4th Annual KUMUNU Conference in Partial Differential Equations, Dynamical Systems and Applications

该奖项将为与会者，特别是来自科学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2018年4月21-22日在堪萨斯大学举行的KUMUNU关于PDE、动力系统和应用的第四届年度会议。这次会议是由堪萨斯大学(KU)、密苏里大学(MU)和内布拉斯加大学(NU)的教职员工联合举办的。几乎所有的物理现象都受基本定律和设计原则的支配，它们直接将一个量的变化率与另一个量的变化率联系起来。这个强大的想法自然导致了微分方程，它被广泛用作数学物理中的模型，并在许多领域具有潜在的应用，包括玻色-爱因斯坦凝聚体、流体动力学、图案形成、气体动力学和光纤通信。这次会议将汇聚来自堪萨斯州、密苏里州和内布拉斯加州附近地理区域的研究人员，交流思想并报告在微分方程和应用方面的新成果。在本系列会议前三次会议取得成功的基础上，会议将为区域初级和高级研究人员以及研究生提供一个场所，讨论各自领域的最新进展和挑战。此外，年轻的研究人员将有机会介绍他们的工作，并通过与该领域资深专家的互动来深入了解这一重要主题。在会议网站上可以找到http://dept.ku.edu/~math/conferences/2018/KUMUNUPDE/Complex，科学和工程中充斥着非线性系统，它们的行为通常是用非线性偏微分方程组来建模的。在了解其解决方案的行为方面取得的任何进展，对于各种实际应用都是至关重要的，包括流体流动、火焰前沿传播和光纤通信。许多偏微分方程可以方便地描述为无限维动力系统，允许使用动力系统理论的工具和方法来对这些系统的解进行定性和定量的预测。像不变流形这样的对象对理解有限维动力系统的行为有很大的帮助，但非线性偏微分方程和动力系统之间的联系仍然是当前活跃的研究领域。在过去的几十年里，这些领域的研究人员及其应用领域的研究人员之间的合作，为我们理解这种非线性偏微分方程中相干结构的动力学行为、稳定性和稳健性提供了巨大的进步。这次会议的主题包括(I)流体动力学、水波和色散PDE，(Ii)耗散系统中非线性波的存在性、动力学和稳定性，以及(Iii)动力系统、不变流形和吸引子。这些主题由地区专家以及受邀的全体演讲者很好地代表了。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 4th Annual KUMUNU Conference on PDE, Dynamical Systems, and Applications to be held at the University of Kansas on April 21-22, 2018.  This conference is co-organized by faculty from the University of Kansas (KU), the University of Missouri (MU), and the University of Nebraska (NU).  Nearly all physical phenomena are governed by fundamental laws and design principles that directly relate rates of change of one quantity to that of some other quantity.  This powerful idea leads naturally to differential equations, which are widely used as models in mathematical physics and have potential applications to many fields including Bose-Einstein condensates, fluid dynamics, pattern formation, gas dynamics, and fiber optical communication.  This conference will bring together researchers from the geographic area close to Kansas, Missouri and Nebraska to exchange ideas and report new results in differential equations and applications.  Building on the success of the three prior conferences in this conference series, the conference will provide a venue for regional junior and senior researchers, as well as graduate students, to discuss recent advances and challenges in their respective fields.  Additionally, young researchers will be given the opportunity to present their work and to gain insight into this important subject through interactions with senior experts in the field.  The conference website can be found at http://dept.ku.edu/~math/conferences/2018/KUMUNUPDE/Complex nonlinear systems abound in science and engineering, and their behavior is often modeled by systems of nonlinear partial differential equations (PDE). Any progress towards understanding the behavior of their solutions is of paramount importance for a variety of practical applications, including fluid flow, flame front propagation and fiber optical communication. Many PDE can be conveniently described as infinite dimensional dynamical systems, allowing for the use of tools and methodologies from dynamical systems theory to make qualitative and quantitative predictions about the solutions of these systems. Objects like invariant manifolds have been a great aid in understanding the behavior of finite-dimensional dynamical systems, but the connections between nonlinear PDE and dynamical systems is still an area of active current research. In the last few decades, collaborations between researchers in these fields, as well as with those working in their applications, have provided tremendous progress in our understanding of the dynamical behavior, stability and robustness of coherent structures in such nonlinear PDE.  The themes of this conference include (i) fluid dynamics, water waves and dispersive PDE, (ii) existence, dynamics and stability of nonlinear waves in dissipative systems, and (iii) dynamical systems, invariant manifolds and attractors.  These themes are well represented by the regional experts as well as the invited plenary speakers.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.