Midwestern Conference on Partial Differential Equations, 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2019年4月27日至28日在密苏里州哥伦比亚举行的第二届区域会议“KUMUNU 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、堪萨斯大学劳伦斯分校和内布拉斯加大学林肯分校联合组织的。会议将展示在偏微分方程和复杂系统动力学方面的最新进展，并促进思想的交流。自然界中许多基本的第一原理都采用守恒（或平衡）定律的形式，这些定律自然地导致了偏微分方程（PDE）。因此，PDE几乎在所有科学领域都遇到；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、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。今年，KUMUNU还将首次推出由Bjorn Sandstede（布朗大学）教授的三节系列讲座组成的迷你课程。由PDE控制的复杂非线性问题可以被重新定义为构成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。库穆努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PDE动力学；以及时空结构。上述每一个话题最近都引发了大量的活动。库穆努会议将有助于推动这些努力，特别是在区域机构。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.