Warwick EPSRC Symposium in the Statistical Mechanics / Mathematics of Phase Transitions

沃里克 EPSRC 统计力学/相变数学研讨会

• 批准号: EP/K015400/1
• 负责人: Roman Kotecky
• 金额: $ 18.94万
• 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: 2013
• 资助国家: 英国
• 起止时间: 2013 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FK015400%2F1
• 关键词: Warwick; EPSRC; Symposium; Statistical; Mechanics

This is a proposal for a symposium to be held during the academic year 2013-2014 at the Mathematics Research Centre (MRC) of the University of Warwick. The overall theme is mathematical statistical physics with a particular emphasis on the extension of its methods to a range of disciplines within mathematics as well as its applications in physics and other sciences. Mathematical statistical mechanics developed from its focus on rigorous foundations of statistical physics to become an exciting and active area of research devoted to various aspects of collective phenomena. Remarkably, its methods designed originally for exploring phase transitions are providing effective tools in other branches of mathematics: combinatorics, discrete mathematics, probability, analysis, and computer science. They turned out to be especially useful for investigations of asymptotics with abrupt thresholds and universal behaviour at criticality, the topics brought together under the heading "Mathematics of Phase Transitions". This is exemplified by impressive successes in various disciplines. a) In probability: studies of universal critical behaviour of various two-dimensional systems based on Schramm's SLE led to spectacular advances and opened a whole new field of modern mathematics with Fields Medals awarded in 2006 and 2010. b) In discrete mathematics and computer science: the theory of random discrete structures that is crucial for these disciplines has been truly revolutionised by new ideas from statistical mechanics. c) In analysis: investigations of macroscopic nonlinear PDE, as applied, for example, in nonlinear elasticity or in investigations of phase coexistence, based on underlying microscopic atomic models are gaining prominence.The symposium will facilitate a year-long sustained research activity on mathematical aspects of statistical physics with emphasis on its links to other mathematical disciplines. It will foster international links and collaborations and attract the attention of the UK mathematical community to this newly emerging and highly active area and enable the innovative use of the potential of branches of mathematics that are well established in the UK.In practical terms the symposium will be structured around six week-long workshops in various research areas of international significance pertaining to the general theme of the symposium. All important areas of mathematics where the methods of statistical physics play a significant role will be covered, with participation of leading international and national experts.In addition, there will be a visitor programme and a number of other supporting activities (mini-courses, seminars) designed to sustain the level of activity through the year.

这是一项关于在2013-2014学年在沃里克大学数学研究中心（MRC）举行一次专题讨论会的建议。总体主题是数理统计物理学，特别强调将其方法扩展到数学中的一系列学科以及其在物理学和其他科学中的应用。数理统计力学从其对统计物理严格基础的关注发展成为一个令人兴奋和活跃的研究领域，致力于集体现象的各个方面。值得注意的是，它最初设计用于探索相变的方法在其他数学分支中提供了有效的工具：组合数学，离散数学，概率，分析和计算机科学。他们原来是特别有用的调查渐近突然阈值和普遍的行为在临界状态下，题目汇集在一起的标题下“数学相变”。在各个学科取得的令人印象深刻的成功就是一个例证。a）在概率方面：基于Schramm的SLE的各种二维系统的普遍临界行为的研究导致了惊人的进步，并在2006年和2010年获得菲尔兹奖章，开辟了现代数学的全新领域。B）在离散数学和计算机科学中：对这些学科至关重要的随机离散结构理论已经被来自统计力学的新思想真正地革命化了。c）在分析中：基于微观原子模型的宏观非线性偏微分方程的研究，如应用于非线性弹性力学或相共存的研究，正日益受到重视。研讨会将促进为期一年的统计物理数学方面的持续研究活动，重点是它与其他数学学科的联系。它将促进国际联系和合作，吸引英国数学界对这一新兴和高度活跃的领域的关注，并使英国建立良好的数学分支的潜力得到创新利用。实际上，研讨会将围绕六个为期一周的研讨会进行组织，这些研讨会涉及与研讨会主题相关的具有国际意义的各个研究领域。将包括统计物理学方法发挥重要作用的所有重要数学领域，国际和国内的主要专家将参加，此外，还将有一个访问者方案和一些其他支助活动（小型课程、研讨会），旨在保持全年的活动水平。