越南數(shù)學(xué)家Ngo Bao Chau證明的一個基本引理被.doc

越南數(shù)學(xué)家Ngo Bao Chau證明的一個基本引理被時代雜志列為2009年朗蘭茲綱領(lǐng)由加拿大數(shù)學(xué)家羅伯特朗蘭茲發(fā)起，是一個旨在聯(lián)系數(shù)論和群表示論的數(shù)學(xué)藍(lán)圖，包含一系列相互關(guān)聯(lián)的猜想，其中的基本引理在過去三十年間只給出了特殊情形的證明。2008年Ng Bo Chu給出了一般情形下基本引理的證明，其證明在今年被認(rèn)定是正確無誤的， Peter Sarnak評論說Ng Bo Chu的證明讓相關(guān)領(lǐng)域的數(shù)學(xué)家舒了一口氣。 Ng Bo Chu生于1972年，其父是一位物理學(xué)家，Ng Bo Chu少年時是奧數(shù)金牌得主，成年后赴巴黎深造。2004年和Laumon一起因給出基本引理在酉群情形的證明而獲得clay數(shù)學(xué)研究獎，33歲時成為越南最年輕的教授。 鑒于朗蘭茲綱領(lǐng)已經(jīng)造就了德林費(fèi)爾德、洛朗拉福格兩位菲爾茲獎得主，Ng Bo Chu有望今年在印度海得拉巴舉行的國際數(shù)學(xué)家大會上問鼎菲爾茲獎。 Ngo在宏偉的長達(dá)幾十年的langlands綱領(lǐng)里面消除了一個重大的障礙，揭示了看似沒有關(guān)系的數(shù)學(xué)領(lǐng)域隱藏的聯(lián)系，他給理論的一大部分提供了堅實(shí)的基礎(chǔ)，他新開發(fā)的技術(shù)將引發(fā)新結(jié)論即將到來的洪水大爆發(fā)。Ngo取得的成就的道路始于1967年，當(dāng)年數(shù)學(xué)家R.langlands有一個看來就象相隔幾億光年外的空間有蟲洞連接那種大膽的數(shù)學(xué)領(lǐng)域的設(shè)想。他的建議是如此龐大，看起來幾乎不可能，當(dāng)他第一次寫信給偉大的數(shù)論學(xué)家A.Weil時，卻用著羞怯的字條：“如果你愿意看我這個純粹的猜測我將不勝感激信;如果不愿意看的話，你有可以將他丟進(jìn)你的廢紙簍?！袄侍m茲然后制定了一個已被證明是一個大面積研究領(lǐng)域的路線圖的一系列令人眼花繚亂的猜測。這些絕大多數(shù)仍未經(jīng)證實(shí)的猜測，預(yù)計占用將來幾代數(shù)學(xué)家的精力。即使如此，Langlands綱領(lǐng)迄今取得的進(jìn)展已為新的數(shù)學(xué)結(jié)果證明提供了強(qiáng)大的動力，包括A.Wiles對費(fèi)馬最后定理和Taylor的Sato-Tate猜想的證明。該Langlands綱領(lǐng)將全面實(shí)現(xiàn)統(tǒng)一很多現(xiàn)代數(shù)學(xué)領(lǐng)域，包括數(shù)論，群論，表示理論，代數(shù)幾何。從Langlands綱領(lǐng)發(fā)展而來的一個工具是Arthur-Selberg trace formula的公式，這個公式準(zhǔn)確的顯示了利用“幾何信息”如何計算“算術(shù)信息”。這本身是有價值的，而且它是證明作為langlands綱領(lǐng)偉大支柱之一的Langlands Principle of Functoriality的基石。但langlands在試圖使用跡公式時繞過一個惱人的絆腳石。他不斷地遇到看上去顯然相等的復(fù)雜的有限和，但他不能完全弄清楚如何證明這一點(diǎn)。這就好像一個簡單直接的問題，人們可以隨便組合擺弄一下就解決了，所以langlands稱它是“引理” ，并分配到一個研究生。當(dāng)研究生無法證明這一引理時，langlands他又叫了一個研究生來證.，后來實(shí)在沒有人能證，于是他就只能自己親自出馬。然而這個問題并不是那么簡單，于是他征求了其他數(shù)學(xué)家的意見。在同一時間，因為每個人都依然無法證明這一點(diǎn)，迫切需要這個結(jié)果變得越來越明顯。所以，問題來了一個稍微宏偉標(biāo)題：“基本引理?！苯?jīng)過三十幾年的工作，只有少數(shù)特殊情況下取得了驗證。這個引理缺少證明將會成為那些假設(shè)它是真實(shí)的并開創(chuàng)了許多新結(jié)果和理論的數(shù)學(xué)家們繼續(xù)前進(jìn)的路障，如果這個引理不正確，那么這些數(shù)學(xué)家開創(chuàng)的新理論將會全部崩潰。Ngo就是那個最終解決這個開放問題的人。他意識到，在基本引理的出現(xiàn)的神秘復(fù)雜，可以看作是自然產(chǎn)生出來的復(fù)雜的數(shù)學(xué)對象稱為Hitchen fibrations。他的做法是完全新穎和出人意料的：Hitchen fibrations是最接近數(shù)學(xué)物理的純粹的幾何對象，也幾乎是人們所能想象的到的在最純的純數(shù)學(xué)里最接近這個問題的最后一個概念。這立即清楚的表明Ngo已經(jīng)作出了深刻的聯(lián)系。他的方法將惱人的，復(fù)雜的基本引理變成了一個簡單的，關(guān)于Hitchen fibrations的基本聲明。甚至在他還沒成功地完成證明之前，他已經(jīng)取得了令人印象深刻的成績：他已經(jīng)真正的理解了。此外，通過把這一問題放在更大的框架下，Ngo創(chuàng)造了強(qiáng)大的新工具來攻克它。 2004年，他與Laumon教授一同證明了一些重要而艱巨的特殊情況，2008年，Ngo利用他自己的新方法，攻克了這個問題。Ngo的方法是如此新奇，數(shù)學(xué)家期望他的這些方法也能撬開其他的一些問題，一個主要目標(biāo)就是用他的“內(nèi)窺鏡的理論”攻克langlands綱領(lǐng)的另一部分。他的技術(shù)甚至可能給the full Principle of Functoriality的證明指明方向，這將非常接近全部實(shí)現(xiàn)langlands最初的愿景。現(xiàn)在已是超過70歲的langlands，仍然在努力工作，已制定了一個高度機(jī)敏，但誘人的方法來解決問題。但仍遠(yuǎn)遠(yuǎn)沒有明確表示這些想法會導(dǎo)致一個證明，但是如果他們這樣做的話，他們將不得不依賴于Ngo已推出的各種幾何觀念。 過去三十年相關(guān)領(lǐng)域的數(shù)學(xué)家一致期望Langlands Program中的一個基本引理會被證明的確是精確的。