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.

这是在2010年至2011年在沃里克大学的数学研究中心（MRC）举行的一项研讨会的建议。研讨会的总体主题是厄贡理论和动力学系统，这是纯数学中的两个紧密耦合的科学领域，这是现代科学研究的最前沿。从广义上讲，他们俩都涉及转换在合适的空间上的迭代应用下的轨道行为，以及这些基本原理在系统演变的全球行为上的各种应用。有人可能会说，动态系统涉及更全球的拓扑方面，而千古理论则更多地涉及度量理论方面（例如，典型要点）。这些领域之间的亲密互动被封装在基于数学系的领先国际杂志的厄尔贡理论和动态系统的标题中相对年轻（也许只是一个世纪的发展）。但是，他们不仅自己拥有自己的精神和活跃的领域，而且还提供了数学其他领域的有效工具 - 通常为在看似不同的领域中长期持久猜想的令人惊叹的决议提供了关键。这是一个例证。千古理论在数字理论上的应用，其中马古利斯对oppenheim猜想的解决方案； Furstenberg的Szemerdi猜想证明； Einseidler-katok-Lindenstrauss对利特伍德的猜想的方法都是这种方法的快速发展。沃里克（Warwick）拥有最长的传统，并且仍然是先驱。确实，该领域的许多国家领导人都接受了沃里克的培训。由于这些原因，沃里克（Warwick）是这样一个专题讨论会的自然之家 - 尽管沃里克（Warwick）在主持研讨会上的传统和经验并没有多年。首先，要借鉴英国和最高口径的海外专家的才能，为该领域做出最大的科学贡献。其次，以此为机会借此机会利用该国众多的土著人才以统一和连贯的方式支持英国的这一领域的发展。通过促进英国研究小组之间的更大互动，我们希望开发一项比实际零件总和更大的运动，将有六个组成的研讨会，将邀请国际和国家专家领先。为了使专题讨论会尽可能包容性，并尽可能广泛地影响，为每个研讨会的许多专业熟练组织提供了帮助的组织者。此外，还将有一个访问者计划和许多其他辅助活动，旨在维持全年的活动水平。在沃里克。他们致力于使本次研讨会在阵亡理论和动力学系统以及更广泛的数学社区中支持和促进前沿研究（无论是在国内外）的尖端研究（无论是在国内还是国际上）。