A New Yorker Article on the Poincaré Conjecture

Yesterday I finished reading a rather long, but interesting article published in the New Yorker. The article, written by Sylvia Nasar (of Beautiful Mind fame) and David Gruber, describes some of the developments surrounding the proof of the Poincaré conjecture, has excerpts of an interview with Perelman, and offers us a glimpse of what happens behind the scenes of the mathematical arena. The former Fields medal winner and top-notch mathematician Shing-Tung Yau appears as the "villain" in the story.

I do not know if the content of the article is truly trustworthy, but it makes for some interesting, and at times arresting, reading. This excerpt, for one, tells the remarkable story of the recent publication of what could be a key paper in the story of the solution of the Poincaré conjecture:

On April 13th of this year, the thirty-one mathematicians on the editorial board of the Asian Journal of Mathematics received a brief e-mail from Yau and the journal’s co-editor informing them that they had three days to comment on a paper by Xi-Ping Zhu and Huai-Dong Cao titled “The Hamilton-Perelman Theory of Ricci Flow: The Poincaré and Geometrization Conjectures,” which Yau planned to publish in the journal. The e-mail did not include a copy of the paper, reports from referees, or an abstract. At least one board member asked to see the paper but was told that it was not available. On April 16th, Cao received a message from Yau telling him that the paper had been accepted by the A.J.M., and an abstract was posted on the journal’s Web site.

Quite a remarkable refereeing process for a paper proving one of the Millennium Problems of the Clay mathematical institute!

Italian TCS Presence at the ICM 2006

Today was a good day for Italian TCS at the International Congress of Mathematicians 2006. The inaugural talk in the section on Mathematical Aspects of Computer Science was delivered by Luca Trevisan (UC Berkeley). Luca's talk was based on the paper Pseudorandomness and Combinatorial Constructions.

Congratulations to Luca for being invited to deliver a talk at ICM 2006.

Question: How many Italian computer scientists have been invited speakers at the section on Mathematical Aspects of CS at the ICM so far?

I do not know the answer myself. Does any of my readers do?

Live Transmission from ICM 2006

The web pages for ICM 2006 point to this link for live trasmission of the sessions and recordings of previous sessions. Warning: I have not tried to view anything myself yet, so I hope this works :-)

One of yesterday's highlights for my family and close environment was Richard Stanley's invited plenary talk. Stanley is the "godfather of algebraic combinatorics", or so says Doron Zeilberger on his links page, and the former supervisor of Bridget Tenner (Kári's girlfriend) , and of Einar Steingrimsson, the head of the algebraic combinatorics research group at Reykjavik University.

For those of you who would like to read it, Stanley's paper for ICM 2006 is Increasing and decreasing subsequences and their variants (34 pages).

Fields and Nevanlinna Prizes

This is old news by now, but, in case you have not seen it already, at the opening ceremony of the 2006 International Congress of Mathematicians (ICM), four Fields Medals were awarded. The medalists are Andrei Okounkov, Grigory Perelman, Terence Tao, and Wendelin Werner. Perelman has apparently declined the award. At a press conference, John Ball (president of the IMU) said that Perelman will be recorded as having been awarded a Fields Medal but as having declined to accept it. Jon Kleinberg received the Nevanlinna Prize, and Kiyoshi Itô, who is 91, received the first-ever Gauss Prize. Congratulations to Jon, who also got a Mac Arthur fellowship in 2005. An AMS press release has more details about the six winners.

Luca Trevisan has "live commentary" from ICM 2006. Make sure you follow his lively blog reports! (For instance, look at his report on the laudationes for the prize winners.)

Today is a great day for TCS at ICM 2006. Avi Widgerson delivered his plenary talk "P, NP and mathematics: a computational complexity perspective", and brought one of the fundamental notions in Computer Science to the attention of a hord of mathematicians. I strongly advice all of you to read the beautiful paper he wrote for the occasion, and on which the talk is based. I look forward to reading Luca Trevisan's report on the talk.

Thanks Luca!

Addenda: BBC coverage, Guardian story, New York Times article.

I could not resist checking my distance from the 2006 Fields medal winners. According to the data on the AMS web site, my collaboration distance from all of the winners of the Fields medal is 6, apart from the one from W. Werner, which is 5. My Kleinberg distance is 4. Finally, my K. Ito number is infinite.

Scientifically speaking, my distance from each of these guys is infinite.

A Good Newpaper Article on Maths

Readers of this diary might enjoy looking at the article "Elusive Proof, Elusive Prover: A New Mathematical Mystery". This is an excellent example of coverage of mathematics in the press, and deals with the developments surrounding Perelman's proof of Poincaré’s conjecture.

