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

这是一个研讨会的建议，将于2010 - 2011学年在数学研究中心（MRC），沃里克大学举行。研讨会的总体主题是遍历理论和动力系统，两个密切耦合的科学领域内纯数学是在现代科学研究的前沿。从广义上说，他们都处理的行为轨道的点下迭代应用的变换在一个合适的空间，和不同的应用程序，这些基本原则的全球行为的演变系统。有人可能会说，动力系统处理更多的全球拓扑方面和遍历理论处理更多的测度理论方面（例如，典型点）。这两个领域之间的密切互动被封装在他们的配对在领先的国际期刊遍历理论和动力系统的标题，总部设在数学系，在沃里克大学。与其他数学领域相比，遍历理论和动力系统都相对年轻（也许只有世纪的发展）。然而，它们不仅发展成为令人兴奋和活跃的领域，而且还在其他数学领域提供了有效的工具-通常为似乎不同领域的长期存在的问题提供了惊人的解决方案。在英国，我们很幸运地拥有许多研究遍历理论和动力系统的中心，其中沃里克的研究历史最悠久，并且仍然是先驱。事实上，这个领域的许多国家领导人都是在沃里克接受培训的。由于这些原因，沃里克是一个自然的家庭这样一个研讨会-尽管沃里克的传统和经验，主办研讨会多年。首先，尽可能为该领域做出最大的科学贡献，利用英国和海外最高水平专家的才能。第二，利用这一机会，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，我们希望发展一个运动，这是大于其个别部分的总和在实践中，将有六个组成讲习班，将邀请国际和国内领先的专家。为了使研讨会尽可能具有包容性，并使影响尽可能广泛，沃里克的组织者将在每个研讨会上得到一些专家合作组织者的协助。此外，还将有一个参观者方案和一些其他支助活动，目的是保持全年的活动水平。研讨会的组织者（和本建议的调查员）是马克波利科特和塞巴斯蒂安货车斯特里恩，都在沃里克教授。他们致力于使本次研讨会尽可能有效地支持和促进尖端研究（国内和国际）在遍历理论和动力系统和更广泛的数学界。

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.