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【转帖】越南数学家Ngo Bao Chau证明朗兰兹纲领基本引理
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越南数学家Ngo Bao Chau证明朗兰兹纲领基本引理 Riemann 写道 "《时代》2009十大科学发现之七基本引理被证明写道： 朗兰兹纲领由加拿大数学家罗伯特·朗兰兹发起，是一个旨在联系数论和群表示论的数学蓝图，包含一系列相互关联的猜想，其中的基本引理在过去三十年间只给出了特殊情形的证明。2008年Ngo Bao Chau给出了一般情形下基本引理的证明，其证明在今年被认定是正确无误的，Peter Sarnak评论说Ngo Bao Chau的证明让相关领域的数学家舒了一口气。 Ngo Bao Chau生于1972年，其父是一位物理学家，跟Terence Tao一样，Ngo Bao Chau少年时也是奥数金牌得主，成年后赴巴黎深造。2004年和Laumon一起因给出基本引理在酉群情形的证明而获得clay数学研究奖，33岁时成为越南最年轻的教授。 鉴于朗兰兹纲领已经造就了德林费尔德、洛朗·拉福格两位菲尔兹奖得主，Ngo Bao Chau有望在明年印度海得拉巴举行的国际数学家大会上问鼎菲尔兹奖。" http://www.time.com/time/specials/packages/article/0,28804,1945379_1944416_1944435,00.html -- ※ 来源:·瀚海星云 bbs.ustc.edu.cn· |
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7. The Fundamental Lemma, Solved In 1979 the Canadian-American mathematician Robert Langlands developed an ambitious and revolutionary theory that connected two branches of mathematics called number theory and group theory. In a dazzling set of conjectures and insights, the theory captured deep symmetries associated with equations that involve whole numbers, laying out what is now known as the Langlands program. Langlands knew that the task of proving the assumptions that underlie his theory would be the work of generations. But he was convinced 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. But proving the general case proved more difficult than Langlands anticipated — so difficult, in fact, that it took 30 years to finally achieve. Over the past few years, Ngo Bao Chau, a Vietnamese mathematician working at Université Paris-Sud and the Institute for Advanced Study (IAS) in Princeton, formulated an ingenious proof of the fundamental lemma. When it was checked this year and confirmed to be correct, mathematicians around the globe breathed a sigh of relief. Mathematicians' work in this area in the last three decades was predicated on the principle that the fundamental lemma was indeed accurate and would one day be proved. "It's as if people were working on the far side of the river waiting for someone to throw this bridge across," says Peter Sarnak, a number theorist at IAS. "And now all of sudden everyone's work on the other side of the river has been proven." |
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