一小时邀请报告简介之十八：庞加莱猜想

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一小时邀请报告简介之十八：庞加莱猜想
（转自2006年国际数学家大会官方网站）

Plenary Lecture: Richard Hamilton
The Poincaré Conjecture

The North American mathematician Richard Hamilton will be required to explain very little about the subject of his lecture at the forthcoming International Congress of Mathematicians in Madrid. In it he will deal with results on “Poincaré’s Conjecture”, one of the subjects in mathematics that has been the object of great media interest in recent months.

Whether because of the succulent prize awarded for proof of the conjecture, its one hundred-year history, or the discussion surrounding the proof itself, Poincaré and his conjecture have aroused the interest of experts and lay persons alike. This is unusual to say the least, given the difficulty of the proof and its indirect practical application, since it belongs to an area of mathematics that the uninitiated are wont to classify as “of no use at all”. It is worth repeating again that this is obviously not the case; efforts to find the proof of the conjecture have been the driving force behind research in areas such as geometry and topology, and while it is true that aircraft will not be built on the results, the conjecture has applications in theoretical physics and to relativity in particular. Furthermore, the techniques employed by Grigori Perelman in his proof are related to statistical mechanics.

What is Hamilton’s contribution to the proof of the conjecture? An equation similar to heat transfer has been used to address the demonstration. Heat is propagated, and this behaviour is described by means of an equation known as a "diffusion equation”. The Ricci-Hamilton equation, which derives its name from the American mathematician who will deliver the lecture, is precisely the one used in the proof of the conjecture and can be interpreted as a diffusion equation of the curvature (in reality this is more complicated, although it may serve as a simplification), and would tend to distribute this curvature uniformly in the variety to produce a homogeneous space.

Richard Hamilton was born in 1943. In 1966 he obtained his doctorate at the University of Princeton. He is currently a professor at Columbia University. In 1996 he was awarded the Oswald Veblen Prize by the American Mathematical Society in recognition of his work. He is a member of the American Academy of Arts and Sciences and the National Academy of Sciences.

Speaker: Richard Hamilton
Title: The Poincaré Conjecture
Date: Tuesday, August 22nd:17:15-18:15