.

Connes explicitly states in the pdf version of his talk “Spectral action and gravity coupled with matter III” that is on the web at http://www.newton.cam.ac.uk/webseminars/pg+ws/2006/ncg/1011/connes/all.pdf

“… The spectral action principle asserts that the fundamental action functional S

that makes it possible to compare different geometric spaces at the classical level

and is used in the functional integration (after Wick rotation to euclidean signature) to go to the quantum level,

is itself of the form … Trace (f( D / /\ )) …

where D is the Dirac operator and f is a positive even function of the real variable while the parameter /\ fixes the mass scale. …”.

Maybe some people don’t like such use of Wick rotation, but Connes is model-building,

and if he can construct a physically realistic model using such Wick rotation

then

in my opinion it will be so useful that it will be (and should be) as widely accepted as are

some not-yet-rigorously proven aspects of the Standard Model

and

any objections as to rigor should be motivation for further work on the model

rather than justification for trashing the model.

Tony Smith

http://www.valdostamuseum.org/hamsmith/

well Tony, that is what I meant by lighthearted. Something like Osterwalder Schrader is not lighthearted.

But I agree with you that it is not illegetimate to do that and (as long as results are interesting and one does not forget that there is a conceptual problem) defer such questions to a later date (although this has been going on for more than a decade). However it is only a theory after these quations have been settled.

As to objections about localization,

Connes said in the pdf file that is on the web at http://www.newton.cam.ac.uk/webseminars/pg+ws/2006/ncg/1011/connes/all.pdf

“… Assuming first that we deal with a classical manifold, one can form a number of such invariants (under suitable convergence conditions) as the integrals of the form

[Integral over M] F(K) sqrt(g) d^4x (9)

where F(K) is a scalar invariant function … of the Riemann curvature K.

Such invariants, of the form (9) appear as the single integral observables i.e. those which add up when evaluated on the direct sum of geometric spaces.

Now while in theory a quantity like (9) is observable it is almost impossible to evaluate since it involves the knowledge of the entire spacetime and is in that way highly non localized.

On the other hand, spectral data …

(the data of spectral lines are intimately related to the Dirac Hamiltonian, hence to the geometry of “space”) …

are available in localized form anywhere,

and

are (asymptotically) of the form (9) when they are of the additive form

Trace (f(D / /\ )),(10)

where D is the Dirac operator and f is a positive even function of the real variable while the parameter /\ fixes the mass scale. …”.

Again,

Connes is NOT ignoring the issues of localization and Wick rotation,

but is explicitly stating how he is building his model,

and

if his model is realistic, I think that it is useful.

Tony Smith

http://www.valdostamuseum.org/hamsmith/

The goal in that paper was to get coincidence with Veltman’s Diagrammar. Let me note that one of the first impulses, fifteen years ago, was Daniel Kastler, who did a lot of the calculations of the Higgs potential in the old models.

The idea about spectral data of Dirac operator as a manner to code nonlocal data locally is beautiful. I cannot avoid temptation to briefly mention (Peter can delete this posting if it is too much about pet ideas) an approach in which Dirac operator associated with lightlike 3-surfaces which by Diff^4 invariance can be chosen to be fundamental dynamical objects. Vacuum functional is coded as a Dirac determinant (appropriately defined) having interpretation as action exponential characterizing interior dynamics of space-time. In this case lightlikeness is the source of all superconformal symmetries, it defines parton level dynamics as almost topological CFT, and it gives rise to quantum gravitational holography. Everything would be lost by Euclidization trick.

On the topic of the conference in memory of Joel Scherk. Obviously Joel Scherk did very great work, and it’s very tragic that he died. The proceedings of the 1979 Stony Brook supergravity conference, which were dedicated to his memory, said he had diabetes, and got stuck somewhere without his insulin, and went into a coma. But the Wikipedia article, which is just a stub, doesn’t mention diabetes, and contains a link to a review of a book by Leonard Mlodinow, which contains a paragraph that provides different information. Could anyone provide more historical information?