Countdown to the 2010 Fields medal(s)
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From: Jean-Claude Evard on 10 Aug 2010 00:27 ================================= Here is some additional information about the 26-th International Congress of Mathematicians (ICM2010), that will be held in Hyderabad, in India, from Thursday, August 19, to Friday, August 27, 2010. ================================= The schedule of the 20 plenary lectures of the above congress is given on the following Web page: http://www.icm2010.in/wp-content/icmfiles/docs/schedule/programme_aug9.pdf We can see on this schedule that the first plenary lecture will be the following: Plenary Lecture 1 Day 3 of the congress Saturday, August 21, 2010 09:00-10:00 Artur Avila Dynamics of renormalization operators --------------------------------------------------------------- Here are some pieces of information about the speaker of this first plenary lecture, Artur Avila. --------------------------------------------------------------- The Web site of Artur Avila is the following: http://w3.impa.br/~avila/ His list of publications is posted on the following Web page: http://w3.impa.br/%7Eavila/papers.html --------------------------------------------------------------- Pieces of information about Artur Avila extracted from the following Web page: http://www.sciencesmath-paris.fr/index.php?page=37&lien=22&lang=en Artur Avila was born in Rio de Janeiro, Brazil, in 1979. At the age of 16, he wins the International Mathematical Olympiad gold medal, in Toronto, and then enters the Instituto Nacional de Matemática Pura y Aplicada (IMPA) of Rio de Janeiro, where he begins mathematical studies while finishing highschool. He is 19 years old when he starts a thesis directed by Welington de Melo, that he finishes in 2001. He spends two years from 2001 to 2003 at the Collège de France doing a postdoc before being hired by the CNRS in 2003. CNRS = [Centre National de la Recherche Scientifique] In 2005, he gives the Collège de France's Cours Peccot on the theme : "Dynamique des cocycles quasipériodiques et spectre de l'opérateur presque-Mathieu". In 2006, at the age of 27, he wins two important awards : the CNRS Bronze Medal and the Salem Prize. He also receives a 3 years research fellowship from the Clay Mathematics Institute, that gives him the opportunity to spend much time in the IMPA. CNRS Research Director since 2008, he currently works in Rio and Paris. During the 5th European Congress of Mathematics in July 2008, he receives the European Society of Mathematics Prize for his work on dynamical systems and especially his contributions on the Teichmuller Flow and the intervals exchanges. In july 2009, he receives from the french Academy of Sciences the Grand Prix Jacques Herbrand, which rewards every two years a young researcher aged of less than 35. The last awardees of the prize was [were] Cédric Villani (2007), Franck Barthe (2005) and Wendelin Werner (2003). --------------------------------------------------------------- Below is a description of some of his most recent research work extracted from the following Web page of his Web site: http://w3.impa.br/%7Eavila/new.html It is known that Schr\"odinger operators with one-frequency analytic quasiperiodic potential behave distinctly for small and large values of the coupling constant. Most progress in the field so far has concerned with the understanding of those two distinct regimes, but no authentic global theory could be constructed since their interface has remained a mystery. The goal of this series is precisely to describe the phase transition. The highlights of the first paper are the following. Energies in the spectrum can be separated into three regimes, ``supercritical'', ``critical'' and ``subcritical''. Both supercritical and subcritical regimes are stable. The critical regime is not (in fact it can be shown to correspond to the boundary of the supercritical one in the joint ``potential times energy'' parameter space, but this is delayed to the second paper because of a technicality). The critical regime is contained in a countable union of codimension-one submanifolds. --------------------------------------------------------------- One of his publications related to his plenary lecture at the next International Congress of Mathematicians is the following: On the dynamics of the renormalization operator. A. Avila, Marco Martens and Welington de Melo. In ``Global Analysis of Dynamical Systems: Festschrift dedicated to Floris Takens for his 60th birthday'', Ed. H.Broer, B. Krauskopf, G. Vegter, Institute of Physics Publishing, Bristol and Philadelphia, pp. 449-460, 2001. I extracted this piece of information from the following Web page: http://w3.impa.br/%7Eavila/papers.html ================================= Countdown: The Fields medals 2010 will be awarded in 9 days, on Thursday, August 19, 2010. =================================
