WORKSHOP: The Algebraic Structure of Profinite Groups; Visitor: Dr. A. Jaikin-Zaprain

这项提议的目的有两个。首先，我们想于2008年4月在伦敦大学皇家霍洛威举办一个为期两天的研讨会，主题是“泛函群的代数结构”。其次，我们想支持--与研讨会有关--我们的主要演讲人之一Andrei Jaikin-Zapirain教授为期两周的研究访问。数学对象的对称性，如正方形或立方体，形成称为群的代数结构。渐近群论主要研究某些群序列的性质。每个涉及的基团都有有限的大小，但随着序列的进展，它们的大小变得越来越大。无限群是一种在单个物体中捕捉这样的序列的方法。这使得人们可以通过研究一个对象来研究组成序列的群的渐近行为。原限群的研究是数学中一个非常活跃的研究领域。该领域的一个大问题是由著名数学家让-皮埃尔·瑟尔在20世纪60年代提出的。这个问题近40年来一直没有得到解决。直到最近，尼古拉·尼古洛夫博士(帝国)和丹·西格尔教授(牛津)才出色地解决了这个问题。我们提议举办一个研讨会，调查与Serre问题及其解决方案相关的进一步研究。本次会议的演讲者将包括尼科洛夫博士和西格尔教授以及Jaikin-Zapirain教授。他是这一特定数学领域的国际领先研究人员之一。两位研究人员，巴尼亚博士和Klopsch博士，之前都与Jaikin-Zapirain教授合作过。他的访问将使三位研究人员能够启动新的联合研究项目。为了实现这一目标，我们建议抓住机会，将Jaikin-Zapirain教授的访问延长到两周。

The aim of this proposal is twofold. Firstly, we want to organize a two-day workshop on ``The Algebraic Structure of Profinite Groups'' at Royal Holloway, University of London, in April 2008. Secondly, we want to support -- in connection with the workshop -- a two-week research visit of Prof. Andrei Jaikin-Zapirain (Madrid), one of our key speakers.The symmetries of a mathematical object, like a square or a cube, form an algebraic structure which is called a group. Asymptotic group theory is concerned with the properties of certain sequences of groups. The groups involved each have finite size but their sizes become larger and larger as one progresses along the sequence. A profinite group is a way to capture such a sequence in a single object. This allows one to study the asymptotic behaviour of the groups which make up the sequence by studying one object. The study of profinite groups constitutes a very active research area in mathematics. One of the big problems in that area was suggested by the famous mathematician Jean-Pierre Serre in the 1960s. This problem was unsolved for nearly 40 years. Only recently it has being resolved brilliantly by Dr. Nikolay Nikolov (Imperial) and Prof. Dan Segal (Oxford). We propose a workshop that will investigate possible further research related to Serre's problem and its solution.The speakers in this conference will include Dr. Nikolov and Prof. Segal as well as Prof. Jaikin-Zapirain. He is one of the internationally leading researchers in this particular mathematical area. Both investigators, Dr. Barnea and Dr. Klopsch, previously collaborated with Prof. Jaikin-Zapirain. His visit will enable the three researchers to initiate new joint research projects. In order to achieve that we propose to seize the opportunity and extend Prof. Jaikin-Zapirain's visit to two weeks.