Conference: PDE in Moab: Advances in Theory and Application

该奖项的目的是资助偏微分方程（PDE）研究会议将于2024年6月3日至7日在位于犹他州摩押的犹他州州立大学（USU）大楼举行。这次会议名为“PDE在摩押：理论和应用的进展”，将有14个特邀演讲，沿着9个来自早期职业数学家的演讲，共有约40名与会者。这笔赠款所附资金将用于支持与会者的差旅和住宿费用，优先考虑无法获得其他差旅资金来源的初级与会者。该会议的网站是https://pdemoab.byu.eduThis会议旨在探索偏微分方程（PDE）的工具和方法，以及它们在几何测度理论（GMT），调和分析和自由边界问题等相关领域的应用。从历史上看，这些数学领域受益于许多富有成效的相互联系。事实上，自由边界问题的开拓性进展适应了PDE和GMT中正则性理论的技术。此外，非线性和非局部偏微分方程的最新进展扩大了上述领域的交叉，从而增加了这些领域的相互作用，合作和整体进步。 本次会议将汇集来自PDE，GMT，谐波分析和自由边界问题领域的专家，以探索和建立在最近的进展。发言者名单是由一个充满活力的数学家小组专门从事互补领域，其中许多人已经有交叉的利益。通过将这些研究人员聚集在一起，研究领域之间将有进一步的互动，导致技术和新的研究成果的交叉授粉。该奖项反映了NSF的法定使命，并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，被认为值得支持。

The purpose of this award is to fund a research conference on Partial Differential Equations (PDE) to take place on June 3-7, 2024, at the Utah State University (USU) building located in Moab, Utah. The conference, called "PDE in Moab: Advances in Theory and Application" will feature 14 invited talks, along with 9 contributed talks from early career mathematicians, with a total of approximately 40 participants. Funding attached to this grant will be used to support travel and lodging expenses for participants in the conference, with priority for junior participants who do not have access to other sources of travel funding. The conference website is https://pdemoab.byu.eduThis conference aims to explore the tools and methods of partial differential equations (PDE), and their applications in related fields such as geometric measure theory (GMT), harmonic analysis, and free boundary problems. Historically, these areas of mathematics have benefited from many fruitful interconnections. Indeed, pioneering advancements in free boundary problems adapted techniques from regularity theory in both PDE and GMT. Moreover, recent advances in both nonlinear and nonlocal PDE have enlarged the intersection of the aforementioned fields, thereby increasing interactions, collaborations, and the overall advancement of these areas. This conference will bring together experts from the areas of PDE, GMT, harmonic analysis, and free boundary problems to explore and build on recent progress. The list of speakers is comprised of a dynamic group of mathematicians specializing in complementary fields, many of whom already have intersecting interests. It is expected that by bringing these researchers together, there will be further interaction between research areas, leading to the cross-pollination of techniques and novel research results.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.