Ngo Bao Chau一位在法國Universit Paris-Sud 和普林斯頓Institute for Advanced Study (IAS) 工作的越南數(shù)學(xué)家（1972年生于越南河內(nèi)），證明了這一引理，2009年相關(guān)領(lǐng)域的數(shù)學(xué)家驗證了他的證明。這一結(jié)果被時代雜志列為2009年度十大科學(xué)發(fā)現(xiàn)的第七項。Ngo Bao Chau accepts invitation to become Chicago University professor16:50 27/01/2010 (GMT+7) VietNamNet Bridge Renowned Vietnamese mathematician Ngo Bao Chau has accepted an invitation to become a professor at the University of Chicago. Chau will officially begin his new position on September 1, 2010.Robert Fefferman, Professor of Mathematics and Dean of the Physics Department at the University of Chicago remarked said that Chau is clearly one of the greatest mathematicians in modern times and that he had high expectations for the young man.Peter Constantin, Dean of the Mathematics Department who will work closely with Chau, noted that Chau has made breakthrough achievements with with his work, successfully connecting two important fields of mathematics, arithmetic and geometry. Peter believes that with Ngo Bao Chau and other excellent faces such as Kato, Beilinson and Drinfeld, Chicago University will have a brilliant staff lineup.When asked about the decision to become a UC professor, Chau replied that the opportunity to cooperate more closely with UC colleagues played a very important role in his decision.On December 9, Time Magazine 9 announced its top ten lists for 2009 and included Professor Ngo Bao Chaus solution of the “fundamental lemma.” With his work, Chau has become a brilliant candidate for the highest mathematics prize the Fields Medal.According to Dr. Ngo Viet Trung, head of the Mathematics Institute, with Chau solving the “fundamental lemma”, the Langlands program has entered a new stage.According to Time Magazine, the Canadian-American mathematician Robert Langlands developed an ambitious and revolutionary theory in 1979 that connected two branches of mathematics called number theory and group theory. The theory captured deep symmetries associated with equations involving whole numbers, laying out what is now known as the Langlands program. Langlands believed that the task of proving his theory would take generations. He was convinced, however, that one stepping stone that needed confirmation dubbed, the fundamental lemma - would be reasonably straightforward. He, his collaborators and his students were able to prove special cases of this fundamental theorem. Proving the general case proved more difficult than anticipated - so difficult, in fact, that it took 30 years to finally achieve. Ngo Bao Chau was born in 1972. He was once a member of the mathematics majors at Hanoi University of Natural Sciences.In 1988, Chau won the gold medal at the International Mathematics Olympiad in Australia. In 1989, he won another gold medal at the International Mathematics Olympiad in Germany.Chau defended his doctoral dissertation in France when he was just 25.In 2005, Chau was recognized as an exceptional mathematics professor when he was 33 years old, becoming the youngest professor in Vietnam.Ngo Viet Trung said that Chau is planning to invite some leading mathematics experts to Vietnam to conduct research on Langslands programme.