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2007年 數學科學獎

羅伯特.朗蘭茲,
理察.泰勒

以表彰他們開展了一個集大成的數學體系,連結素數及對稱性。

 

得獎人簡介

羅伯特.朗蘭茲,<br/>理察.泰勒

貢獻

2007年邵逸夫數學科學獎將平均頒予羅伯特·朗蘭茲和理察·泰勒教授。

羅伯特.朗蘭茲教授承先啟後,以幾個世紀數學家的工作為基礎,創建了一個集大成的數學體系,把素數和對稱性連結起來。這個數學體系可溯源於高斯和希爾伯特的互逆理論,目前總稱為朗蘭茲綱領。這個綱領自提出以後四十多年,一直指引數論研究工作,在未來歲月,仍將發揮提綱挈領的作用。

 

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得獎者獲獎介紹

The work of Robert Langlands and Richard Taylor, taken together, provides us with an extraordinary unifying vision of mathematics. This vision begins with "Reciprocity", the fundamental pillar of arithmetic of previous centuries, the legacy of Gauss and Hilbert. Langlands had the insight to imbed Reciprocity into a vast web of relationships previously unimagined. Langlands' framework has shaped – and will continue to shape, unify, and advance - some of the most important research programmes in the arithmetic of our time as well as the representation theory of our time. The work of Taylor has, by a route as successful as it is illuminating, established - in the recent past - various aspects of the Langlands programme that have profound implications for the solution of important open problems in number theory.

 

For a prime number p form the (seemingly elementary) function that associates to an integer n the value +1 if n is a square modulo p, the value – 1 if it isn't, and the value 0 if it is divisible by p. It was surely part of Langlands' initial vision that such functions and their number theory might be relatively faithful guides to the vast number-theoretic structure concealed in the panoply of automorphic forms associated to general algebraic groups. Langlands, viewing automorphic forms as certain kinds of representations (usually infinite-dimensional) of algebraic groups, discovered a unification of the two subjects, number theory and representation theory, that has provided mathematics with the astounding dictionary it now is in the process of developing and applying. Namely, the Langlands Philosophy: a dictionary between number theory and representation theory which has the uncanny feature that many elementary representation-theoretic relationships become - after translation by this dictionary – profound, and otherwise unguessed, relationships in number theory, and conversely.

 

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得獎者簡介

羅伯特 • 朗蘭茲 (Robert Langlands)

羅伯特 • 朗蘭茲 (Robert Langlands)

羅伯特 • 朗蘭茲 (Robert Langlands) (1936年出生)現為美國普林斯頓高等研究所教授。

 

朗蘭茲教授在加拿大出生,1957年英屬哥倫比亞大學畢業,取得學士學位,1958年獲理學碩士學位,1960年從耶魯大學取得博士學位。他曾任教於普林斯頓大學和耶魯大學,1972年始轉職普林斯頓高等研究所。朗蘭茲教授是英國皇家學會和加拿大皇家學會會員,及美國科學院院士。

 

2007年6月12日 香港

 

得獎者自傳

 

 

 

 

理察 • 泰勒 (Richard Taylor)

理察 • 泰勒 (Richard Taylor)

理察 • 泰勒 (Richard Taylor) (1962年出生)現為美國哈佛大學數學系教授。2002年成為該校赫雪爾史密夫數學教授。

泰勒教授在英國出生,1984年英國劍橋大學學士畢業,1988年獲普林斯頓大學博士,1989至1995年曾任教於英國劍橋大學,1996至1997年在牛津大學當薩維爾幾何學講座教授。


2007年6月12日 香港

 

得獎者自傳

 

 

 

 

得獎者特寫

 

2007年度邵逸夫數學科學獎講座

"Automorphic Forms, Geometry and Arithmetic: Past, Present and Future" 由羅伯特 • 朗蘭茲教授主講

2007年度邵逸夫數學科學獎講座

"Reciprocity Laws" 由理察 • 泰勒教授主講