Workshop on Trends in Soliton Dynamics and Singularity Formation for Nonlinear Dispersive PDEs

该奖项将支持为期3天的研讨会“非线性色散偏微分方程的孤子动力学和奇点形成趋势”将于2022年10月21日至23日在德克萨斯州学院站的德克萨斯农工大学校园内举行。研讨会的主题是在非线性波动方程研究的前沿。波动方程是一系列自然现象的核心，包括电磁学、流体动力学、非线性光学、量子力学、广义相对论和粒子物理学。因此，对这些方程进行严格的数学分析是深入了解我们生活的世界的基础。该研讨会旨在汇集国际领先的专家和初级研究人员，为年轻一代提供与该领域领导者互动并了解前沿数学发展的机会。初级研究人员也可以以贡献演讲的形式展示他们的研究。本次研讨会旨在创造更多的讨论机会，并为合作和思想交流创造一个良好的环境。研讨会的数学重点是非线性色散偏微分方程孤子动力学和奇异性形成研究的最新进展，以及与相关领域发展的相互作用。在本研讨会的背景下，孤子是指，粗略地说，表现出某种形式的相干结构的偏微分方程的解决方案。预计它们将在整体动态中发挥重要作用。这是一个活跃和快速发展的研究分支，最近的想法和技术正在许多其他领域中找到应用。PI希望这次研讨会将为所有参与者提供一个机会，了解这一领域令人着迷的新发展，形成新的合作，并探索与其他领域的有趣联系。资金将用于支付初级学员的住宿和旅费。关于研讨会及其目标的更多信息可以在网站上找到：https://sites.google.com/tamu.edu/solitons-workshop-tamu/aboutThis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知识价值和更广泛的影响审查标准进行评估来支持。

This award will support the 3-day workshop "Trends in Soliton Dynamics and Singularity Formation for Nonlinear Dispersive PDEs" to be held on the campus of Texas A&M University in College Station, Texas, on October 21-23, 2022. The topic of the workshop lies at the forefront of research on nonlinear wave equations. Wave equations are at the heart of a wide range of natural phenomena, including electromagnetism, fluid dynamics, nonlinear optics, quantum mechanics, general relativity, and particle physics. As such, the rigorous mathematical analysis of these equations is fundamental in obtaining a deeper understanding of the world we live in. This workshop aims to bring together leading international experts and junior researchers, providing an opportunity for the younger generation to interact with leaders of the field and to learn about cutting edge mathematical developments. Junior researchers also can present their research in the form of contributed talks. The workshop is structured to create many opportunities for discussions and to foster an environment for collaboration and for the exchange of ideas.The mathematical focus of the workshop is on recent developments in the study of soliton dynamics and singularity formation for nonlinear dispersive PDEs, and on the interplay with developments in related areas. In the context of this workshop, solitons refer, roughly speaking, to solutions to partial differential equations that exhibit some form of coherent structure. It is expected that they play an essential role for the overall dynamics. This is an active and fast developing branch of research, where recent ideas and techniques are finding applications in many other areas. The PIs hope this workshop will provide an opportunity for all participants to learn about the fascinating new developments in this area, to form new collaborations, and to explore interesting connections to other areas. Funds will be used for the accommodation and travel costs for junior participants. More information about the workshop and its goals can be found on the website: https://sites.google.com/tamu.edu/solitons-workshop-tamu/aboutThis 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.