吳寶珠 是在巴黎高等師范學(xué)院練過的 又在最令人心儀的普林斯頓高等研究院訪問研究 而郎蘭茲就在那里當(dāng)教授 天時地利人和 是他被譽(yù)為 近三十年來最偉大的數(shù)學(xué)家 而且現(xiàn)在他才虛歲38 估計獲獎是沒多大問題了2010年菲爾茲獎揭曉2010年菲爾茲獎揭曉 前天下午3點(diǎn)，據(jù)印度班加羅爾四年一屆的國際數(shù)學(xué)家大會現(xiàn)場消息，素有數(shù)學(xué)諾貝爾獎之稱的菲爾茲獎揭曉，獲得這個具有崇高聲望的大獎的數(shù)學(xué)家有： Bao Chau Ngo ：越南數(shù)學(xué)家，目前在美國普林斯頓高等研究院工作，獲獎理由：證明了朗蘭茲綱領(lǐng)中的自守形式理論的基本引理。 Elon Lindenstrauss：以色列數(shù)學(xué)家，目前在美國普林斯頓大學(xué)工作，獲獎理由是：遍歷理論的測度剛性及其在數(shù)論中的應(yīng)用。 Stanislav Smirnov ：俄羅斯數(shù)學(xué)家，目前在瑞士日內(nèi)瓦大學(xué)工作，獲獎理由是：證明了統(tǒng)計物理中平面伊辛模型和滲流的共形不變量。 Cdric Villani ：法國數(shù)學(xué)家，目前在法國龐加萊研究所工作，獲獎理由是證明了玻爾茲曼方程的非線性阻尼以及收斂于平衡態(tài)。 其它獎項（都是終身成就獎）及其獲獎人包括： 高斯獎，Yves Meyer，法國巴黎高等師范學(xué)校，以在數(shù)論、調(diào)和分析、小波分析等方面的基礎(chǔ)貢獻(xiàn)獲獎。 那望林納獎，Daniel Spielman，美國耶魯大學(xué)應(yīng)用數(shù)學(xué)家，以線性規(guī)劃研究中的諸多貢獻(xiàn)獲獎 陳省身獎（首次頒發(fā)），Louis Nirenberg ，美國紐約大學(xué)柯朗研究所，以奠基現(xiàn)代非線性橢圓方程理論獲獎。 值得一提的是，本次獲獎名單與此前多數(shù)預(yù)測只有少數(shù)符合。例如菲爾茲獎，除了Bao Chau Ngo 外，其他3個都被認(rèn)為不太熱門，而很多熱門人物都落選，如英國Ben Green， 巴西Artur Avila，印度Manjul Bhargava（他有主場優(yōu)勢） 等。其它3個成就獎更是早就被認(rèn)為不可預(yù)測，因為符合條件的人太多了。另外，法國和美國是最大贏家。法菲爾茲獎除Alon與法國沒有淵源外，其它三個與法國都有很深的淵源，另外三個成就獎中，法國也占了1位，可見法國數(shù)學(xué)之強(qiáng)。當(dāng)然，還是美國最強(qiáng)了！ICM 2006Invited SpeakersICM 2006Invited Speakers 1. Logic and Foundati* Model theory. Set theory and general topology. Recursion. Logics. Proof t heory. Applicati*. INVITED SPEAKERS Rod Downey Victoria University, Wellington, New Zeeland Itay Neeman University of California, Los Angeles, USA Michael Rathjen The Ohio State University, Columbus, USA Thomas Scanlon University of California, Berkeley, USA Simon Thomas Rutgers University, New Brunswick, USA 2. Algebra Finite groups and their representati*. Infinite and topological groups (except as specified in section 7). Combinatorial group theory. Rings, algebra s and modules (except as specified in section 7). Algebraic K-theory. Category theory and homological algebra. Computational algebra. INVITED SPEAKERS William Crawley-Boevey University of Leeds, Leeds, United Kingdom Bernard Keller Universit Denis Diderot, Paris, France Raphael Rouquier Universit Denis Diderot, Paris, France Mark Sapir Vanderbilt University, Nashville, USA Akos Seress The Ohio State University, Columbus, USA Agata Smoktunowicz Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland JOINT LECTURE Marcus du Sautoy University of Oxford, Oxford, United Kingdom Fritz Grunewald Heinrich-Heine-Universit?t Dsseldorf, Dsseldorf, Germany 3. Number Theory Analytic number theory. Algebraic number theory. Local and global fields, thei r Galois groups and representati* of these groups. Zeta and L-functi* and their special values. Diophantine equati*. Arithmetic on algebraic varieties . Diophantine approximation, transcendental number theory and geometry of numb ers. Arakelov theory. Modular forms and curves. p-adic analysis. p-adic repres entati* of p-adic groups. Computational number theory. INVITED SPEAKERS Manjul Bhargava Princeton University, Princeton, USA Ching-Li Chai University of Pennsylvania, Philadelphia, USA Henri Darmon McGill University, Montral, Canada Kazuhiro Fujiwara Nagoya University, Nagoya, Japan Ben J. Green University of Bristol, Bristol, United Kingdom Grard Laumon Universit de Paris-Sud, Orsay, France Philippe Michel Universit de Montpellier II, Montpellier, France Wieslawa Niziol University of Utah, Salt Lake City, USA Vinayak Vatsal University of British Columbia, Vancouver, Canada JOINT LECTURE Chris Skinner University of Michigan, Ann Arbor, USA Eric Urban Columbia University, New York, USA 4. Algebraic and Complex Geometry Algebraic varieties, their cycles, cohomologies and motives (including positiv e characteristics). Schemes. Commutative algebra. Low dimensional varieties. S ingularities and classification. Birational geometry. Moduli spaces. Abelian v arieties and p-divisible groups. Sheaves. Transcendental methods, topology of algebraic varieties. Complex differential geometry, Kahler manifolds and Hodge theory. Relati* with mathematical physics and representation theory. Real a lgebraic and analytic sets. Rigid and p-adic analytic spaces. Non-commutative algebraic geometry. INVITED SPEAKERS Valery Alexeev University of Georgia, Athens, USA Jean-Beno?t Bost Universit Paris-Sud, Orsay, France Tom Bridgeland University of Sheffield, Sheffield, United Kingdom Lawrence Ein University of Illinois at Chicago, Chicago, USA Tom Graber University of California, Berkeley, USA Jun-Muk Hwang Korea Institute for Advanced Study, Seoul, Korea Tomohide Terasoma University of Tokyo, Tokyo, Japan Yuri Tschinkel Georg-August Universit?t G?ttingen, G?ttingen, Germany Jaroslaw Wlodarczyk Purdue University, West Lafayette, USA 5. Geometry Local and global differential geometry. Applicati* of PDE to geometric probl ems including harmonic maps, minimal submanifolds and flows on the space of me trics. Geometric structures on manifolds. Riemannian and metric geometry. Geom etric aspects of group theory. Symplectic and contact manifolds. Convex geomet ry. Discrete geometry. Geometric rigidity. INVITED SPEAKERS Simon A. Brendle Princeton University, Princeton, USA Ko Honda University of Southern California, Los Angeles, USA Michael Kapovich University of California, Davis, USA Bruce Kleiner University of Michigan, Ann Arbor, USA Fran?ois Lalonde Universit de Montral, Montral, Canada Xiaobo Liu University of Notre Dame, Notre Dame, USA Toshiki Mabuchi Osaka University, Osaka, Japan Grigory Mikhalkin University of Utah, Salt Lake City, USA William P. Minicozzi Johns Hopkins University, Baltimore, USA Yong-Geun Oh University of Wisc*in, Madison, USA Antonio Ros Universidad de Granada, Granada, Spain Chuu-Lian Terng University of California, Irvine, USA Burhard Wilking Universit?t Mnster, Mnster, Germany 6. Topology Algebraic, differential and geometric topology. 