Jacques Tits
Jacques Tits  

Jacques Tits in May 2008


Born 
Uccle, Belgium 
12 August 1930
Residence  France 
Citizenship  Belgian (1930–1974) French (since 1974) 
Fields  Mathematics 
Institutions 
Free University of Brussels Vrije Universiteit Brussel University of Bonn Collège de France French Academy of Sciences 
Doctoral advisor  Paul Libois 
Doctoral students 
Francis Buekenhout Jens Carsten Jantzen KarlOtto Stöhr JeanPierre Tignol 
Known for  The Tits group, the Tits alternative, Tits buildings 
Notable awards 
Cantor medal (1996) Abel Prize (2008, with John G. Thompson) 
Jacques Tits (French: [tits]; born 12 August 1930 in Uccle) is a Belgiumborn French mathematician who works on group theory and incidence geometry, and who introduced Tits buildings, the Tits alternative, and the Tits group.
Career
Tits was born in Uccle to Léon Tits, a professor, and Lousia 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. His academic career includes 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. He has been a member of the French Academy of Sciences since then.
Tits was an "honorary" member of the Nicolas Bourbaki group; as such, he helped popularize Harold Scott MacDonald Coxeter's work, introducing terms such as Coxeter number, Coxeter group, and Coxeter graph.^{[1]}
Honors
Tits received the Wolf Prize in Mathematics in 1993, the Cantor Medal from the Deutsche MathematikerVereinigung (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.”^{[2]} He is a member of several Academies of Sciences.
He is a member of the Norwegian Academy of Science and Letters.^{[3]} He became a foreign member of the Royal Netherlands Academy of Arts and Sciences in 1988.^{[4]}
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 padic 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. In the rank2 case spherical building are generalized ngons, and in joint work with Richard Weiss he classified these when they admit a suitable group of symmetries (the socalled 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 wellknown 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 Tits–Koecher construction are named after him. He introduced the Kneser–Tits conjecture.
Publications
 Tits, Jacques (1964). "Algebraic and abstract simple groups". Annals of Mathematics. Second Series. 80 (2): 313–329. ISSN 0003486X. JSTOR 1970394. MR 0164968. doi:10.2307/1970394
 Tits, Jacques (1974). "Buildings of spherical type and finite BNpairs". Lecture Notes in Mathematics, Vol. 386. 386. Berlin, New York: SpringerVerlag. ISBN 9783540067573. MR 0470099. doi:10.1007/9783540383499^{[5]}
 Tits, Jacques; Weiss, Richard M. (2002). Moufang polygons. Springer Monographs in Mathematics. Berlin, New York: SpringerVerlag. ISBN 9783540437147. MR 1938841
 J. Tits, Oeuvres  Collected Works, 4 vol., Europ. Math. Soc., 2013. J. Tits, Résumés des cours au Collège de France, S.M.F., Doc.Math. 12, 2013.
References
 ^ Siobhan Roberts, "Donald Coxeter: The man who saved geometry", Toronto Life, January 2003

^ "Thompson and Tits share the Abel Prize for 2008". The Niels Henrik Abel Memorial Fund. 20080517. Archived from the original on 20 May 2008. Retrieved 20080520.
The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2008 to John Griggs Thompson, University of Florida and Jacques Tits, Collège de France. This was announced by the Academy’s President, Ole Didrik Lærum, at a press conference in Oslo today. Thompson and Tits receives the Abel Prize “for their profound achievements in algebra and in particular for shaping modern group theory”.
 ^ "Gruppe 1: Matematiske fag" (in Norwegian). Norwegian Academy of Science and Letters. Archived from the original on 10 November 2013. Retrieved 7 October 2010.
 ^ "J.L. Tits". Royal Netherlands Academy of Arts and Sciences. Archived from the original on 14 February 2016. Retrieved 14 February 2016.
 ^ Curtis, Charles W. (1975). "Review: Buildings of spherical type and finite BNpairs, by Jacques Tits". Bull. Amer. Math. Soc. 81 (4): 652–657. doi:10.1090/s000299041975138080.
External links
 Jacques Tits at the Mathematics Genealogy Project
 O'Connor, John J.; Robertson, Edmund F., "Jacques Tits", MacTutor History of Mathematics archive, University of St Andrews.
 Biography at the Abel Prize site (pdf)
 List of publications at the Université libre de Bruxelles
 1930 births
 Living people
 People from Uccle
 20thcentury French mathematicians
 21stcentury French mathematicians
 Abel Prize laureates
 Belgian expatriates in France
 Belgian mathematicians
 Collège de France faculty
 Free University of Brussels alumni
 Group theorists
 Members of the French Academy of Sciences
 Members of the Norwegian Academy of Science and Letters
 Members of the Royal Netherlands Academy of Arts and Sciences
 Members of the United States National Academy of Sciences
 Nicolas Bourbaki
 Officiers of the Ordre national du Mérite
 University of Bonn faculty
 Wolf Prize in Mathematics laureates