孔涅Alain Connes

孔涅出生于德拉吉尼昂，这是法国东南部普罗旺斯-阿尔卑斯-蓝色海岸地区戛纳附近的一个城镇。他于1966年进入巴黎高等师范学院，1970年毕业。毕业后，孔涅成为国家科学研究中心的研究员。他的学位论文A classification of factors of type III是关于算子代数，特别是冯·诺依曼代数的，这项工作由雅克·迪克斯米耶指导。该学位论文于1973年提交给巴黎高等师范学院。

孔涅在1974-75学年在加拿大安大略省皇后大学度过。1976年，他被任命为巴黎第六大学的讲师，随后晋升为教授。他在1978-79学年在普林斯顿高等爱德华·斯图迪研究所度过。1980年，他离开了巴黎第六大学，但在前一年，他已被任命为比尔斯-伊维特高等科学研究所的教授。孔涅仍担任这一教授职位。

1981年，孔涅回到国家科学研究中心，这次担任研究主任。他担任此职八年。1984年，他还被任命为巴黎乌尔姆街法兰西学院的教授。孔涅目前同时担任高等科学研究所和法兰西学院的职位。

孔涅的工作是关于算子代数的，Moore [5]将其置于背景之中：-

为了把孔涅对算子代数的根本性和开创性贡献置于背景之中，回想一下，冯·诺伊曼和詹姆斯·D·默里在20世纪30年代和40年代，除其他因素外，受到大卫·希尔伯特空间上算子的谱理论以及为quantum mechanical systems构造数学模型的考虑的引导，引入了他们所称的算子环——后来更名为冯·诺依曼代数。……主要问题之一过去是、现在仍然是把这些代数作为内在的代数对象和topological对象进行分类。

在5中，Moore将孔涅的学位论文描述为：-

……在分类问题上已经是一个重大的、令人震惊的突破。

孔涅最早获得的重大国际荣誉之一，是受邀在1978年赫尔辛基国际数学家大会上作邀请报告。四年后，1982年8月初在华沙举行的国际数学联盟全体大会上宣布将菲尔兹奖授予孔涅。该奖章直到华沙国际数学家大会才颁发，该大会未能按原定计划于1982年举行，推迟到了次年。1983年国际数学家大会上作了关于孔涅工作的报告，正是这些工作使他获得了该奖章。Araki描述了孔涅的贡献，见[2]：-

他最杰出的贡献是
(1) III型因子的普遍分类和结构定理，在其学位论文中获得
(2) 超有限因子的自同构分类，这为下一项贡献作了准备
(3) 单射因子的分类，以及
(4) C*-代数理论对叶状结构和一般微分几何的应用。

在描述了这些贡献之后，Araki还指出了孔涅的其他工作，例如他将算子代数应用于微分几何，以及他于1979年发表的关于非交换积分理论的工作。

Moore在[5]中总结了孔涅的一些工作：-

总的来说，孔涅在过去十年中在算子代数及其应用方面的工作已经改变了这一学科，并开辟了全新的研究领域。

孔涅最近的工作是关于非交换几何的，他于1994年出版了一部关于该主题的重要著作。他研究了其在理论物理学中的应用，他的工作具有重大重要性，正如Araki在[2]中所说：-

……孔涅的惊人力量和他贡献的丰富性。

孔涅因其工作获得了许多奖项。除了约翰·查尔斯·菲尔兹奖章外，他于1975年获得Aimeé Berthé奖，1976年获得Pecot-Vimont奖，1977年获得国家科学研究中心金质奖章，1980年获得巴黎Académie des Sciences颁发的安德烈-马里·安培奖，1981年获得法国电力公司奖。

他于1982年当选为Académie des Sciences院士，当时该科学院中只有十三位数学家。他还当选为丹麦皇家科学院（1980年）、Norwegian Academy of Sciences（1993年）和Canadian Academy of Sciences（1995年）的外籍院士。

孔涅继续担任高等科学研究所的Léon Motchane讲席和法兰西公学院的分析与几何讲席。此外，2003年他被任命为美国田纳西州范德堡大学的杰出教授。他继续获得重大荣誉，如2000年5月24日在巴黎颁发的克莱研究奖：-

……因革新了算子代数领域，因发明了现代非交换几何，并因发现这些思想无处不在，包括理论物理学的基础。

2001年1月24日，Royal Swedish Academy of Sciences决定将极负盛名的克拉福德奖授予孔涅：-

……因其在算子代数理论方面的深刻工作以及作为非交换几何创始人之一。

2004年，他获得了法国国家科学研究中心颁发的金质奖章。公告如下：-

在将孔涅命名为2004年金质奖章获得者时，法国国家科学研究中心称他为“我们时代最伟大的数学家之一”。在整个职业生涯中，孔涅致力于解决源自量子物理和相对论的数学问题。他彻底变革了算子代数理论，并且是数学新分支——非交换几何的主要创始人。

除这些奖项外，我们注意到孔涅获得了加拿大安大略省金斯顿皇后大学（1979年）、意大利罗马第二大学（1997年）和挪威奥斯陆大学（1999年）的名誉博士学位。除上述科学院外，他还当选为美国艺术与科学院（1990年）、美国国家科学院（1997年）和俄罗斯科学院（2003年）的成员。

Alain Connes was born in Draguignan, a town near Cannes in the Provence- Alpes-Côte-d'Azur region of southeast France. He entered the École Normale Supérieure in Paris in 1966, graduating in 1970. After graduating, Connes became a researcher at the Centre National de la Recherche Scientifique. His thesis A classification of factors of type III was on operator algebras, in particular on von Neumann algebras, and the work was supervised by Jacques Dixmier. The thesis was presented to the École Normale Supérieure in 1973.