From: Jean-Claude Evard on 10 Aug 2010 21:23 ================================= Part 8 of my comments on the 26-th International Congress of Mathematicians (ICM2010), that will be held in Hyderabad, in India, from Thursday, August 19, to Friday, August 27, 2010. ================================= The second plenary lecture will be the following: Plenary Lecture 2 Day 3 of the congress Saturday, August 21, 2010, 10:15-11:15 AM Irit Dinur Probabilistically checkable proofs and codes This is posted on the schedule of the 20 plenary lectures of the ICM2010, on the following Web page: http://www.icm2010.in/wp-content/icmfiles/docs/schedule/programme_aug9.pdf --------------------------------------------------------------- Here are some pieces of information about the speaker of this second plenary lecture, Irit Dinur. --------------------------------------------------------------- The Web site of Irit Dinur is the following: http://www.wisdom.weizmann.ac.il/~dinuri/ The following information is posted on this Web site: Irit Dinur a professor of computer science at the Weizmann Institute of Science at Rehovot in Israel. Her research is in Foundations of Computer Science and in Combinatorics, especially Probabilistically Checkable Proofs, hardness of approximation. She has posted a list of online publications on the following Web page: http://www.wisdom.weizmann.ac.il/~dinuri/pubs.html As several participants to sci.math are extremely interested in NP, they may be interested to look at her online Publication 23, which is the following: Irit Dinur, Eldar Fischer, Guy Kindler, Ran Raz, and Shmuel Safra PCP Characterizations of NP: Towards a Polynomially-Small Error-Probability. Proc. of 31st STOC, 1999. http://www.wisdom.weizmann.ac.il/~dinuri/mypapers/pcpstoc.ps --------------------------------------------------------------- The Weizmann Institute of Science where Irit Dinur works has been ranked second among the best places to work in academia outside of the USA by the Scientist magazine, in the following publication: The 8th annual worldwide survey of the best places to work in academia posted on June 29, 2010 by the Scientist magazine, on the following Web pages http://wis-ks.scepia-sites.co.il/STORAGE/files/7/5097.pdf http://www.the-scientist.com/fragments/bptw/2010/academia/bptw-academia-top.jsp#small The Top 10 International Institutions outside of the USA are the following: 1. The University of Queensland; Brisbane, Australia 2. Weizmann Institute of Science; Rehovot, Israel 3. University of Dundee; Dundee, UK 4. John Innes Centre; Norwich, UK 5. Hebrew University of Jerusalem; Jerusalem, Israel 6. University of Alberta; Edmonton, Canada 7. INRA; Versailles, France 8. University of Nottingham; Nottingham, UK 9. University of Copenhagen; Copenhagen, Denmark 10. Dalhousie University; Halifax, Canada --------------------------------------------------------------- More information about Irit Dinur can be found on the following Web page of the online Wikipedia encyclopedia: http://en.wikipedia.org/wiki/Irit_Dinur On this Web page, we can see the following comment: In 2005, she discovered a dramatically simple and radically new proof of the PCP theorem. Comments on this new proof are published in the following article: On Dinur proof of the PCP theorem, by Jaikumar Radhakrishnan and Madhu Sudan, Bull. Amer. Math. Soc. 44 (2007) p. 19-61 Abstract. Probabilistically checkable proofs are proofs that can be checked probabilistically by reading very few bits of the proof. In the early 1990s, it was shown that proofs could be transformed into probabilistically checkable ones with only a modest increase in their length. The initial transformations, though elementary, were a little too complex. A recent work due to Irit Dinur gives a dramatically simple (and radically new) construction of probabilistically checkable proofs. This article explains the notion of a probabilistically checkable proof, presents the formal definition and then introduces the reader to Dinur's work along with some of the context. 