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# Jacques Tits

Jacques Tits (born 12 August 1930 in Uccle) is a Belgian and French mathematician who received his doctorate in mathematics at the age of 20. He has written or cowritten many papers on a number of subjects, principally group theory.

Career

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, and 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 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.”[2] He is a member of several Academies of Sciences.

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. 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 F. 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 is named after him.

References

1. ^ Siobhan Roberts, "Donald Coxeter: The man who saved geometry", Toronto Life, January 2003

2. ^ "Thompson and Tits share the Abel Prize for 2008". The Niels Henrik Abel Memorial Fund. 2008-05-17. Archived from the original on 2008-05-20. http://www.webcitation.org/5XxtY4s3z. Retrieved 2008-05-20. "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”."

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, http://www-history.mcs.st-andrews.ac.uk/Biographies/Tits.html .

* Biography at the Abel Prize site (pdf)

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