Connes spent the academic year 1974-75 at Queen's University in Ontario Canada. In 1976 he was appointed a lecturer at the University of Paris VI, then he was promoted to professor. He spent the year 1978-79 at the Institute for Advanced Study at Princeton. He left the University of Paris VI in 1980 but, the previous year, he had been appointed as professor at the Institut des Hautes Études Scientifiques at Bures-sur-Yvette. Connes still holds this professorship.

In 1981 Connes returned to the Centre National de la Recherche Scientifique, this time as its director of research. He held this post for eight years. Another position he was appointed to was professor at the Collège de France at Rue d'Ulm in Paris in 1984. Connes currently holds both the position in the Institut des Hautes Études Scientifiques and the one in the Collège de France.

Connes's work is on operator algebras and it is put in context by Moore [5]:-

To place Alain Connes's fundamental and pioneering contributions to operator algebras in context, recall that von Neumann and Murray in the 1930s and 1940s were led by, among other things, the spectral theory of operators on Hilbert space, and by considerations of constructing mathematical models for quantum mechanical systems, to introduce what they called rings of operators - since renamed von Neumann algebras. ... One of the main problems has been and remains the classification of these algebras as intrinsic algebraic and topological objects.

In [5] Moore describes Connes' thesis as:-

... already a major, stunning breakthrough in the classification problem.

One of the first major international distinctions for Connes was an invitation to give one of the invited lectures at the International Congress in Helsinki in 1978. Four years later the award of a Fields Medal to Connes was announced at a meeting of the General Assembly of the International Mathematical Union in Warsaw in early August 1982. The Medal was not presented until the International Congress in Warsaw which could not be held in 1982 as scheduled and was delayed until the following year. Lectures on the work of Connes which led to his receiving the Medal were made at the 1983 International Congress. Araki, described Connes' contributions, see [2]:-

His most remarkable contributions are
(1) general classification and a structure theorem for factors of type III, obtained in his thesis
(2) classification of automorphisms of the hyperfinite factor, which served as a preparation for the next contribution
(3) classification of injective factors, and
(4) application of the theory of C*-algebras to foliations and differential geometry in general.

After describing these contributions, Araki also notes other work of Connes such as his applications of operator algebras to differential geometry and his work on non-commutative integration theory which he published in 1979.

Moore, in [5], sums up some of Connes' work:-

Taken altogether Connes's work in the last decade on operator algebras and its applications has transformed the subject, and opened up entire new areas of research.

Connes' recent work has been on noncommutative geometry and he published a major text on the topic in 1994. He has studied applications to theoretical physics and his work is of major importance showing, in the words of Araki in [2]:-

... the incredible power of Alain Connes and the richness of his contributions.

Connes has received many awards for his work. In addition to the Fields Medal he was awarded the Prix Aimeé Berthé in 1975, the Prix Pecot-Vimont in 1976, the gold medal of the Centre National de la Recherche Scientifique in 1977, the Prix Ampère from the Académie des Sciences in Paris in 1980 and in 1981 the Prix de Electricité de France.

He was elected to the Académie des Sciences in 1982 being at that time only one of thirteen mathematicians in the Academy. He has been elected as a foreign member of the Royal Danish Academy of Sciences (1980), the Norwegian Academy of Sciences (1993) and the Canadian Academy of Sciences (1995).

Connes continues to hold the Léon Motchane Chair at the Institut des Hautes Études Scientifiques and the Chair of Analysis and Geometry in the Collège de France. In addition, in 2003 he was appointed Distinguished Professor at Vanderbilt University, Tennessee, in the United States. He has continued to receive major honours such as the Clay Research Award, presented on 24 May 2000 in Paris:-

... for revolutionizing the field of operator algebras, for inventing modern non-commutative geometry, and for discovering that these ideas appear everywhere, including the foundations of theoretical physics.

On 24 January 2001 the Royal Swedish Academy of Sciences decided to award Connes their highly prestigious Crafoord Prize:-

... for his penetrating work on the theory of operator algebras and for having been a founder of the non-commutative geometry.

In 2004 he received the Gold Medal from the Centre National de la Recherche Scientifique. The announcement reads:-

In naming Connes the 2004 Gold Medallist, the CNRS called him "one of the greatest mathematicians of our time." Throughout his career, Connes has applied himself to solving mathematical problems arising from quantum physics and the theory of relativity. He revolutionized the theory of operator algebras and was a primary founder of a new branch of mathematics - noncommutative geometry.

In addition to these awards we note that Connes has been given honorary doctorates by Queen's University, Kingston, Ontario, Canada (1979), the University of Rome Tor Vergata, Italy (1997), and the University of Oslo, Norway (1999). In addition to the academies mentioned above, he has been elected to the American Academy of Arts and Sciences (1990), the United States National Academy of Sciences (1997), and the Russian Academy of Sciences (2003).