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

这一建议的目的是双重的。首先，我们想于2008年4月在伦敦大学皇家霍洛威学院组织一个为期两天的关于“无限群的代数结构”的研讨会。其次，我们希望支持我们的主要发言人之一Andrei Jaikin-Zapirain教授（马德里）在研讨会期间进行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。渐近群论研究群的某些序列的性质。所涉及的每个群体都有有限的规模，但随着序列的进展，它们的规模变得越来越大。无限群是在单个对象中捕获这样一个序列的一种方法。这允许人们通过研究一个对象来研究组成序列的群的渐近行为。无穷群的研究是数学中一个非常活跃的研究领域。著名数学家让-皮埃尔·塞尔（Jean-Pierre Serre）在20世纪60年代提出了该领域的一个重大问题。这个问题被解决了将近40年。直到最近，Nikolay Nikolov博士（帝国理工大学）和Dan Segal教授（牛津大学）才出色地解决了这个问题。我们建议举办一个研讨会，探讨与Serre的问题及其解决方案相关的可能的进一步研究。本次会议的主讲人将包括Nikolov博士和Segal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。巴尔内亚博士和克洛普施博士都曾与贾金-扎皮兰教授合作过。他的访问将使三位研究人员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教授的访问延长至两周。

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.