This article is also very timely. The ICM 2006 kicks off tomorrow, and Richard Hamilton (Columbia University, New York, USA) will deliver a talk on the Poincaré conjecture at 17:15. As an Italian abroad, I am also proud to announce that Alfio Quarteroni (École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland and Politecnico di Milano, Milan, Italy) will also deliver a plenary address tomorrow.

The section on Mathematical Aspects of Computer Science starts on August 26.

Colin Stirling in the Gödel Award Committee

I have heard from Mogens Nielsen that Colin Stirling has agreed to serve as one of the EATCS representatives in the Gödel award committee. This is great news for the concurrency theory community, and we should all be proud of Colin's nomination. (Colin is taking the place of P.L. Curien, whose term on the award committee ended this year, when he chaired the award committee.)

The Gödel Prize for outstanding papers in the area of theoretical computer science is sponsored jointly by the European Association for Theoretical Computer Science (EATCS) and the Special Interest Group on Algorithms and Computing Theory of the Association of Computing Machinery (ACM SIGACT). This award is presented annually, with the presentation taking place alternately at the International Colloquium on Automata, Languages, and Programming (ICALP) and ACM Symposium on the Theory of Computing (STOC).

As I have already written in earlier posts devoted to this prize, a look at the list of winners clearly indicates a bias towards SIGACT-friendly research. During his presentation at ICALP 2006, Curien explained that this is a somewhat natural outcome of the fact that the prize is awarded by a committee formed by three SIGACT representatives and three EATCS members. Now, unlike SIGACT, the EATCS is an organization representing the whole of TCS, and its representatives in the Gödel award committee cover the areas of logic and semantics, automata and formal languages and algorithms and complexity theory. When it comes down to voting, papers in algorithms and complexity are more likely to get four votes than those in, say, logic and semantics.

Is this a desirable state of affairs? I am not so sure myself, but I believe that the EATCS should continue being involved in the Gödel prize. Let me wish Colin good luck with his work in the committee. I hope that we'll make his job easier by nominating excellent papers in logic and semantics for the award. After all, isn't it a bit weird that so few Gödel prizes are being given for work done in logic?

Handwritten Slides, Course Notes and Hard Copies of Old Papers

Anna and I had to make some drastic decisions when packing our things in Aalborg. Some of these decisions involved the material stored in the boxes stored in the university cellar that housed the contents of our offices there. We had between 15 and 20 boxes full of books, handwritten slides for talks and courses, hard copies of technical reports and papers, photocopies of (parts of) books and reprints of our papers.

Not having time to sort things, we eventually threw everything away, apart from a few books that we really cared about.

Was that a good decision to take? Well, for a start, we had been packing our things in the house for about a week, and we were sick and tired of it. Disposing of the reprints of our papers was not a painful decision at all since most of the papers are available electronically. However, when we told Kim G. Larsen that we had got rid of our handwritten slides, notes and course folders he immediately said: "That was a stupid thing to do! I still use some of my old handwritten slides for courses and summer schools."

Looking back, it is true that we lost a part of our working life by disposing of those boxes. Some of those notes reported on work that was "in progress", and I feel that I'll never be able to reproduce them. (The person who wrote those notes is not here anymore, and will never come back.) Does this matter? The sad truth is that it probably does not. That work would have never been finished anyway, and, even if it did, it would not have been "important enough".

Would you have made the same choice as we in our situation? Think about it before your next move.

Fulkerson Prize 2006

The Fulkerson Prize is given by the Mathematical Programming Society every three years to up to three papers in discrete mathematics. The winners of the 2006 prizes are the papers:

• Primes in P, Manindra Agrawal, Neeraj Kayal and Nitin Saxena
• A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries, Mark Jerrum, Alistair Sinclair and Eric Vigoda.
• Graph Minors. XX. Wagner's conjecture, Neil Robertson and Paul Seymour.

Note that Agrawal and his students have landed yet another prize for their paper after the Gödel Prize 2006 that was given to them at ICALP 2006. The third paper establishes, after work presented in twenty papers and spanning about 500 pages, the Robertson-Seymour Theorem, which has been hailed as a monumental result in graph theory and one of the deepest results in the whole of mathematics. The authors have a knack for settling long-standing conjectures in graph theory.

The winners of the Fields Medal and the Nevanlinna prize will be announced at ICM 2006 by the end of this month. I am very curious to see who will land the prizes, and whether Perelman will be awarded a Fields Medal for his work on the Poincare conjecture.