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

本基金为参加2012年5月17-19日在明尼苏达大学数学学院举行的“微分方程的对称性：框架、不变量及其应用”会议的研究生、博士后和特邀讲师提供旅费支持。大会主题受到Peter Olver教授终身研究成果的启发，但重点将放在当前的进展，有前途的方向和新的应用上。讨论的主要主题是微分方程的对称性和变分问题，特别强调运动框架，微分形式的卡坦理论和不变理论。此外，哈密顿系统和包括孤子在内的可积系统也将被处理，以及基于对称的方法在图像处理、流体力学和弹性中的应用。组委会是：Niky Kamran（麦吉尔大学数学），Gloria Mari Beffa（威斯康星大学数学），Guillermo R. Sapiro（明尼苏达大学电气与计算机工程）和Willard Miller， Jr（明尼苏达大学数学）。详细信息可在网站http://math.umn.edu/conferences/olver/上查阅，会议的结果，包括摘要、幻灯片和小组讨论也将在网站上公布。与会议一起，在线杂志SIGMA将出版一个特刊，题为“微分方程的对称性：框架，不变量和应用”，会议组织者作为客座编辑，http://www.emis.de/journals/SIGMA/SDE2012.html.The会议的一般主题是利用数学和物理系统的对称性来推断这些系统的性质。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方程的系统的重要结论。这次会议恰逢其时——对称分析的新结果和新方法的爆炸式增长，其应用范围包括几何、微分方程、计算机视觉、数值分析、力学和物理学，这使得这是一个理想的时间，聚集了领先的专家，以及有前途的年轻研究人员来评估该领域的快速进展，就最重要的问题达成共识，并评估最有希望进一步发展的方向。我们期待这次会议成为这一研究领域历史上的一件大事。

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.