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Asymptotic Group Theory and Model Theory - a two-day workshop

渐近群理论和模型理论 - 为期两天的研讨会

基本信息

批准号：
EP/J021113/1
负责人：
Benjamin Klopsch
金额：
$ 1.65万
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：
2012
资助国家：
英国
起止时间：
2012 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FJ021113%2F1
关键词：
Asymptotic Group Theory Model two

项目摘要

The aim of this proposal is twofold. Firstly, we want to organise a two-day international workshop on "Asymptotic Group Theory and Model Theory" at Royal Holloway, University of London, in March 2012. Secondly, we want to support a six-day research visit - including the two days of the workshop - of Uri Onn (University of the Negev) and Christopher Voll (University of Bielefeld). Voll is co-organiser of the workshop and Onn one of the key speakers.The symmetries of a mathematical, physical or chemical object - such as a graph, a molecule or a crystal - form an algebraic structure called a group. The study of finite groups led to one of the most striking achievements of 20th century mathematics: the classification of all finite simple groups. An important tool is to investigate groups by means of their linear representations, i.e. by their images as matrix groups. Asymptotic group theory, which is aimed at understanding finite and infinite groups alike, is concerned with the asymptotic properties of certain arithmetic invariants of groups. A classical direction in this comparatively young area of group theory is the study of word growth, made famous by groundbreaking work of Gromov. In another direction, the theory of representation growth, one studies infinite groups by investigating the distribution of their finite dimensional linear representations. `Zeta functions of groups' - certain infinite series which give rise to complex functions are used for encoding the arithmetic of associated growth sequences. They have proved powerful tools in developing the theory. Over the last decades asymptotic and geometric group theory have very much benefited from the influx of techniques which come from an area of mathematical logic called model theory. Conversely, concrete problems in algebra and other classical areas, such as geometry and number theory, have stimulated important, more general model-theoretic advances. These techniques and results will form the main point of focus of the workshop, with an emphasis on three concrete topics, which can be described by the keywords: approximate groups, limit groups and motivic integration.We envisage that the workshop will bring together researchers with quite distinct backgrounds in group theory, model theory and cognate disciplines. The meeting will allow the participants to exchange ideas and tools in rapidly expanding areas at the interface of group theory and model theory, and to learn from one another. The workshop will form part of the `South England Profinite Groups Meetings', organised by a group of mathematicians who share an interest in profinite groups. They hold about three meetings per year, dedicated to research topics of particular interest which are presented at an accessible level to younger researchers like PhD students and postdocs. The workshop is designed to be of particular benefit to younger mathematicians whose primary background is in group theory. We have deliberately chosen to invite speakers of varied research backgrounds to draw a wide picture of the relevant material.Two participants of the meeting, Onn and Voll, will stay for four extra days to work with the investigator. The aim of their visit will be to draw immediate benefits from the workshop in ongoing joint projects on representation zeta functions of groups and the planning of further research collaborations.

这项建议有两个目的。首先，我们想在2012年3月在伦敦大学皇家霍洛威学院举办一个为期两天的“渐近群理论和模型理论”国际研讨会。其次，我们希望支持Uri Onn（内盖夫大学）和Christopher Voll（比勒费尔德大学）为期六天的研究访问-包括两天的研讨会。Voll是研讨会的共同组织者，Onn也是主要发言人之一。数学、物理或化学对象的对称性--如图形、分子或晶体--形成了一种称为群的代数结构。对有限群的研究导致了20世纪世纪数学中最引人注目的成就之一：所有有限单群的分类。一个重要的工具是通过它们的线性表示来研究群，即通过它们作为矩阵群的图像。渐近群论，旨在理解有限和无限群一样，关注的是某些算术不变量的群的渐近性质。在这个相对年轻的群论领域中，一个经典的方向是研究词的增长，这是由格罗莫夫的开创性工作而闻名的。在另一个方向，表示增长理论，人们通过研究无限群的有限维线性表示的分布来研究它们。“群的Zeta函数”-产生复杂函数的某些无穷级数用于编码相关增长序列的算术。他们已证明是发展这一理论的有力工具。在过去的几十年中，渐近和几何群论非常受益于大量涌入的技术，这些技术来自数理逻辑的一个领域，称为模型论。相反，代数和其他经典领域的具体问题，如几何和数论，已经刺激了重要的，更普遍的模型理论的进展。这些技术和结果将成为研讨会的重点，重点放在三个具体的主题上，这些主题可以用关键词来描述：近似群，极限群和动机整合。我们设想研讨会将汇集具有群论，模型论和同源学科背景的研究人员。会议将允许与会者在群论和模型论的界面上迅速扩展的领域中交流思想和工具，并相互学习。该研讨会将成为“南英格兰Profinite群会议”的一部分，由一群数学家组织，他们对profinite群感兴趣。他们每年举行大约三次会议，专门讨论特别感兴趣的研究课题，这些课题以博士生和博士后等年轻研究人员可以接受的水平提出。讲习班的目的是特别有利于年轻的数学家的主要背景是在群论。我们特意邀请了具有不同研究背景的演讲者，以便对相关材料进行广泛的了解。会议的两位参与者Onn和Voll将与研究人员一起工作四天。他们访问的目的是从讲习班中立即受益于正在进行的关于群体的代表性zeta功能和进一步研究合作的规划的联合项目。