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

该奖项将为与会者提供支持，特别是来自数学和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，参加将于2024年4月6-7日在堪萨斯大学举行的KUMUNU-ISU关于PDE、动态系统和应用的会议。这是由堪萨斯大学(KU)、密苏里大学(MU)、内布拉斯加大学(NU)以及最近爱荷华州立大学(ISU)的教职员工联合举办的年度会议系列的第八版。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将所涉及的各种量的变化率彼此直接联系起来。这个强大的基本概念自然地导致了微分方程，它被广泛用作数学物理中的模型，并在包括玻色-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在内的广泛领域中得到应用。这次会议将汇集来自堪萨斯州、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，报告关于微分方程及其应用的新成果，并交流意见。在这次会议系列的前七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，职业生涯早期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了解最新成果和相关技术。复杂的非线性系统在科学和工程中大量存在，它们的行为通常由非线性偏微分方程组(PDE)来建模。对于流体流动、火焰前沿传播和光纤通信等各种实际应用，了解PDE解决方案的行为的任何进展都是至关重要的。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中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，但识别非线性偏微分方程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及其应用领域的研究人员之间的合作，在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、稳定性和稳健性方面取得了巨大的进步。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)完全可积系统及其应用。区域专家以及受邀的全体发言者很好地代表了这些主题。会议的网站可以在https://kumunu-isu-pde-ds2024.ku.edu/.This上找到，该项目是由数学科学部应用数学项目和既定的激励竞争研究项目共同资助的。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 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.