4-manifolds including connecti * with gauge theory. 3-manifolds including knot theory and connecti* with Kleinian groups and Teichmuller theory. Topological quantum field th eories. INVITED SPEAKERS Ian Agol University of Illinois, Chicago, USA Martin Bridson Imperial College London, London, United Kingdom Mikhail Khovanov University of California, Davis, USA Yair Minsky Yale University, New Haven, USA Fabien Morel Universit?t Mnchen, Mnchen, Germany Kaoru Ono Hokkaido University, Sapporo, Japan Karen Vogtmann Cornell University, Ithaca, USA JOINT LECTURE Peter Ozsvth Columbia University, New York, USA Zoltn Szab Princeton University, Princeton, USA 7. Lie Groups and Lie Algebras Algebraic and arithmetic groups. Structure, geometry and representati* of Li e groups (including real, p-adic and finite of Lie type) and Lie algebras incl uding infinite dimensional ones. Related geometric and algebraic objects, e.g. symmetric spaces, buildings, vertex operator algebras, Coxeter groups, quantu m groups. Non-commutative harmonic analysis. Geometric methods in representati on theory. Automorphic forms over global fields, including Langlands program. Shimura varieties. Discrete subgroups of Lie groups. Lie groups and dynamics, including applicati* to number theory. INVITED SPEAKERS Roman V. Bezrukavnikov Northwestern University, Evanston, USA A. Braverman Brown University, Providence, USA I. Grojnowski University of Cambridge, Cambridge, United Kingdom G. Henniart Universit Paris-Sud, Orsay, France N. Monod University of Chicago, Chicago, USA Bao-Chau Ngo Universit de Paris-Sud, Orsay, France E.M. Opdam Universiteit van Amsterdam, Amsterdam, The Netherlands P. Schneider Universit?t Mnster, Mnster, Germany Y. Shalom Tel Aviv University, Tel Aviv, Israel B. Speh Cornell University, Ithaca, USA D. Soudry Tel Aviv University, Tel Aviv, Israel T.A. Springer Universiteit Utrecht, Utrecht, The Netherlands 8. Analysis Classical analysis, harmonic analysis (including wavelets and computational as pects), complex analysis in one and several variables, potential theory, geome tric function theory (including quasi-conformal mappings), geometric measure theory. INVITED SPEAKERS Mario Bonk University of Michigan, Ann Arbor, USA Steven Hofmann University of Missouri, Columbia, USA Sergey Konyagin Moscow State University, Moscow, Russia Linda Rothschild University of California, San Diego, USA Stanislav Smirnov Universit de Genve, Genve, Switzerland Emil Straube Texas A&M University, College Station, USA Vladimir Temlyakov University of South Carolina, Columbia, USA Xavier Tolsa Universitat Autnoma de Barcelona, Bellaterra, Spain 9. Operator Algebras and Functional Analysis Non-commutative