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

会议：2024 年 KUMUNU-ISU 偏微分方程、动力系统和应用会议

• 批准号: 2349508
• 负责人: Mathew Johnson
• 金额: $ 2.3万
• 依托单位: University of Kansas Center for Research Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-04-01 至 2025-03-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2349508&HistoricalAwards=false
• 关键词: Conference; 2024; KUMUNU; ISU; PDE

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.

该奖项将为参与者，尤其是来自代表性不足的数学和科学团体的研究生，初级研究人员，妇女和数学家提供支持，以参加堪萨斯州PDE的Kumunu-ISU会议，动态系统以及将在堪萨斯大学举行的堪萨斯大学（Univers of Kansas）在2024年4月6日至7日举行。 （KU），密苏里大学（MU），内布拉斯加州大学（NU）以及最近的爱荷华州立大学（ISU）。 几乎所有的物理现象都受基本法律和设计原则的管辖，这些定律和设计原则将涉及的各种数量的变化率直接相关。这种强大的潜在概念自然导致微分方程，这些方程被广泛用作数学物理学的模型，并在包括Bose-Einstein冷凝物，流体动力学，模式形成，气体动力学和光纤通信在内的广泛领域应用。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，以报告有关微分方程及其应用的新结果和交换想法。基于本会议系列赛的前七个会议的成功，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地，讨论各自领域的最新进展和挑战。此外，通过与Field.clex非线性系统的相互作用，早期研究人员将有机会展示他们的工作，并深入了解最先进的结果和相关技术，而科学和工程学中的非线性系统越来越多，并且他们的行为通常由非线性偏微分方程（PDE）的系统建模。了解解决方案对PDE的行为的任何进展对于各种实际应用，包括流体流，火焰前端传播和光纤通信至关重要。许多PDE可以方便地描述为无限维动力学系统，从而允许使用动态系统理论的工具和方法来对这些系统的解决方案进行定性和定量预测。像不变歧管之类的对象非常有助于理解有限维动力学系统的行为，但是识别非线性PDE与动力学系统之间的连接仍然是当前研究的非常活跃的方向。在过去的几十年中，这些领域的研究人员以及在其应用中工作的研究人员之间的合作在我们对这种非线性PDE中相干结构的动态行为，稳定性和鲁棒性方面为我们提供了巨大的进步。 该会议的主题包括（i）流体动力学，水波和色散PDE，（ii）非线性波在耗散系统中的存在，动力学和稳定性，以及（iii）完全可以集成的系统及其应用。这些主题由地区专家以及受邀全体演讲者很好地代表。会议网站可以在https://kumunu-isu-pde-ds2024.ku.edu/..this项目上找到，该项目由数学科学划分（DMS）应用数学计划共同资助，并通过启发NSF的Infortional Internition deem deem deem deem deem deem the Indertial neward award applied数学计划，既定的计划。更广泛的影响审查标准。