1. Introduction As advances in mathematics continue at the current rate, editors of mathematical journals increasingly face the challenge of reviewing long, and often wrong, "proofs" of classical conjectures. Often, even when it is a good guess that a given submission is erroneous, it takes excessive amounts of effort on the editor's/reviewer's part to find a specific error one can point to. Most reviewers assume this is an inevitable consequence of the notion of verifying submissions and expect the complexity of the verification procedure to grow with the length of the submission. One of the main aims of this article is to point out that this is actually not the case: There does exist a format in which we can ask for proofs of theorems to be written. This format allows for perfectly valid proofs of correct theorems, while any purported proof of an incorrect assertion will be "evidently wrong" (in a manner to be clarified below). We refer to this format of writing proofs as Probabilistically Checkable Proofs (PCPs). In order to formalize the notion of a probabilistically checkable proof, we start with ... See the following Web page: http://www.ams.org/journals/bull/2007-44-01/S0273-0979-06-01143-8/S0273-0979-06-01143-8.pdf --------------------------------------------------------------- The following important publication of Irit Dinur is also posted online: The PCP Theorem by Gap Amplification Irit Dinur February 13, 2007 http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.103.2644&rep=rep1&type=pdf --------------------------------------------------------------- Irit Dinur is also co-editor of the following book: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques: 12th International Workshop, APPROX 2009, and 13th International ... Irit Dinur (Editor), Klaus Jansen (Editor), Seffi Naor (Editor), and José Rolim (Editor) Paperback, 740 pages Publisher: Springer; 1 edition, 2009 ISBN-10: 3642036848 ISBN-13: 978-3642036842 $129.00 ====================== Countdown: The Fields medals 2010 will be awarded in 8 days, on Thursday, August 19, 2010. ======================
From: Jean-Claude Evard on 11 Aug 2010 21:18 ================================= Part 9 of my comments on the 26-th International Congress of Mathematicians (ICM2010), that will be held in Hyderabad, in India, from Thursday, August 19, to Friday, August 27, 2010. ================================= The third plenary lecture will be the following: Plenary Lecture 3 Day 3 of the congress Saturday, August 21, 2010, 11:30 AM-12:30 PM Carlos Kenig The global behaviour of solutions to critical nonlinear dispersive equations This is posted on the schedule of the 20 plenary lectures of the ICM2010, on the following Web page: http://www.icm2010.in/wp-content/icmfiles/docs/schedule/programme_aug9.pdf --------------------------------------------------------------- Here are some pieces of information about the speaker of the third plenary lecture, Carlos Kenig. --------------------------------------------------------------- The Web site of Carlos Kenig is the following: http://www.math.uchicago.edu/~cek/ This Web site contains the following information: Carlos Kenig is professor in the department of mathematics of the University of Chicago, in the USA. --------------------------------------------------------------- A summary of his research interests is posted on the following Web page of the university of Chicago: http://experts.uchicago.edu/experts.php?id=568 We can see on this Web page that his main interest is in the application of harmonic analysis to partial differential equations This Web page contains the following summary: Carlos Kenig works in the field of analysis, a major branch of mathematics that includes calculus and other techniques often applied to scientific problems. His contributions to harmonic analysis, partial differential equations and nonlinear dispersive partial differential equations earned him the 2008 Maxime Bocher Memorial Prize, which is awarded by the American Mathematical Society. An outgrowth of the research of Joseph Fourier nearly two centuries ago, harmonic analysis can be applied to the study of heat, light and other phenomena involving wave motion. Carlos Kenig principally studies partial differential equations and one of their subclasses, nonlinear dispersive equations, which describe various aspects of such phenomena. --------------------------------------------------------------- The following Web page of his Web site contains the list of his publications: http://www.math.uchicago.edu/~cek/bibliography.pdf The following of these publications has a title similar to the title of his talk: [193.] The global behavior of solutions to critical non-linear dispersive and wave equations, Proc. El Escorial Conference in Harmonic Analysis and PDE, June 2008, to appear in Contemp. Math. --------------------------------------------------------------- The following Web page of his Web site contains the list of his publications that are available online on the Web site of arxiv: http://front.math.ucdavis.edu/search?a=Kenig&t=&q=&c=&n=50&s=Listings --------------------------------------------------------------- Below is an article about Carlos Kenig receiving the 2008 Bocher Prize in mathematics that has been posted on the following three Web pages: Carlos Kenig receives 2008 Bocher Prize in mathematics The University of Chicago News Office January 8, 2008 http://www-news.uchicago.edu/releases/08/080108.kenig.shtml