Jacques Tits | |
|---|---|
_(cropped).jpg) Tits in 2008 | |
| Born | (1930-08-12)12 August 1930 Uccle, Belgium |
| Died | 5 December 2021(2021-12-05) (aged 91) 13th arrondissement, Paris, France |
| Citizenship | Belgian (1930–1974) French (since 1974) |
| Education | Free University of Brussels |
| Known for | Tits alternative Tits building Tits cone Tits group Tits index Tits metric Tits systems Bruhat–Tits fixed point theorem Freudenthal–Tits magic square Kantor–Koecher–Tits construction Artin-Tits group Kneser–Tits conjecture Field with one element Generalized polygon |
| Awards | Francois Deruyts Prize(1962) Wolf Prize(1993) Pour le Mérite(1995) Cantor medal(1996) Abel Prize(2008) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Free University of Brussels Vrije Universiteit Brussel University of Bonn Collège de France French Academy of Sciences |
| Thesis | Généralisation des groupes projectifs basés sur la notion de transitivité (1950) |
| Doctoral advisor | Paul Libois |
| Doctoral students | Francis Buekenhout Jens Carsten Jantzen Karl-Otto Stöhr |
Jacques Tits (French:[ʒaktits]) (12 August 1930 – 5 December 2021) was a Belgian-born French mathematician who worked ongroup theory andincidence geometry. He introducedTits buildings, theTits alternative, theTits group, and theTits metric.
Tits was born inUccle, Belgium to Léon Tits, a professor, and Lousia André. Jacques attended the Athénée of Uccle and theFree University of Brussels. His thesis advisor wasPaul Libois [fr], and Tits graduated with his doctorate in 1950 with the dissertationGénéralisation des groupes projectifs basés sur la notion de transitivité.[1]
Tits held professorships at the Free University of Brussels (now split into theUniversité libre de Bruxelles and theVrije Universiteit Brussel) (1962–1964), theUniversity of Bonn (1964–1974) and theCollège de France in Paris, until becomingemeritus 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. BecauseBelgian nationality law did not allowdual nationality at the time, herenounced his Belgian citizenship.[1]
Tits was an "honorary" member of theNicolas Bourbaki group; as such, he helped popularizeH.S.M. Coxeter's work, introducing terms such asCoxeter number,Coxeter group, andCoxeter graph.[2]
Tits died on 5 December 2021, at the age of 91[1] in the13th arrondissement, Paris.[3]
Tits received theWolf Prize in Mathematics in 1993, theCantor Medal from theDeutsche Mathematiker-Vereinigung (German Mathematical Society) in 1996, and the German distinction "Pour le Mérite". In 2008 he was awarded theAbel Prize, along withJohn Griggs Thompson, "for their profound achievements in algebra and in particular for shaping modern group theory".[4]
Tits became a member of theFrench Academy of Sciences in 1979.[1] He was a member of theNorwegian Academy of Science and Letters.[5] He became a foreign member of theRoyal Netherlands Academy of Arts and Sciences in 1988.[6]
He introduced the theory ofbuildings (sometimes known asTits buildings), which are combinatorial structures on which groups act, particularly inalgebraic group theory (includingfinite groups, and groups defined over thep-adic numbers). The related theory of(B, N) pairs is a basic tool in the theory ofgroups of Lie type. Of particular importance is his classification of all irreducible buildings of spherical type and rank at least three, which involved classifying allpolar 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 withMark Ronan he constructed those of rank at least four independently, yielding the groups directly. In the rank-2 case spherical building aregeneralized n-gons, and in joint work with Richard Weiss he classified these when they admit a suitable group of symmetries (the so-calledMoufang polygons). In collaboration withFrançois Bruhat he developed the theory of affine buildings, and later he classified all irreducible buildings of affine type and rank at least four.[7]
Another of his well-known theorems is the "Tits alternative": ifG is afinitely generatedsubgroup of alinear group, then eitherG has asolvable subgroup offinite index or it has afree subgroup of rank 2.[8]
TheTits group and theKantor–Koecher–Tits construction are named after him. He introduced theKneser–Tits conjecture.[9][10]
