Conference: 2024 KUMUNU-ISU Conference on PDE, Dynamical Systems and Applications

该奖项将为参与者提供支持，特别是研究生，初级研究人员，妇女和数学家，来自数学和科学代表性不足的群体，参加2024年4月6日至7日在堪萨斯大学举行的KUMUNU-ISU PDE，动力系统和应用会议。 这是由堪萨斯大学（KU）、密苏里州大学（MU）、内布拉斯加大学（NU）和最近的爱荷华州州立大学（ISU）的教师共同组织的年度会议系列的第8版。 几乎所有的物理现象都受基本定律和设计原则的支配，这些基本定律和设计原则直接将所涉及的各种量的变化率相互联系起来。这个强大的基本概念自然导致微分方程，微分方程被广泛用作数学物理中的模型，并应用于广泛的领域，包括玻色-爱因斯坦凝聚，流体动力学，图案形成，气体动力学和光纤通信。本次会议将汇集来自堪萨斯、密苏里州、内布拉斯加州和爱荷华州周围更广泛地理区域的研究人员，报告新成果并就微分方程及其应用交换意见。在本系列会议前七次会议成功的基础上，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，早期职业研究人员将有机会展示他们的工作，并通过与该领域资深专家的互动深入了解最先进的结果和相关技术。复杂的非线性系统在科学和工程中比比皆是，其行为通常由非线性偏微分方程（PDE）系统建模。任何对了解PDE的解决方案的行为的进展是极其重要的各种实际应用，包括流体流动，火焰前锋传播和光纤通信。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预测。像不变流形这样的对象在理解有限维动力系统的行为方面有很大的帮助，但是识别非线性PDE和动力系统之间的联系仍然是当前研究的一个非常活跃的方向。在过去的几十年里，这些领域的研究人员之间的合作，以及与那些在他们的应用工作，提供了巨大的进步，在我们的理解的动力学行为，稳定性和鲁棒性的相干结构在这样的非线性偏微分方程。 本次会议的主题包括（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）完全可积系统及其应用。区域专家和受邀的全体会议发言人充分阐述了这些主题。该会议网站可以在www.example.com上找到https://kumunu-isu-pde-ds2024.ku.edu/.This项目由数学科学部（DMS）应用数学计划和刺激竞争性研究的既定计划（EPSCoR）共同资助。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

This award will provide support for participants, especially graduate students, junior researchers, women and mathematicians from underrepresented groups in mathematics and the sciences, to attend the KUMUNU-ISU Conference on PDE, Dynamical Systems, and Applications to be held at the University of Kansas on April 6-7, 2024. This is the 8th edition of an annual conference series co-organized by faculty from the University of Kansas (KU), the University of Missouri (MU), the University of Nebraska (NU) and, more recently, Iowa State University (ISU). Nearly all physical phenomena are governed by fundamental laws and design principles that directly relate rates of change of the various quantities involved to one another. This powerful underlying concept leads naturally to differential equations, which are widely used as models in mathematical physics and have applications to a wide range of fields including Bose-Einstein condensates, fluid dynamics, pattern formation, gas dynamics, and fiber optical communications. This conference will bring together researchers from the broader geographic region around Kansas, Missouri, Nebraska and Iowa to report new results and exchange ideas on differential equations and their applications. Building on the success of the prior seven 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, early-career researchers will be given the opportunity to present their work and to gain insight into state-of-the-art results and associated techniques through interactions with senior experts in the field.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 the solutions to PDE is of paramount importance for a variety of practical applications, including fluid flow, flame front propagation and fiber optical communications. Many PDE can be conveniently described as infinite-dimensional dynamical systems, allowing for the use of tools and methodologies from the theory of dynamical systems 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 identifying the connections between nonlinear PDE and dynamical systems is still a very active direction of 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) completely integrable systems and their applications. These themes are well represented by the regional experts as well as the invited plenary speakers. The conference website can be found at https://kumunu-isu-pde-ds2024.ku.edu/.This project is jointly funded by the Division of Mathematical Sciences (DMS) Applied Mathematics Program, and the Established Program to Stimulate Competitive Research (EPSCoR).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.