Poincaré Conjecture May Be Solved

Flamerule writes "The New York Times is now reporting that Dr. Grigori (Grisha) Perelman, of the Steklov Institute of Mathematics of the Russian Academy of Sciences in St. Petersburg, appears to have solved the famous Poincaré Conjecture, one of the Clay Institute's million-dollar Millennium Prize problems. I first noticed a short blurb about this at the MathWorld homepage last week, but Google searches have revealed almost nothing but the date and times of some of his lectures this month, including a packed session at MIT (photos), in which he reportedly presented material that proves the Conjecture. More specifically, the relevant material comes from a paper ("The entropy formula for the Ricci flow and its geometric applications") from last November, and a follow-up that was just released last month."

Comments

Poincare Conjecture Solved Ages Ago

[The Real Minister]

http://www.theinformationminister.com/press.php?ID =612212491 we got this ages ago. i swear

Now I Understand...

[masq]

... why we love talking about Linux so much - It's so damn USER-FRIENDLY compared to other geek pursuits!

We present a monotonic expression for the Ricci flow, valid in all dimensions and without curvature assumptions. It is interpreted as an entropy for a certain canonical ensemble. Several geometric applications are given. In particular, (1) Ricci flow, considered on the space of riemannian metrics modulo diffeomorphism and scaling, has no nontrivial periodic orbits (that is, other than fixed points); (2) In a region, where singularity is forming in finite time, the injectivity radius is controlled by the curvature; (3) Ricci flow can not quickly turn an almost euclidean region into a very curved one, no matter what happens far away. We also verify several assertions related to Richard Hamilton's program for the proof of Thurston geometrization conjecture for closed three-manifolds, and give a sketch of an eclectic proof of this conjecture, making use of earlier results on collapsing with local lower curvature bound.

Re:What about the Dunwoody paper?

[Eccles]

So, why the excitment about this later Perelman paper? Has the Dunwoody paper been debunked?

The part of the proof where it says "then a miracle occurs..." is being questioned by numerous mathematicians.

Re:Explanation

[jalet]

> Now, can someone tell me what practical
> applications there might be of this?

An application would be to make better doughnuts, I suppose.

Perl?

[comet_11]

I swear that looks like perl.