2017-03-27  

2017-03-22 何其乐 和乐数学

法国数学家Yves Meyer因在小波的数学理论方面的贡献获2017年Abel奖。小波可以用于图像处理等领域。

The Abel Prize Laureate 2017

The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2017 to Yves Meyer of the école normale supérieure Paris-Saclay, France

“for his pivotal role in the development of the mathematical theory of wavelets.”

陶哲轩在其博客也公布了这个消息。陶哲轩说他正在奥斯陆。他撰文介绍了Meyer的工作。其中提到一个有趣而简单的知识。

我们知道斐波那契数列，1, 1, 2, 3, 5, 8, . . .。这个数列很简单，但却在纯数学中经常出现。这个数列的每一项与其前项之比1/1, 2/1, 3/2, 5/3, 8/5, . . .及其快速收敛到黄金分割数 φ = 1+√ 5 2 = 1.61803。这个数也不简单，其各次幂 φ, φ^2 , φ^3 , . . . 出乎意料地逼近整数,例如 φ^11 = 199.005，非常接近199。Meyer的一项工作就是研究有此类特殊性质的数，即所谓的 Pisot 数。

Meyer还研究过奇异积分。

陶哲轩还特别提到另一位数学家，美国杜克大学客座教授英格丽·多贝西（Ingrid daubechies）是国际数学联盟会长，也是有史以来的首任女性会长。

她是《小波十讲》的作者，也对小波理论有重要贡献。

原著《小波十讲》因杰出贡献和优美风格荣获1994年Leroy P.Steele奖。该书印数超过15000册，风行全世界，这在学术著作中是极为罕见的。

“该书原作者Daubechies是小波分析理论的主要创始人之一，书中用精辟的语言描述了小波分析的主要原理和方法，可作为小波课程的精读教材。该书读起来极为有趣，如同阅读一本优秀的俄罗斯长篇小说。Daubechies十分巧妙地组织素材，在许多地方给出说明和注释，有效化解难点。本书可满足个人阅读及大学生、研究生、大学教师、科研人员等多方面的需求，并将成为经典读物。”

然而，因为她曾作为数学联盟的主席提名了阿贝尔奖委员会，因而避嫌没能分得此荣誉。因此，陶认为，阿贝尔奖不应该被视为对贡献大小的评价。

陶哲轩在其博客的原文：

Just a short post to note that Norwegian Academy of Science and Letters has just announced that the 2017 Abel prize has been awarded to Yves Meyer, “for his pivotal role in the development of the mathematical theory of wavelets”. The actual prize ceremony will be at Oslo in May.

I am actually in Oslo myself currently, having just presented Meyer’s work at the announcement ceremony (and also having written a brief description of some of his work). The Abel prize has a somewhat unintuitive (and occasionally misunderstood) arrangement in which the presenter of the work of the prize is selected independently of the winner of the prize (I think in part so that the choice of presenter gives no clues as to the identity of the laureate). In particular, like other presenters before me (which in recent years have included Timothy Gowers, Jordan Ellenberg, and Alex Bellos), I agreed to present the laureate’s work before knowing who the laureate was! But in this case the task was very easy, because Meyer’s areas of (both pure and applied) harmonic analysis and PDE fell rather squarely within my own area of expertise. (I had previously written about some other work of Meyer in this blog post.) Indeed I had learned about Meyer’s wavelet constructions as a graduate student while taking a course from Ingrid Daubechies. Daubechies also made extremely important contributions to the theory of wavelets, but my understanding is that due to a conflict of interest arising from Daubechies’ presidency of the International Mathematical Union (which nominates members of the Abel prize committee) from 2011 to 2014, she was not eligible for the prize this year, and so I do not think this prize should be necessarily construed as a judgement on the relative contributions of Meyer and Daubechies to this field. (In any case I fully agree with the Abel prize committee’s citation of Meyer’s pivotal role in the development of the theory of wavelets.)