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

研讨会：有限群的代数结构；

• 批准号: EP/F056125/1
• 负责人: Yiftach Barnea
• 金额: $ 1.8万
• 依托单位: Royal Holloway University of London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2008
• 资助国家: 英国
• 起止时间: 2008 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FF056125%2F1
• 关键词: WORKSHOP; Algebraic; Structure; Profinite; Groups

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.

该提案的目的是双重的。首先，我们希望于 2008 年 4 月在伦敦大学皇家霍洛威学院举办为期两天的“有限群代数结构”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）对研讨会进行为期两周的研究访问。数学对象的对称性，例如正方形或正方形 立方体，形成称为群的代数结构。渐近群论涉及某些群序列的性质。每个涉及的组的大小都是有限的，但随着顺序的进展，它们的大小会变得越来越大。有限群是一种在单个对象中捕获此类序列的方法。这使得人们可以通过研究一个对象来研究构成序列的群体的渐近行为。有限群的研究构成了数学中非常活跃的研究领域。该领域的重大问题之一是由著名数学家 Jean-Pierre Serre 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，Nikolay Nikolov 博士（帝国理工学院）和 Dan Segal 教授（牛津大学）才出色地解决了这个问题。我们提议举办一个研讨会，调查与塞尔问题及其解决方案相关的可能的进一步研究。本次会议的演讲者包括 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。 Barnea 博士和 Klopsch 博士这两位研究人员此前都曾与 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，我们建议抓住这次机会，将Jaikin-Zapirain教授的访问期限延长至两周。