EPSRC-Warwick Symposium on Geometry, Topology and Dynamics in Low Dimensions

EPSRC-Warwick 低维几何、拓扑和动力学研讨会

• 批准号: EP/N034023/1
• 负责人: Brian Bowditch
• 金额: $ 23.28万
• 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: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FN034023%2F1
• 关键词: EPSRC; Warwick; Symposium; Geometry; Topology

The EPSRC-Warwick Symposium has met every year for the past fifty years to advance the state of mathematics in the UK. Each symposium concentrates on a particular theme; in 2017-2018 the topic will be "Geometry, topology and dynamics in low dimensions". We will hold seven workshops where experts from the UK and around the world will gather at the University of Warwick to discuss their researches and to propose new research directions. In addition to this, we will host a number of distinguished international long-term visitors who will also visit other UK universities. We will also organise a number of lectures aimed at the public.Basic geometric concepts such as length, angle, area and volume are familiar to most from high school mathematics. In modern research mathematics these notions have evolved a great deal, considerably widening the range of problems which geometry can help to solve. Increasingly exotic geometric structures have appeared; for example, the idea that space has some sort of intrinsic "curvature" instead of being totally flat is key to Einstein's view of the universe, and the notion of infinite "self-similarity" gives rise to spectacular fractal images. Exotic geometric structures often arise in unexpected situations which do not immediately appear to be related to geometry, and they reflect the presence of deeper underlying structures.Topology is a subject developed in the twentieth century. It is an offshoot of geometry, but offers different perspectives and different tools. The basic objects it studies are curves, surfaces and higher dimensional spaces focusing on the question of when one such can be continuously deformed into another. For example, the question of whether a knot in a closed loop of string can be untied without cutting the string is a topological question.This symposium brings together top researchers with diverse backgrounds to offer their perspectives on recent developments, advance their research, and consolidate the UK as a hub for mathematical research in this important and internationally active field.The field of dynamical systems is the study of the long-term behaviour of mathematical models of systems which change over time, such as physical systems or biological phenomena. Some of the mathematical models are simple, such as that which describes the motion of a billiard ball on a billiard table, and some are extremely complex, such as the motion of satellites in the solar system or the weather patterns.There are many deep, non-obvious links between the fields of geometry, topology and dynamics. These were first brought to light by the mathematician Poincare in the early twentieth century and have been studied intensely ever since. This symposium will build on and further develop these connections in order to make advances in all three areas. The symposium will focus on low-dimensional phenomena, especially those which occur in dimension one, two and three. There has been spectacular progress in the last decade on understanding such phenomena. For example, in mathematics, an important question raised by Poincare about the topology of 3 dimensional objects has only recently been resolved. In physics fascinating new mathematical conjectures have been raised about surfaces (and other spaces) in the context of string theory which is a new approach to understanding basic laws of physics.This symposium brings together top researchers with diverse backgrounds to offer their perspectives on recent developments, advance their research, and consolidate the UK as a hub for mathematical research in this important and internationally active field.

在过去的50年里，EPSRC-Warwick研讨会每年都举行会议，以推动英国的数学状况。每个专题讨论会都集中讨论一个特定的主题；2017-2018年的主题将是“低维的几何、拓扑和动力学”。我们将举办七个研讨会，来自英国和世界各地的专家将聚集在华威大学讨论他们的研究并提出新的研究方向。除此之外，我们还将接待一批杰出的国际长期访客，他们还将参观英国其他大学。我们还将组织一些针对公众的讲座。长度、角度、面积和体积等基本几何概念是高中数学中最熟悉的概念。在现代研究数学中，这些概念有了很大的发展，大大拓宽了几何学可以帮助解决的问题的范围。越来越奇异的几何结构已经出现；例如，爱因斯坦宇宙观的关键是空间具有某种内在的“曲率”，而不是完全平坦的，无限“自相似”的概念产生了壮观的分形图。奇异的几何结构经常出现在意想不到的情况下，这些情况看起来并不直接与几何有关，它们反映了更深层次的潜在结构的存在。拓扑学是20世纪发展起来的一门学科。它是几何学的一个分支，但提供了不同的视角和不同的工具。它研究的基本对象是曲线、曲面和高维空间，重点是一个这样的空间何时可以连续变形成另一个的问题。例如，一个闭合的绳环中的一个结是否可以在不切断绳子的情况下解开的问题是一个拓扑问题。这次研讨会聚集了具有不同背景的顶尖研究人员，就最近的发展提出他们的观点，推进他们的研究，并巩固英国作为这个重要的国际活跃领域的数学研究中心的地位。动力系统领域是研究随着时间变化的系统的数学模型的长期行为，如物理系统或生物现象。数学模型有的简单，如描述台球在台球桌上的运动，有的极其复杂，如卫星在太阳系中的运动或天气模式，几何、拓扑和动力学领域之间有许多深刻而不明显的联系。这些最早是由数学家庞加莱在二十世纪初发现的，从那时起人们就一直在对它们进行深入研究。这次研讨会将在这些联系的基础上进一步发展，以便在这三个领域取得进展。研讨会将集中讨论低维现象，特别是那些发生在一维、二维和三维的现象。在过去的十年里，在理解这种现象方面取得了令人瞩目的进展。例如，在数学中，庞加莱提出的关于三维物体拓扑的一个重要问题直到最近才得到解决。在物理学中，在弦理论的背景下提出了关于表面(和其他空间)的引人入胜的新的数学猜想，弦理论是理解物理基本定律的一种新方法。这次研讨会聚集了具有不同背景的顶尖研究人员，就最近的发展提供他们的观点，推进他们的研究，并巩固英国作为这一重要和国际活跃领域的数学研究中心的地位。