KUMU Conference on PDE, Dynamical Systems, and Applications

该奖项将为参与者提供支持，特别是来自科学领域代表性不足群体的研究生、初级研究人员、女性和数学家，参加将于2016年4月23日至24日在密苏里州哥伦比亚举行的第二届区域会议“KUMU PDE、动力系统和应用会议”。这次会议是由密苏里-哥伦比亚大学数学系和劳伦斯的堪萨斯大学联合组织的。会议将展示偏微分方程（PDEs）和复杂系统动力学的最新进展，促进思想交流。自然界中许多基本的第一原理都以守恒（或平衡）定律的形式出现，这些定律会随时间和空间的变化而变化，这些定律自然会导致偏微分方程。因此，几乎所有科学领域都遇到了方案设计方案；它们描述波动、扩散、变形、混合、模式形成和许多其他现象。当前感兴趣的具体应用包括气候建模、水波、复杂介质中的电动力学现象和神经科学。虽然参与者集中在密苏里州和堪萨斯州附近的中西部和南部各州，但许多在美国其他地方机构工作的研究人员也将被包括在内。早期职业数学家将有机会展示他们的工作，以获得认可和宝贵的反馈。由偏微分方程控制的复杂非线性问题可以被重新定义为在无限维空间上的动力系统。这一策略已被证明是有效的，并且作为一种解决非线性科学中大量未解决问题的手段，它无疑显示出巨大的前景。为了实现这一承诺，PDE和动态社区之间强有力和持续的合作是必不可少的。KUMU会议的目标是支持和促进这种合作。今年会议的主要主题是：动力系统技术在流体力学和水波中的应用；色散偏微分方程动力学；以及非线性波稳定性研究中的指标公式。上述每一个话题最近都引发了大量的活动。KUMU会议将有助于推进这一研究。

This award will provide support for participants, especially graduate students, junior researchers, women and mathematicians from under-represented groups in the sciences, to attend the second regional conference "KUMU Conference in PDE, Dynamical Systems and Applications" to be held in Columbia, Missouri on of April 23-24, 2016. The meeting is organized jointly by the Departments of Mathematics at the University of Missouri-Columbia and the University of Kansas in Lawrence. The conference will showcase recent advances and facilitate exchange of ideas in partial differential equations (PDEs) and dynamics of complex systems. Many basic first principles in nature take the form of conservation (or balance) laws for quantities that vary in space and time, and these laws lead naturally to partial differential equations. PDEs are therefore encountered in nearly all areas of science; they describe wave motion, diffusion, deformation, mixing, pattern formation, and many other phenomena. Specific application of current interest include climate modeling, water waves, electrodynamics phenomena in complex media, and neuroscience. While participants are clustered in the Midwestern and Southern states near Missouri and Kansas, many researchers working at institutions elsewhere in the US will be included. Early career mathematicians will be given an opportunity to present their work to gain recognition and invaluable feedback. The conference website is http://faculty.missouri.edu/~walshsa/kumu2016/Many of the complex nonlinear problems governed by PDEs can be reframed as dynamical systems posed on infinite-dimensional spaces. This strategy has proved to be effective, and it certainly shows tremendous promise as a means to attack a host of open problems in nonlinear science. To realize this promise, a strong and continuing collaboration between the PDE and dynamics communities is essential. The goals of the KUMU Conference are to support and facilitate this collaboration. The major themes of this year's meeting are as follows: applications of dynamical system techniques to fluid mechanics and water waves; dynamics of dispersive PDEs; and index formulas in the study of stability of nonlinear waves. Each of these topics has generated a great deal of recent activity. The KUMU Conference will help to advance this research.