The Abel of Mathematics Award was awarded, Wednesday, March 23, to the American Dennis Sullivan, 81, “for its revolutionary contributions to topology in its broadest sense, and in particular in its algebraic aspects, geometric And dynamic, “announced the Norwegian Academy of Science and Letters. While the Fields medal is attributed to a mathematician under 40, the Abel Prize is closer to the Nobel Prize (nonexistent in mathematics) and rewards the entire career.
Towards the end of the XVII e century, Leibniz dreamed of manipulating forms, in the manner of the abstract symbols of algebra. He gave the name of Analysis situated to this theory, that he will not be able to develop and which will only be set up only at the end of the XIX e century, by Henri Poincaré. In this theory, now called topology, it is considered that the surface of a sphere is equivalent to that of a cube, because one can deform one in the other, if they imagine made of rubber . On the other hand, the sphere is not equivalent to an air chamber. Curves are studied, surfaces and more generally more complicated “varieties” in any dimensions. Among the major contributions of Sullivan, one can mention its theory of rational homotopy, which makes it possible to understand the topological structure of varieties by associating them with objects of algebraic nature, that one can in principle calculate, realizing somehow the dream the dream of Leibniz.
unsuspected gateways
Sullivan effortlessly passes from one chapter of mathematics to another and discovers unsuspected gateways that lead him to entirely new points of view. For example, it establishes a “dictionary” between two theories that we believed independent (Kleinian groups and holomorphic dynamics). It is then sufficient to translate a theorem from one to obtain the solution of a significant problem in the other, which has resisted, however, for almost seventy years (the non-wandering domain theorem). It is neither geometer nor topologist nor algebracted nor analyst: he is a little all that at a time. Very few mathematicians have such a sharp sense of the deep unit of mathematics. In recent years, he has been trying to export his topological ideas in a major fluid dynamics problem. The experts are not (still) convinced, but it may lead to resounding success.
It is also by his exceptional charism that Sullivan is remarkable. It has been a hub for many years in the mathematical community. Always surrounded by very diverse researchers, especially very young, it has an incredible ability to listen, sharing, motivation and encouragement. It is the opposite of the image of Epinal of the solitary mathematician. When he was a professor at the IHES, Bures-sur-Yvette (Essone), it was necessary to see him at the time of tea put in touch with mathematicians of all stripes and all ages who did not know each other, in all simplicity. His seminar in New York is very busy and has nothing to do with a traditional presentation: the questions fuse on all sides and the speaker must be prepared to speak for many hours until the general depletion. It is one of the first to have registered these seminars on VHS video cassettes, from the early 1980s. These are collectors today.
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