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

该奖项为在美国的数学家出席2024年6月23-29日在澳大利亚麦格理大学举行的“几何测量理论、调和分析和偏微分方程式：最新进展”会议提供差旅支持。将优先支持职业生涯早期的研究人员、数学领域代表性不足的群体成员，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量理论领域的国际知名学者、早期职业研究人员和博士生，传播最新的进展。调和分析是一门基础的数学学科，涉及许多不同的研究领域。自其诞生以来，调和分析学科的发展与偏微分方程组理论密切相关。近年来，人们对使用调和分析作为工具来解决几何测度论和数论等其他领域中出现的问题产生了浓厚的兴趣。高级研究生和早期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、偏微分方程式和几何测量理论的专家，以突出和传播最新的研究进展。这三个主体长期以来一直是一种共生关系。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，这是调和分析中的一个经典问题。欧氏空间中集合的可直性可以通过其边界上的调和测度的性质来研究，该性质与偏微分方程组中的关键学科和工具有关。这次讲习班的目标是，通过利用这三个领域内在的相互关联性，并通过聚集一批领先的研究人员来讨论最近的进展和规划未来进展的方向，促进在所有这三个领域取得进展。活动网站是https://event.mq.edu.au/harmonic-analysis.This奖项，反映了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 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.