Carlos Kenig receives 2008 Bocher Prize in mathematics EurekAlert! Public release date: 8-Jan-2008 http://www.eurekalert.org/pub_releases/2008-01/uoc-ckr010808.php AMS honors Kenig for work in field of analysis with Bôcher Prize By Steve Koppes The University Chicago Chronicle January 10, 2008 http://chronicle.uchicago.edu/080110/kenig.shtml Here are some comments extracted from this article: University of Chicago mathematician Carlos Kenig has been named a co-recipient of the 2008 Maxime Bocher Memorial Prize from the American Mathematical Society (AMS) for his work in the field of analysis. The AMS awarded the prize to Kenig at the Joint Mathematics Meetings in San Diego, Calif., on Jan. 7. The AMS cited Carlos Kenig specifically "for his important contributions to harmonic analysis, partial differential equations, and in particular to nonlinear dispersive partial differential equations." Carlos Kenig principally studies partial differential equations and one of their subclasses, nonlinear dispersive equations, which describe various aspects of such phenomena. When Carlos Kenig began working with dispersive equations approximately 20 years ago, he suspected that the field could benefit from the application of sophisticated mathematical techniques from harmonic analysis. "I found that using techniques from harmonic analysis could get a lot of results that were not conceivable before," Carlos Kenig said. "This opened up the field. This approach was successful beyond my wildest dreams." The AMS awards the Bocher Prize every three years. --------------------------------------------------------------- Carlos Kenig is author, co-author, or co-editor of the following books, ordered in chronological order: ---------------------------------------------------------------------- Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems Carlos E. Kenig Paperback, 146 pages American Mathematical Society, 1994 ISBN-10: 0821803093 ISBN-13: 978-0821803097 $22.00 ---------------------------------------------------------------------- Harmonic Analysis and Partial Differential Equations: Essays in Honor of Alberto P. Calderon Michael Christ, Carlos E. Kenig, and Cora Sadosky Paperback, 360 pages University Of Chicago Press, 2001 ISBN-10: 0226104559 ISBN-13: 978-0226104553 $38.00 ---------------------------------------------------------------------- Mathematical Aspects of Nonlinear Dispersive Equations Edited by Jean Bourgain, Carlos E. Kenig, and Sergiu Klainerman Paperback, 296 pages Princeton University Press, April 9, 2007 ISBN-10: 069112955X ISBN-13: 978-0691129556 $52.50 ---------------------------------------------------------------------- Degenerate Diffusions Panagiota Daskalopoulos and Carlos E. Kenig Hardcover, 207 pages European Mathematical Society, May 15, 2007 ISBN-10: 3037190337 ISBN-13: 978-3037190333 $62.00 ---------------------------------------------------------------------- Selected Papers of Alberto P. Calderon with Commentary Alexandra Bellow (Author and Editor), Carlos E. Kenig (Author and Editor), and Paul Malliavin (Author and Editor) Hardcover, 639 pages American Mathematical Society, 2008) ISBN-10: 0821842978 ISBN-13: 978-0821842973 $119.00 ====================== Countdown: The Fields medals 2010 will be awarded in 7 days, on Thursday, August 19, 2010. ======================
From: Jean-Claude Evard on 12 Aug 2010 21:43
================================= Part 10 of my comments on the 26-th International Congress of Mathematicians (ICM2010), that will be held in Hyderabad, in India, from Thursday, August 19, to Friday, August 27, 2010. ================================= I have posted all of my comments on MathForum, and, some of my comments have been automatically posted on some other Web sites in a chaotic way. Notably, my original posting is missing on all of the other Web sites, and it seems impossible to find it with a Google search. So, for everyone using the other Web sites, it is useful that I give the Web page of MathForum where my thread of comments on the ICM2010 starts, and where everything is posted correctly. My thread of comments starts on the following Web page: http://mathforum.org/kb/message.jspa?messageID=7137304&tstart=0 In this thread, everything is correctly posted, except the format. I have terrible difficulties with the change of format from my PC to the previewer of MathForum, and a lot worse than this, with the changes of format from this previewer to the actual postings. As a consequence, the lengths of the lines of my postings are never normal. ================================= There is a posting about the ICM2010 on the following Web page: http://www.math.columbia.edu/~woit/wordpress/?p=2255 This posting contains interesting guesses about who has some chances to be awarded a Fields medal, or one of