Sunday, October 17, 2010

Alain Connes: Fun with F1



References:

Connes' Blog: NCG and F_un

Connes: On the Notion of Geometry over F_1 (PDF)

4 comments:

Kea said...

LOL, cool! It's a bit bizarre that he didn't go on for longer, don't you think? Or are there more parts to it?

Now we just need a picture version for simple minded people like me ...

kneemo said...

I'll have to look for more parts. The Riemann Zeta as partition function for the BC system is deeply interesting. I'll have to look into this story some more. The C. Soule relation reminds me of the cohomology rings you'd get for an m-dimensional projective space over C or H.

Kea said...

Don't forget that we have been working with Fun Math for some time now (in the guise of MUB quantum arithmetic). Sets are like vector spaces over the Fun field ... except that we have to re-axiomatise the category of sets in a suitable quantum way to make this more knotty (that was what the second half of my thesis was about, tho of course I did not get far with the maths).

kneemo said...

Even though I couldn't find another video, I did find Connes blog post on F_1:

http://noncommutativegeometry.blogspot.com/2008/05/ncg-and-fun.html

What I found interesting is that Yuri Manin found that the stable homotopy groups of spheres should be viewed as the algebraic K-theory of F_1. This should lend itself to an F_1 description of the four Hopf fibrations which underlie the "four curious supergravities" discussed by Duff and Ferrara in arXiv:1010.3173