Fifth Workshop on Nonlinear Dispersive Equations

该奖项支持美国数学家，包括研究生、博士后研究人员和初级教师，参加2022年11月8-11日在巴西贝洛奥里藏特米纳斯吉拉斯联邦大学举行的“第五届非线性色散方程研讨会”。这是一次分析和非线性微分方程领域的合作会议，旨在通过汇聚北美和南美该领域的研究人员，建立国际联系，特别是为初级数学家创造联系。研讨会将为从事非线性波动方程研究的大量研究人员提供协作、教育和网络机会，并为美国早期职业研究人员提供独特的职业机会，包括那些来自数学科学中历史上代表性不足的群体的研究人员。这是其系列会议中的第五次；以前的会议在促进研究各种实际应用中出现的非线性模型、波、湍流和奇异性方面越来越成功，包括流氓波和空气湍流、光学和通信以及力学。在过去的三十年里，非线性发展方程领域经历了戏剧性的发展。新的思想和技术使数学家能够探索以前似乎难以解决的问题，这项工作使人们在理解几个基本的非线性波动方程方面取得了进展，如非线性薛定谔方程、Korteweg-de Vries方程、Benjamin-Ono方程和非线性Klein-Gordon方程，包括它们的各种推广和扩展。然而，一些重要的问题，如稳定和相干结构的描述，还没有得到充分的探索。会议将集中讨论与非线性色散模型的数学描述相关的常见问题和该领域的最新进展。更多信息可在会议网站上找到：https://sites.google.com/view/v-wndeThis奖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 supports participation of U.S.-based mathematicians, including graduate students, postdoctoral researchers, and junior faculty, in the “Fifth Workshop on Nonlinear Dispersive Equations,” held November 8-11, 2022, at the Federal University of Minas Gerais, Belo Horizonte, Brazil. This is a collaborative meeting in the area of analysis and nonlinear differential equations that is geared towards creating international connections, especially for junior mathematicians, by bringing together North and South American researchers in the field. The workshop will provide collaborative, educational, and networking opportunities for a significant number of researchers working in nonlinear wave equations and offers unique professional opportunities to early-career U.S.-based researchers, including those from historically underrepresented groups in the mathematical sciences. This is the fifth such meeting in its series; previous meetings have been increasingly successful in promoting research that studies nonlinear models, waves, turbulence, and singularities arising in various practical applications, including rogue waves and air turbulence, optics and communication, and mechanics. The field of nonlinear evolution equations has been experiencing dramatic growth over the last thirty years. New ideas and techniques have enabled mathematicians to explore questions that previously seemed intractable, and the work has led to advances in understanding several fundamental nonlinear wave equations such as the nonlinear Schrödinger, Korteweg-de Vries, Benjamin-Ono, and nonlinear Klein-Gordon equations, including their various generalizations and extensions. However, some important questions, such as the description of stable and coherent structures, are yet to be fully explored. The conference will focus on common questions associated with the mathematical description of nonlinear dispersive models and the latest advances in the field. Additional information can be found at the conference website: https://sites.google.com/view/v-wndeThis 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.