2006国际数学家大会一小时邀请报告摘要简介之二

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2006国际数学家大会一小时邀请报告摘要简介之二

2006-7-12  [国际数学动态]
2006国际数学家大会一小时邀请报告摘要简介之二
一小时邀请报告简介之二：空中的纽结
（转自2006年国际数学家大会官方网站）
Plenary Lecture: Étienne Ghys
Knots in the Air
“When a fluid moves in a recipient, each particle follows a trajectory, which forms a curve in the space. Sometimes it happens that this curve closes, and that is when a knot is created”. In this way Étienne Ghys seeks to provide a graphic description of the mathematical element that is the subject of his lecture, Knots and Dynamics.
However, he is quick to point out that it is “only an analogy”, since Ghys field of study is more abstract. Nevertheless, he believes that these kinds of ideas provide a clue toward explaining how three-dimensional dynamical systems could be studied by observing the characteristics of their trajectories. Ghys’ field of study is a combination of topology, geometry, dynamical systems and group theory.
The periodic orbits define knots whose topology can sometimes be extremely complicated. In his lecture, Ghys will show some advances in the quantitative and qualitative description of this type of phenomena. The French mathematician will divide the lecture into three parts. In the first two he will focus on the characteristics of the trajectories, and end by describing an important example of the geodesic flow on the modular surface, where the linking between geodesics turns out to be related to well-known arithmetical functions.
Étienne Ghys was born in 1954 in Lille (France). He graduated in mathematics from the university of his home town in 1979. He is at present "Directeur de Rechercher du CNRS" at l';École Normale Supérieure in Lyon, and since 2005 has been a member of the Academy of Sciences in Paris. He gave one of the invited lectures at the International Congress in Kyoto in 1990. In 1991 he was awarded the silver medal of the French National Centre for Research (CNRS).
Speaker: Étienne Ghys
Title: Knots and Dynamics
Date: Thursday, August 24th. 11:45-12:45
ICM2006 Scientific Programme: http://www.icm2006.org/scientificprogram/plenarylectures