on May 21, 2009 by lieven in geometry, lazy blogging, Comments (4)
noncommutative space quiz
Creating (or taking) an image and explaining how it depicts your mental picture of a noncommutative space is one thing. Ideally, the image should be strong enough so that other people familiar with it might have a reasonable guess what you attempt to depict.
But, is there already enough concordance in our views of noncommutative spaces? I doubt it, whence this experiment. Below my attempt1 to depict one of the most popular noncommutative spaces around :
Can you guess what space this is? How does it agree with (resp. differ from) your own mental image of it?
Further, if you know of links to other depictions of noncommutative spaces, please leave a comment, or, send me an email.
- the image is taken from Cran’s fractal art [↩]
Hi, I'm a professor of mathematics at the University of Antwerp, in Belgium. My research areas are non-commutative algebra and non-commutative geometry. Sometimes, you can also find me here :
Errol
June 2, 2009 @ 1:11 am
I have recently started reading your blog and its very interesting; I like the fact that its about noncommutative geometry. Hey man, keep it up; it would be nice to read an interview with the Grand-master himself but I leave this entirely up to you
Errol
Jan
July 1, 2009 @ 5:00 pm
As a starting PhD student in noncommutative geometry, I have no idea what this picture would be.
My mental image would have distinct “points” for each component which commutes with the other component, making for example noncommutative torus some sort of fuzzy grey roughly in the shape of a torus, never sharpening to distinct points, no matter how far you zoom in. However, if you tweak the “noncommutativity” parameter theta, sometimes, suddenly your fuzzy patches would collapse into nice sharp tori, showing the behaviour when theta becomes rational.
lieven
July 11, 2009 @ 11:05 am
@errol : if you mean Alain Connes by “the Grand-master” there are interviews available online : Tehran interview and a shorter Skandalis-Goldstein interview. Have fun with them!
@jan : my bad then. i was hoping to depict something of the adelic-class-space, different colors corresponding to different primes…
Jan
July 13, 2009 @ 9:20 am
Ah, that makes sense. In some sense there are too many ways of looking at noncommutative geometry…