雅克·蒂茨1930—2021

生平

蒂茨得以发现数学，缘于他偷偷地到同是数学家的父亲的藏书室取阅书籍。他年轻已才智超群，14岁就给准备报考法国高等师范学院的学生私人补习，20岁在布鲁塞尔自由大学发表博士论文，其中已有他将来工作的精髓。

他自1962年至1964年任教于布鲁塞尔自由大学，1964年到波恩大学任教至1974年，自1973年至1974年是法兰西学士院副教授，自1975年任群论讲座教授，至2000年退休。

他发明厦理论和BN对，于代数群（包括一些有限群）有用，尤其是定义在p进数上的群。

奖项和荣誉

蒂茨1996年获得德国数学学会的康托尔奖，1993年获得沃尔夫奖。2008年3月他和约翰·格里格斯·汤普森一同获得阿贝尔奖。

他1979年起是法兰西科学院院士。1988年成为荷兰皇家艺术与科学学院外籍院士。是挪威科学与文学院成员

Jacques Tits (French: [ʒak tits]; 12 August 1930 – 5 December 2021) was a Belgian-born French mathematician who worked on group theory and incidence geometry. He introduced Tits buildings, the Tits alternative, the Tits group, and the Tits metric.

Early life and education

Tits was born in Uccle, Belgium to Léon Tits, a professor, and Louisa André. Jacques attended the Athénée of Uccle and the Free University of Brussels. His thesis advisor was Paul Libois, and Tits graduated with his doctorate in 1950 with the dissertation Généralisation des groupes projectifs basés sur la notion de transitivité.

Career

Tits held professorships at the Free University of Brussels (now split into the Université libre de Bruxelles and the Vrije Universiteit Brussel) (1962–1964), the University of Bonn (1964–1974) and the Collège de France in Paris, until becoming emeritus in 2000. He changed his citizenship to French in 1974 in order to teach at the Collège de France, which at that point required French citizenship. Because Belgian nationality law did not allow dual nationality at the time, he renounced his Belgian citizenship.

Tits was an "honorary" member of the Nicolas Bourbaki group; as such, he helped popularize H.S.M. Coxeter's work, introducing terms such as Coxeter number, Coxeter group, and Coxeter graph.

Death

Tits died on 5 December 2021, at the age of 91 in the 13th arrondissement, Paris.

Awards and honors

Tits received the Wolf Prize in Mathematics in 1993, the Cantor Medal from the Deutsche Mathematiker-Vereinigung (German Mathematical Society) in 1996, and the German distinction "Pour le Mérite". In 2008 he was awarded the Abel Prize, along with John Griggs Thompson, "for their profound achievements in algebra and in particular for shaping modern group theory".

Tits became a member of the French Academy of Sciences in 1979. He was a member of the Norwegian Academy of Science and Letters. He became a foreign member of the Royal Netherlands Academy of Arts and Sciences in 1988.

Contributions

He introduced the theory of buildings (sometimes known as Tits buildings), which are combinatorial structures on which groups act, particularly in algebraic group theory (including finite groups, and groups defined over the p-adic numbers). The related theory of (B, N) pairs is a basic tool in the theory of groups of Lie type. Of particular importance is his classification of all irreducible buildings of spherical type and rank at least three, which involved classifying all polar spaces of rank at least three. The existence of these buildings initially depended on the existence of a group of Lie type in each case, but in joint work with Mark Ronan he constructed those of rank at least four independently, yielding the groups directly. In the rank-2 case spherical building are generalized n-gons, and in joint work with Richard Weiss he classified these when they admit a suitable group of symmetries (the so-called Moufang polygons). In collaboration with François Bruhat he developed the theory of affine buildings, and later he classified all irreducible buildings of affine type and rank at least four.

Another of his well-known theorems is the "Tits alternative": if G is a finitely generated subgroup of a linear group, then either G has a solvable subgroup of finite index or it has a free subgroup of rank 2.

The Tits group and the Kantor–Koecher–Tits construction are named after him. He introduced the Kneser–Tits conjecture.