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.

EPSRC-沃里克研讨会在过去的50年里每年都举行会议，以促进英国数学的发展。每个研讨会集中在一个特定的主题;在2017-2018年的主题将是“几何，拓扑和动力学在低维”。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沃里克大学，讨论他们的研究，并提出新的研究方向。除此之外，我们还将接待一些杰出的国际长期访问者，他们也将访问其他英国大学。此外，我们亦会举办多场讲座，让市民认识几何学的基本概念，例如长度、角度、面积及体积等，这些概念都是高中数学的基本概念。在现代数学研究中，这些概念已经发展了很多，大大拓宽了几何学可以帮助解决的问题的范围。越来越多的奇异几何结构出现了;例如，空间具有某种内在的“曲率”而不是完全平坦的想法是爱因斯坦宇宙观的关键，无限的“自相似性”概念产生了壮观的分形图像。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，专注于一个这样的问题时，可以连续变形成另一个。例如，在不切断绳子的情况下，闭合的绳子环中的结是否可以解开，这是一个拓扑问题。本次研讨会汇集了来自不同背景的顶尖研究人员，他们对最近的发展提出了自己的观点，推进了他们的研究，并巩固英国作为数学研究在这一重要和国际活跃领域的枢纽。动力系统领域是长期的研究，随时间变化的系统的数学模型的项行为，例如物理系统或生物现象。有些数学模型很简单，比如描述台球桌上台球运动的模型，有些则极其复杂，比如太阳系中卫星的运动或天气模式。几何学、拓扑学和动力学之间有许多深刻而不明显的联系。世纪初，数学家庞加莱（Poincare）首次揭示了这一点，并从那时起就开始了深入的研究。本次研讨会将建立并进一步发展这些联系，以便在所有三个领域取得进展。研讨会将集中在低维现象，特别是那些发生在一维，二维和三维。在过去十年里，人们在理解这种现象方面取得了惊人的进展。例如，在数学中，庞加莱提出的一个关于三维物体拓扑结构的重要问题直到最近才得到解决。在物理学领域，弦论是理解物理学基本定律的一种新方法，在弦论的背景下，人们提出了关于表面（和其他空间）的令人着迷的新数学概念。本次研讨会汇集了具有不同背景的顶尖研究人员，就最近的发展发表他们的观点，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。