报告人：洛朗•拉福格教授，法国高等科学研究所

时间：10:00-12:00, 11月8日

地点：清华大学近春园西楼三楼报告厅

 

 

洛朗•拉福格，法国著名数学家。他为数论与分析领域中的朗兰兹纲领做出了突出贡献，并对函数域中的自守群证明了朗兰兹猜想。拉福格教授花了六年来完成这项证明，在解决这一问题的过程中，他最重要的工作是构造了Shtukas堆积的紧化。

 

1994年，拉福格在巴黎第十一大学获博士学位，现时在法国国家科学研究中心任研究室主任，在法国高等科学研究所担任数学终身教授。

 

2000，拉福格教授获得克雷研究奖。由于他在数学上所取得的成就，拉福格分别在2001年获得法国科学院颁发的雅克•赫尔布兰德奖，在2003年获法国政府颁发的荣誉骑士级勋章，同年当选为法兰西科学院院士。

 

在2002年中国北京举行的第24届国际数学家大会上洛朗•拉福格被授予菲尔兹奖，以此来表彰他对数论和代数几何的突出贡献。他秉承同是菲尔兹奖得主乌克兰数学家弗拉基米尔•德林费尔德证明 GL2的方法，将朗兰兹猜想推广到在特征为正的代数曲线函数域的GLn上成立。尽管德林费尔德的证明已经非常困难，拉福格上百页简洁的证明可以称得上是天才之作。这项证明充分展现了拉福格作为一名伟大数学家所具有的恒心和毅力。

 

 

Speaker: Laurent Lafforgue (Institut des Hautes Études Scientifiques)

 

Time: 10:00-12:00, Nov. 8 (Friday)

 

Place: Lecture hall, Floor 3, Jin Chun Yuan West Building

 

 

Title: Non linear Fourier transforms and Poisson formulas on reductive Lie groups

 

 

The purpose of the lecture will be starting from the classical Poisson formula, to introduce the statement of generalized Poisson formulas for generalized Fourier transforms on reductive Lie groups.

 

These Poisson formulas are conjectural but they can be shown to be equivalent to the famous "Langlands functoriality principle".

 

Even in the case of the general linear groups GL(r), these formulas are not associated anymore with the linear structure of the space M(r) of r x r matrices in which GL(r) is embedded.

 

For each reductive group, even GL(2), there is not a single Poisson formula but an infinite family of such formulas. They are phrased as statements in functional analysis: the stability of some linear functional under the action of some linear operator acting on some spaces of functions on reductive Lie groups.

 

It is a way to express Langlands' functoriality principle in a quite elementary and explicit way: in particular, the notion of automorphic representation is not needed at all in the statement.

 

 

 

Laurent Lafforgue is a French mathematician. He has made outstanding contributions to Langlands' program in the fields of number theory and analysis, and in particular proved the Langlands conjectures for the automorphism group of a function field. The crucial contribution by Lafforgue to solve this question is the construction of compactifications of certain moduli stacks of Shtukas. The monumental proof is the result of more than six years of concentrated efforts.

 

In 1994 he received his Ph.D. at the Université de Paris-Sud. Currently he is a research director of CNRS, detached as permanent professor of mathematics at the Institut des Hautes Études Scientifiques (I.H.E.S.) in Bures-sur-Yvette, France.

 

He received the Clay Research Award in 2000. Lafforgue received major prizes for his remarkable mathematical achievements. He received the Jacques Herbrand Prize from the Academy of Sciences in 2001 and then, in 2002 at the opening ceremonies of the International Congress of Mathematicians in Beijing, China, he received what is considered the greatest honour for any mathematician, namely a Fields Medal. In 2003 Lafforgue became Chevalier de la Légion d'Honneur and was elected to the Paris Académie des Sciences.

 

Laurent Lafforgue was awarded the Fields Medal for his proof of the Langlands correspondence for the general linear groups GLr over function fields of positive characteristic. His approach to this problem follows the basic strategy introduced twenty-five years ago by V Drinfeld in his proof for GL2. Already Drinfeld's proof is extremely difficult. Lafforgue's proof is a real tour de force, taking up as it does several hundred pages of highly condensed reasoning. By his achievement Lafforgue has proved himself a mathematician of remarkable strength and perseverance.

 

 

Source:

http://www-history.mcs.st-andrews.ac.uk/Biographies/Lafforgue.html