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Warwick Symposium on Ergodic Theory and Dynamical Systems (ETDS) 2010-2011

沃里克历经理论和动力系统研讨会 (ETDS) 2010-2011

基本信息

批准号：
EP/H022171/1
负责人：
Mark Pollicott
金额：
$ 24.22万
依托单位：
University of Warwick
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2010
资助国家：
英国
起止时间：
2010 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FH022171%2F1
关键词：
Warwick Symposium Ergodic Theory Dynamical

项目摘要

This is a proposal for a symposium on to be held during the academic year 2010 - 2011 at the the Mathematics Research Center (MRC), of the University of Warwick. The overall theme of the Symposium is Ergodic Theory and Dynamical Systems , two closely coupled scientific fields within Pure mathematics which are at the forefront of modern scientific research. Broadly speaking, they both deal with the behaviour of orbits of points under iterative applications of transformations on a suitable space, and diverse applications of these basic principles to the global behaviour of the evolution of systems. One might say that Dynamical Systems deals with more global topological aspects and Ergodic Theory deals more with measure theoretic aspects (e.g., typical points). The intimate interaction between these fields is encapsulated in their pairing in the title of the leading international journal Ergodic Theory and Dynamical Systems , based in the Department of Mathematics, at Warwick University.Compared with other fields of mathematics, both Ergodic Theory and Dynamical Systems are relatively young (with perhaps merely a century of development). However, they have not only developed into exciting and active areas in their own right, but they have also provided effective tools in other areas of mathematics - often providing the key to stunning resolutions of long standing conjectures in seeming different fields.This is exemplified by applications of Ergodic Theory to Number Theory, where Margulis' solution of the Oppenheim Conjecture; Furstenberg's proof of the Szemerdi Conjecture; and the Einseidler-Katok-Lindenstrauss approach to the Littlewood Conjecture have all been landmarks in the rapid advancement of this approach.Within the UK, we are fortunate to have a number of individual centres of excellence for both Ergodic Theory and Dynamical Systems, among which Warwick has the longest tradition, and remains a pioneer. Indeed, many of the national leaders in this field were trained at Warwick. For these reasons, Warwick is a natural home to such a symposium - not withstanding Warwick's tradition and experience in hosting symposia over many years.The aim of this symposium is two fold. Firstly to make the greatest possible scientific contribution to the field, drawing upon the talents of both UK and overseas experts of the highest calibre. Secondly, to use this as an opportunity to draw upon the very considerable native talent within this country to support the development of this field in the UK in a unified and coherent way. By promoting greater interaction between the UK research groups we hope to develop a movement which is greater than the sum of its individual parts In practical terms, there will be six constituent workshops, to which will be invited leading international and national experts. To make the symposium as inclusive as possible, and to make the impact as broad as possible, the Warwick based organisers will be assisted by a number of specialist coorganisers for each of the workshops. In addition, there will be a visitor programme and a number of other supporting activities designed to sustain the level of activity throughout the year.The organizers of the symposium (and the Investigators of this proposal) are Mark Pollicott and Sebastian van Strien, both professors at Warwick. They are committed to making this Symposium as effective as possible in supporting and promoting cutting edge research (both nationally and internationally) in Ergodic Theory and Dynamical Systems and the broader mathematical community.

这是一份将于2010 - 2011学年在华威大学数学研究中心（MRC）举行的研讨会的提案。研讨会的总体主题是遍历理论和动力系统，这是纯数学中两个紧密结合的科学领域，处于现代科学研究的前沿。广义地说，它们都处理在适当空间上变换的迭代应用下点的轨道行为，以及这些基本原理在系统演化的全局行为中的各种应用。有人可能会说，动力系统更多地处理全局拓扑方面，而遍历理论更多地处理测量理论方面（例如，典型点）。华威大学数学系的国际领先期刊《遍历理论与动力系统》将这两个领域之间的密切互动结合在一起，并命名为《遍历理论与动力系统》。与数学的其他领域相比，遍历理论和动力系统都相对年轻（可能只有一个世纪的发展）。然而，它们不仅以自己的方式发展成为令人兴奋和活跃的领域，而且还为其他数学领域提供了有效的工具——通常为看似不同领域长期存在的猜想提供了惊人解决的关键。这可以通过遍历理论在数论中的应用来证明，其中马古利斯对奥本海姆猜想的解；Furstenberg对Szemerdi猜想的证明；以及einseidler - katk - lindenstrauss对Littlewood猜想的方法都是该方法快速发展的里程碑。在英国，我们很幸运地拥有许多卓越的遍历理论和动力系统的个人中心，其中华威拥有最悠久的传统，并且仍然是先驱。事实上，这一领域的许多国家领导人都曾在华威接受过培训。出于这些原因，华威大学是举办此类研讨会的天然场所——尽管华威大学多年来一直有举办研讨会的传统和经验。这次研讨会的目的是双重的。首先，尽可能在该领域做出最大的科学贡献，吸收英国和海外最高水平专家的才能。其次，以此为契机，利用国内相当多的本土人才，以统一和连贯的方式支持英国这一领域的发展。通过促进英国研究小组之间更大的互动，我们希望发展一项运动，这比其个别部分的总和更大。实际上，将有六个组成讲习班，将邀请国际和国内领先的专家参加。为了使研讨会尽可能具有包容性，并使影响尽可能广泛，沃里克的组织者将得到每个研讨会的一些专家共同组织者的协助。此外，将有一个访客方案和一些其他支助活动，旨在维持全年的活动水平。研讨会的组织者（以及该提案的调查者）是马克·波利科特和塞巴斯蒂安·范·斯特里恩，他们都是华威大学的教授。他们致力于使本次研讨会尽可能有效地支持和促进遍历理论和动力系统以及更广泛的数学界的前沿研究（无论是国内还是国际）。