一小时邀请报告简介之十四：新问题，新领域

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一小时邀请报告简介之十四：新问题，新领域
（转自2006年国际数学家大会官方网站）

Plenary Lecture: Yakov Eliashberg
New areas for New Questions

Every day on the planet millions of questions are posed. Some people seek their solution with existing tools, while others seek new methods and techniques. Thanks to these new approaches, fresh areas of knowledge arise. One might think that pure mathematics belonged more to the first alternative, where the well-established areas of knowledge leave little room for innovation. But that is not the case; in the 1980s the new discipline of “Symplectic Topology” came into being, a field in which Yakov Eliashberg is an expert. Eliashberg will give a lecture on this subject at the forthcoming ICM2006 International Congress of Mathematicians in Madrid.

In 1911, Poincaré posed the first problem associated with this new mathematical discipline, but it was not until the 1980s that the work of various mathematicians give impetus to symplectic topology.

As professor Eliashberg explains, “symplectic topology took shape as a result of the attempt to answer some qualitative questions that appeared in classical mechanics and in optics”. Together with two colleagues, Givental and Hofer, this mathematician from Stanford University is responsible for the symplectic field theory, a new approach to the Gromov-Witten calculus of invariants, which form the basis of the discipline. Symplectic Field Theory “is a wide-ranging project, and while it has yielded results and new applications, it is by no means complete”, adds Yakov Eliashberg, who goes on to outline the project itself: “The idea is to study how a holomorphic curve behaves when a type of nonlinear variety is divided into small pieces, and to try to reconstruct the whole puzzle with non-elemental pieces”.

Yakov Eliashberg was born in Leningrad in 1946. He studied mathematics in his native city, where he obtained his doctorate in 1972. He continued working in the former Soviet Union until 1987, and one year later moved to the United States. Since 1989 he has been a professor at Stanford University. In 1973 he was awarded the Leningrad Mathematical Society Prize, and more recently, in 2001, he was awarded the Veblen Prize from the American Mathematical Society in recognition of his work. He has been a member of the USA Academy of Sciences since 2003.

Speaker: Yakov Eliashberg
Title: Symplectic Field Theory and its Applications
Date: Wednesday, August 30th: 10:15-11:15

ICM2006 Scientific Programme：http://www.icm2006.org/scientificprogram/plenarylectures/
（转自2006年国际数学家大会官方网站）