Conference: Geometric Measure Theory, Harmonic Analysis, and Partial Differential Equations: Recent Advances

该奖项为美国提供旅行支持-数学家参加会议“几何测度理论，调和分析和偏微分方程：最新进展”，将在麦考瑞大学（澳大利亚），2024年6月23日至29日举行。支持将优先考虑早期职业研究人员，数学代表性不足的群体的成员，以及无法获得其他NSF资金来源的研究人员。会议的目的是召集调和分析，偏微分方程和几何测度理论领域的国际领先学者，早期职业研究人员和博士生，以传播最新进展。谐波分析是一个基础数学课题，涉及许多不同的研究领域。自成立以来，谐波分析的主题已经发展密切联系的偏微分方程理论。近年来，大量的兴趣集中在使用调和分析作为一种工具，以解决在其他领域，如几何测度论和数论中出现的问题。高年级研究生和早期职业美国研究人员的参与将促进新的研究合作的发展，并将加强美国在这一活跃领域的研究社区。本次会议将汇集调和分析，偏微分方程和几何测量理论的专家，以突出和传播最新的研究进展。这三个主题长期以来一直存在着共生关系。偏微分方程解的存在唯一性可以通过Calderón-Zygmund算子的映射性质和正则性来理解，这是调和分析中的经典话题。欧氏空间中集合的可求正性可以通过其边界上调和测度的性质来研究，这与偏微分方程的核心学科和工具有着密切的联系。本次研讨会的目标是促进所有这三个领域的进展，利用其内在的相互关联性，并汇集了一批领先的研究人员，讨论最近的进展，并为未来的进展指明方向。该活动的网站是https://event.mq.edu.au/harmonic-analysis.This奖反映了NSF的法定使命，并已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的支持。

This award provides travel support for U.S.-based mathematicians to attend the conference "Geometric Measure Theory, Harmonic Analysis and Partial Differential Equations: Recent Advances", to be held at Macquarie University (Australia), June 23--29, 2024. Support will be prioritized for early-career researchers, members of underrepresented groups in mathematics, and researchers without access to other sources of NSF funding. The aim of the conference is to convene leading international scholars, early career researchers, and PhD students in the fields of harmonic analysis, partial differential equations, and geometric measure theory, to disseminate the most recent advances. Harmonic analysis is a foundational mathematical subject that touches upon many different areas of study. Since its inception, the subject of harmonic analysis has developed in close connection to the theory of partial differential equations. In recent years, substantial interest has focused on the use of harmonic analysis as a tool to address questions arising in other fields such as geometric measure theory and number theory. The participation of advanced graduate students and early-career U.S. researchers in this event will facilitate the development of new research collaborations and will strengthen the U.S. research community in this active field.This conference will bring together experts in harmonic analysis, partial differential equations and geometric measure theory to highlight and disseminate recent research progress. These three subjects have had a symbiotic relationship for a long time. Existence and uniqueness of solutions to partial differential equations can be understood through mapping properties and regularity of Calderón-Zygmund operators, a classical topic in harmonic analysis. Rectifiability of sets in Euclidean spaces can be studied through the properties of harmonic measure on their boundaries, which connects to key subjects and tools in partial differential equations. The goal of this workshop is to foster progress in all three of these areas by leveraging their inherent interconnectedness and by bringing together a collection of leading researchers to discuss recent advances and to chart the directions for future progress. The event website is https://event.mq.edu.au/harmonic-analysis.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.