Midwestern Conference on Partial Differential Equations, Dynamical Systems, and Applications

该奖项将为与会者，特别是来自科学界代表性不足群体的研究生、初级研究人员、女性和数学家提供支持，以参加将于2019年4月27-28日在密苏里州哥伦比亚举行的第二届区域会议--KUMUNU关于PDE、动力系统和应用的会议。这次会议是由密苏里大学哥伦比亚分校数学系、劳伦斯堪萨斯大学和内布拉斯加大学林肯分校联合组织的。会议将展示偏微分方程式和复杂系统动力学方面的最新进展并促进思想交流。自然界中的许多基本第一原理都以时空变化的量的守恒定律(或平衡定律)的形式存在，这些定律自然而然地导致了偏微分方程组(PDE)。因此，在几乎所有的科学领域都会遇到偏微分方程；它们描述了波动、扩散、变形、混合、图案形成和许多其他现象。目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、堪萨斯州和内布拉斯加州附近的中西部和南部各州，但许多在美国其他机构工作的研究人员将被包括在内。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。今年，KUMUNU还将首次推出一个迷你课程，由Bjorn Sandstede(Brown)进行三次系列讲座。会议的网站是http://faculty.missouri.edu/~walshsa/kumunu2019/Many，由偏微分方程管理的复杂的非线性问题可以被重构为在无限维空间上提出的动力系统。这一策略已经被证明是有效的，而且作为一种解决非线性科学中许多公开问题的手段，它无疑显示出了巨大的前景。要实现这一承诺，PDE和Dynamic社区之间强大而持续的合作是必不可少的。KUMUNU会议的目标是支持和促进这一合作。今年会议的主要主题如下：动力系统技术在流体力学和水波中的应用；色散PDE的动力学；以及时空结构。这些话题中的每一个都产生了大量的近期活动。KUMUNU会议将有助于推动这些努力，特别是在地区机构。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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 "KUMUNU Conference on PDE, Dynamical Systems and Applications" to be held in Columbia, Missouri on April 27-28th, 2019. The meeting is organized jointly by the Departments of Mathematics at the University of Missouri-Columbia, the University of Kansas in Lawrence, and the University of Nebraska-Lincoln. The conference will showcase recent advances and facilitate exchange of ideas in partial differential equations 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 (PDE). PDE are therefore encountered in nearly all areas of science; they describe wave motion, diffusion, deformation, mixing, pattern formation, and many other phenomena. Specific applications 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, Kansas, and Nebraska, 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. For the first time this year, KUMUNU will also feature a mini-course consisting of a series of three lectures to be given by Bjorn Sandstede (Brown). The conference website is http://faculty.missouri.edu/~walshsa/kumunu2019/Many of the complex nonlinear problems governed by PDE 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 KUMUNU 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 PDE; and spatio-temporal structures. Each of these topics has generated a great deal of recent activity. The KUMUNU Conference will help to advance these efforts, particularly at regional institutions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.