the other prizes, on August 19, that is, in six days. This posting is named "Not Even Wrong powered by WordPress." It was posted last year, on August 27, 2009. There are 35 answers with additional guesses about the possible winners, posted from August 27, 2009 to October 8, 2009, on the same Web page. This Web page says that its discussion is now closed. ================================= The abstracts of the plenary lectures, invited lectures, and panel discussions, have now been posted on the following Web page of the ICM2010: http://www.icm2010.org.in/wp-content/icmfiles/abstracts/Invited-Abstracts.pdf This pdf file has 139 pages of abstracts. This gives a feeling of the huge size of the congress. ================================= The table of contents of this pdf file is posted on pdf-file-page number 3. It is easy to miss this table when the scrolling system goes too fast. The first four pages of the pdf file are not numbered, so that [pdf file page number] = [Page number written on the page] + 4 = [Page number given in the table of contents] + 4 ================================= In my previous postings, I gave comments on several of the lectures of the ICM2010, but I did not have the abstracts for these lectures then. So, in this posting, I give the information about the page numbers in the above pdf file of the abstracts of the lectures I have been talking about so far. ================================= In my posting of August 2, I gave additional information about the following lecture: -------------------------------------------------------- Plenary Lecture 15 Day 8 of the congress Thursday, August 26, 2010, 11:30 AM -12:30 PM Kim Plofker Indian rules, Yavana rules: Foreign identity and the transmission of mathematics: -------------------------------------------------------- The abstract of this lecture is located on the following page of the pdf file of abstracts: [Page number written on the page] = 12 [pdf file page number] = 12 + 4 = 16 ================================= In my posting of August 7, I gave additional information about the following lecture: -------------------------------------------------------- The Abel lecture Thursday, August 19, 2010, 16:45-17:45 Srinivasa Varadhan Courant Institute of Mathematical Sciences, New York University, USA Large Deviations -------------------------------------------------------- The abstract of this lecture is located on the following page of the pdf file of abstracts: [Page number written on the page] = 18 [pdf file page number] = 18 + 4 = 22 ================================= In my posting of August 8, I gave additional information about the following lecture: -------------------------------------------------------- Friday, August 27, 2010, 13:45-14:45 Emmy Noether Lecture Idun Reiten, NTNU, Norway Cluster categories -------------------------------------------------------- The abstract of this lecture is located on the following page of the pdf file of abstracts: [Page number written on the page] = 17 [pdf file page number] = 17 + 4 = 21 ================================= In my posting of August 10, I gave additional information about the following lecture. -------------------------------------------------------- Plenary Lecture 1 Day 3 of the congress Saturday, August 21, 2010 09:00-10:00 Artur Avila Dynamics of renormalization operators -------------------------------------------------------- The abstract of this lecture is located on the following page of the pdf file of abstracts: [Page number written on the page] = 3 [pdf file page number] = 3 + 4 = 7 ================================= In my posting of August 11, I gave additional information about the following lecture: -------------------------------------------------------- Plenary Lecture 2 Day 3 of the congress Saturday, August 21, 2010, 10:15-11:15 AM Irit Dinur Probabilistically checkable proofs and codes -------------------------------------------------------- The abstract of this lecture is located on the following page of the pdf file of abstracts: [Page number written on the page] = 6 [pdf file page number] = 6 + 4 = 10 ================================= In my posting of August 12, I gave additional information about the following lecture: -------------------------------------------------------- Plenary Lecture 3 Day 3 of the congress Saturday, August 21, 2010, 11:30 AM-12:30 PM Carlos Kenig The global behaviour of solutions to critical nonlinear dispersive equations -------------------------------------------------------- The abstract of this lecture is located on the following page of the pdf file of abstracts: [Page number written on the page] = 9 [pdf file page number] = 9 + 4 = 13 ====================== Countdown: The Fields medals 2010 will be awarded in 6 days, on Thursday, August 19, 2010. ====================== |