Professor at the College de France, where he occupied the Chair from 1973 to 1999, he had received the prestigious Abel Prize in 2008. He died on December 5, at the age of 91.
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The immense work of the mathematician Jacques Tits, dead on December 5, in Paris, at the age of 91, deeply transformed the geometry to the XX e century. Born on August 12, 1930 in Uccle (Belgium), this child prodigy supports a doctorate in Brussels at the age of 20. After a passage in Germany, he made the essence of his career at the College de France, where he held the Chair theory of groups from 1973 to 1999. Among the many awards he received, we can mention the Wolf Award. in 1993 and the Abel Prize in 2008.
The concept of groups is central in contemporary mathematics. Has Henri Poincaré not affirmed that “mathematics are just a history of groups”? Here’s how Jacques Tits described his research theme in the introduction of the notice presenting his work at the Academy of Sciences: “The theory of groups can be summarily defined as a theory of symmetry, indiscernability and the homogeneity; the link between these notions is clear: an object has some symmetry if different angles of view give indistinguishable images, a medium is homogeneous if its points are indistinguishable. The idea already appears in the Greek mathematics where the figures High degree of symmetry play a vital role. “
He geometrized the algebra
Tits has dedicated his scientific life to a long reflection around the symmetries in a very general sense. The groups appeared in science at the beginning of the XIX e century thanks to the imagination of Galois Evarist. It was then purely algebraic ideas: we manipulated equations and we were looking for symmetries. Towards the end of the century, Felix Klein publishes his “Erlangen program”, which states that the study of geometry returns to that of the groups. Geometry was thus infected with algebra. Jacques Tits works in the other direction: he geged the algebra.
To realize his program, he invented what is now called “title buildings”, which are geometric objects that embody the algebraic groups. It must be said that mathematicians often use words that have very little relationship with the meaning they are given in the current language, which often contributes to the fact that we do not understand them. These title buildings have apartments, rooms and walls, but the analogy stops there because a room can be located both in two different apartments.
In fact, the terminology originally offered by Tits was very bad: there were cemeteries, ossuaries and skeletons! And yet its buildings are concrete, made up of segments, triangles or tetrahedra assembled between them, in the manner of the polyhedra of Plato. On the occasion of a symposium in his honor, in 2000, he explained that he preferred “palpable” mathematics, which could surprise a neophyte who might be to read one of his articles. By caricaturing to the extreme, we can indeed say that algebra is the field of abstraction while the geometry deals with more manipulable objects. Geometers and algebrans have very different approaches to mathematical activity. Jacques Tits was above all a surveyor. He who was always joking and a good mood had shot me with a black look a day when I had dared to suggest that he was also an algebraist.
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