Jacques Tits


Born: 12 Aug 1930 in Uccle, Belgium

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Jacques Tits was born in Uccle, on the southern outskirts of Brussels. His parents were Leon Tits, who was a professor, and Lousia Andre. Jacques attended the Athenee of Uccle and then studied at the Free University of Brussels. His thesis advisor in Brussels was Paul Libois, and Tits graduated with his doctorate in 1950 having submitted his dissertation Generalisation des groupes projectifs bases sur la notion de transitivite . From 1948 to 1956 he was funded by the Belgium Fonds National de la Recherche Scientifique.

Tits' first papers, following the work he had undertaken for his doctoral dissertation, were on generalisations of triply transitive groups. He published a two part paper Generalisations des groupes projectifs in 1949 on this topic generalising the group of one-dimensional projective transformations. Among the results proved were characterisations of projective groups among triply transitive groups. In Groupes triplement transitifs et generalisations (1950), Tits went on to look at generalisations of n-tuply transitive groups, defining an almost n-tuply transitive group. This generalises the group of collineations of the plane which is almost quadruply transitive. In Sur les groupes triplement transitifs continus; generalisation d'un theoreme de Kerekjarto (1951) Tits looked at triply transitive groups of transformations of a topological space using his earlier results which characterised the projective groups among triply transitive groups.

Tits married Marie-Jeanne Dieuaide, a historian, on 8 September 1956. From 1956 to 1962 he was an assistant at the University of Brussels. He was promoted to professor in 1962 and remained in this role at Brussels for two years before accepting a professorship at the University of Bonn in 1964. Among Tits' doctoral students in Brussels we mention Francis Buekenhout who was awarded his doctorate in 1965. In 1973 Tits accepted the Chair of Group Theory at the College de France. Shortly after taking up this post, he became a naturalised French subject in 1974. Tits held this chair until he retired in 2000.

The large and important mathematical developments introduced by Tits are far too numerous to cover here in any detail. Perhaps the most important part of his work was the introduction of buildings and this is put into context by Ronan in [3]. We give his summary:-

This paper is an essay on how the development of group theory led to the discovery of various families of simple groups, and how these in turn led to the theory of buildings. In outline the story is this. Galois first used the term 'group' in the technical sense, and found the first simple groups. Jordan, in his famous Traite des substitutions et des equations algebriques, published in 1870, promoted Galois' work and put the theory of groups on a firm foundation. At this time groups were treated as groups of permutations, but other aspects of group theory were soon on the way. Lie visited Paris in 1870 as a graduate student, and went on to create the theory of continuous transformation groups. Killing came to such groups independently, and in 1888 found the classification of the simple Lie groups, using semisimple complex Lie algebras (families A through G). Cartan refined this classification in 1894, correcting some errors in the proofs, and it is now known as the Killing-Cartan classification. The classical families (A through D) soon led to groups over fields other than the real or complex numbers, and a comprehensive study was published by Dickson in 1901. Later he dealt with E6 and G, but progress on the others did not occur until after the Second World War. Tits was working on the problem, as was Chevalley, who was a more established mathematician at that time. Chevalley succeeded in 1955, and his paper was soon followed by variations due to Steinberg, Tits, Suzuki, and Ree. During this time Tits was gradually developing the theory of buildings, and his book "Buildings of spherical type and finite BN-pairs" in 1974 produced a fully-fledged theory that has since found many uses. ... we mention some of Tits' early work on buildings, and we discuss the contents of his above-mentioned book concerning buildings of spherical type. Finally ... a later approach to buildings, also due to Tits, is mentioned, and we return at the end to the construction of the exceptional groups of Lie type using building theory.

Though a lage number of other important roles, Tits had played a major part in mathematical life. For example he was editor-in-chief for mathematical publications at I.H.E.S. from 1980 to 1999. He served on the committee awarding the Fields medals in 1978 and again in 1994. He also served on the committee awarding the Balzan Prize in 1985.

Tits has received, and continues to receive, many honours. Among these we mention the Prix scientifique Interfacultataire L Empain (1955), the Wettrems Prize of the Royal Belgium Academy of Science (1958), the Prix decennal de mathematique from the Belgium government (1965), the Grand Prix of the French Academy of Sciences (1976), the Wolf Prize in Mathematics (1993), and the Cantor Medal from the German Mathematical Society (1996). He was elected to many academies and societies including the German Academy of Scientists Leopoldina (1977), the Royal Netherlands Academy of Sciences (1988), founder member of Academia Europaea (1988), the Royal Belgium Academy of Science (1991), the American Academy of Arts and Sciences (1992), the National Academy of Sciences of the United States (1992), and London Mathematical Society (1993). He has been awarded honorary doctorates from the universities of Utrecht (1970), Ghent (1979), Bonn (1988) and Leuwen (1992). He was made Chevalier de la Legion d'Honneur (1995) and Officier de l'Ordre National du Merite (2001).

After retiring in 2000, Tits became the first holder of the Vallee-Poussin Chair from the University of Louvain. He gave his inaugural lecture Immeubles : une approche geometrique des groupes algebriques simples et des groupes de Kac-Moody on 18 October 2001. He followed this with three series of lectures on the following topics

(1) Generalites sur les nombres p-adiques. Groupes algebriques simples sur les corps p-adiques;
(2) Schemas en groupes a fibre generique simple sur les anneaux d'entiers;
(3) Reseaux invariants dans les espaces de representations. Applications algebriques.

Article by: J J O'Connor and E F Robertson Click on this link to see a list of the Glossary entries for this page


List of References (4 books/articles)
Mathematicians born in the same country
Honours awarded to Jacques Tits
(Click below for those honoured in this way)
International Congress Speaker 1962, 1974
British Mathematical Colloquium plenary speaker 1964, 1973
Speaker at Groups St Andrews 1985
LMS Honorary Member 1993
Wolf Prize 1993
DVR Cantor Medal 1996