Conference on "Symmetries of Differential Equations: Frames, Invariants and Applications"

“微分方程的对称性：框架、不变量和应用”会议

• 批准号: 1157714
• 负责人: Willard Miller
• 金额: $ 4.47万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-05-01 至 2013-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1157714&HistoricalAwards=false
• 关键词: Conference; Symmetries; Differential; Equations; Frames

This grant provides travel support for graduate students, postdocs, and invited lecturers to participate in the Conference on "Symmetries of Differential Equations: Frames, Invariants and Applications" to be held at the School of Mathematics, University of Minnesota, May 17-19, 2012. The general conference theme is inspired by the lifetime research achievements of Professor Peter Olver, but focus will be on current advances, promising directions, and novel applications. The main topics addressed are symmetries of differential equations and variational problems, with special emphasis on moving frames, Cartan theory of differential forms and invariant theory. Also Hamiltonian systems and integrable systems including solitons will be treated, as well as applications of symmetry based methods to image processing, fluid mechanics and elasticity. The organizing committee is: Niky Kamran (Mathematics, McGill University), Gloria Mari Beffa (Mathematics, University of Wisconsin), Guillermo R. Sapiro (Electrical and Computer Engineering, University of Minnesota), and Willard Miller, Jr, (Mathematics, University of Minnesota). Detailed information is available on the website http://math.umn.edu/conferences/olver/ and results of the meeting, including abstracts, slides and a panel discussion, will also be posted there. In conjunction with the conference the on line journal SIGMA will publish a special issue entitled ``Symmetries of Differential Equations: Frames, Invariants and Applications'' with the conference organizers as guest editors, http://www.emis.de/journals/SIGMA/SDE2012.html.The general theme of the conference is the exploitation of symmetries of mathematical and physical systems to deduce properties of these systems. More specifically, most physical theories are expressed in terms of differential equations and the mathematical symmetries of these equations can be exploited to reach important conclusions about the systems that obey the equations. The meeting comes at a propitious time - an explosion of new results and new methods in symmetry analysis, with applications ranging over geometry, differential equations, computer vision, numerical analysis, mechanics, and physics, make this an ideal time to assemble the leading experts, and promising younger researchers to assess the rapid advances in the area, reach a consensus on what are the most important problems, and evaluate the most promising directions for further advance. We expect the conference to be a major event in the history of this research area.

该补助金为研究生，博士后提供旅行支持，并邀请讲师参加将于2012年5月17日至19日在明尼苏达大学数学学院举行的“微分方程对称性：框架，不变量和应用”会议。大会主题的灵感来自Peter Olver教授的终身研究成就，但重点将放在当前的进展，有前途的方向和新的应用上。讨论的主要议题是微分方程和变分问题的对称性，特别强调移动框架，微分形式和不变理论的嘉当理论。此外，哈密顿系统和可积系统，包括孤子将被处理，以及应用对称性为基础的方法，以图像处理，流体力学和弹性。组委会是：尼基·卡姆兰（数学，麦吉尔大学）、格洛丽亚马里·贝法（数学，威斯康星州大学）、吉列尔莫·R·Sapiro（电气和计算机工程，明尼苏达大学）和Willard米勒，Jr（数学，明尼苏达大学）。详细资料可在网站http://math.umn.edu/conferences/olver/上查阅，会议结果，包括摘要、幻灯片和小组讨论也将张贴在该网站上。在会议的同时，在线杂志SIGMA将出版一个题为“微分方程的对称性：框架，不变量和应用”的特刊，会议组织者作为客座编辑，http://www.emis.de/journals/SIGMA/SDE2012.html.The会议的总主题是利用数学和物理系统的对称性来推导这些系统的属性。更具体地说，大多数物理理论都是用微分方程来表达的，这些方程的数学对称性可以用来得出关于服从这些方程的系统的重要结论。这次会议是在一个有利的时间-爆炸的新成果和新方法的对称性分析，与应用范围超过几何，微分方程，计算机视觉，数值分析，力学和物理学，使这一理想的时间来聚集领先的专家，并有前途的年轻研究人员评估该地区的快速发展，达成共识，什么是最重要的问题，并评估最有前途的进一步发展方向。我们希望这次会议将成为这一研究领域历史上的一件大事。