geometry, random matrices and free probability, K-theory of C* -algebras, structure of factors and their automorphism groups, subfactors, ope rator-algebraic aspects of quantum field theory, linear and non-linear functio nal analysis, geometry of Banach spaces, asymptotic geometric ana 7mlysis. INVITED SPEAKERS Franck Barthe Universit Paul Sabatier, Toulouse, France Boz Klartag Institute for Advanced Study, Princeton, USA Ozawa Narutaka University of Tokyo, Tokyo, Japan Mikael Rordam University of Southern Denmark, Odense, Denmark Stanislaw Szarek Case Western Reserve University, Cleveland, USA and Universit Pierre et Marie Curie, Paris, France Guoliang Yu Vanderbilt University, Nashville, USA 10. Ordinary Differential Equati* and Dynamical Systems Topological and formal dynamics. Geometric and qualitative theory of ODE and s mooth dynamical systems, bifurcati* and singularities. Hamiltonian systems a nd dynamical systems of geometric origin, e.g. geodesic flows. One-dimensional and holomorphic dynamics. Billiards including rational billiards. Multidimens ional acti* and rigidity in dynamics. Ergodic theory including applicati* to combinatorics and combinatorial number theory. INVITED SPEAKERS Oleg N. Ageev Max-Planck- Institut fr Mathematik, Bonn, Germany and Moscow State Technical University, Moscow, Russia Vitaly Bergelson Ohio State University, Columbus, USA Rafael de la Llave The University of Texas at Austin, Austin, USA Dmitry Dolgopyat University of Maryland College Park, College Park, USA Robert Ghrist University of Illinois at Urbana-Champaign, Urbana, USA Vadim Kaloshin California Institute of Technology, Pasadena, USA Bryna Kra Northwestern University, Evanston, USA Patrice le Calvez Universit Paris XIII, Villetaneuse, France Elon Lindenstrauss Princeton University, Princeton, USA Michael Shub University of Toronto, Toronto, Canada Anton Zorich Universit de Rennes, Rennes, France 11. Partial Differential Equati* Solvability, regularity and stability of linear and non-linear equati* and s ystems. Qualitative properties (singularities, symmetry, asymptotics, long tim e behaviour). Spectral theory, scattering, inverse problems. Variational metho ds and calculus of variati*. Homogenization and multiscale problems. Relatio ns to continuous media and control. INVITED SPEAKERS Stefano Bianchini SISSA-ISAS, Trieste, Italy and Istituto per le Applicazioni del Calcolo M.Picone, Roma, Italy Patrick Grard Universit de Paris-Sud, Orsay, France Fran?ois Golse Universit Pierre et Marie Curie, Paris, France Matthew Gursky University of Notre Dame, Notre Dame, USA Hitoshi Ishii Waseda University, Tokyo, Japan Mario Pulvirenti Universit di Roma-La Sapienza, Roma, Italy Ovidiu Savin University of California, Berkeley, USA Sylvia Serfaty Courant Institute of Mathematical Sciences, New York University, New York, USA Neil Trudinger Australian National University, Camberra, Australia