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

会议：几何测度理论、调和分析和偏微分方程：最新进展

• 批准号: 2402028
• 负责人: Brett Wick
• 金额: $ 4.2万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-01-15 至 2024-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2402028&HistoricalAwards=false
• 关键词: Conference; Geometric; Measure; Theory; Harmonic

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.

该奖项为美国数学家参加将于 2024 年 6 月 23 日至 29 日在麦考瑞大学（澳大利亚）举行的“几何测度理论、调和分析和偏微分方程：最新进展”会议提供差旅支持。优先考虑处于职业生涯早期的研究人员、数学领域代表性不足的群体的成员以及无法获得国家科学基金会其他资助来源的研究人员。调和分析、偏微分方程和几何测度理论领域的顶尖国际学者、早期职业研究人员和博士生传播最新进展调和分析是涉及许多不同研究领域的基础数学学科。自诞生以来，调和分析学科的发展就与偏微分方程理论密切相关。近年来，人们的极大兴趣集中在使用调和分析作为解决其他领域（例如几何测量）中出现的问题的工具。理论和数论。高级研究生和早期职业美国研究人员参加本次活动将促进新研究合作的发展，并将加强美国在这一活跃领域的研究界。本次会议将汇集调和分析、偏微分方程和几何测度理论方面的专家突出和传播最近的研究进展，这三个主题长期以来一直存在共生关系，可以通过卡尔德隆-齐格蒙德的映射性质和规律性来理解偏微分方程解的存在性和唯一性。算子是调和分析中的一个经典主题，可以通过其边界上的调和测度的性质来研究集合的可修正性，这与偏微分方程中的关键主题和工具相关。本次研讨会的目标是促进该领域的进展。所有这三个领域都利用其固有的相互联系，并汇集了一批领先的研究人员来讨论最新进展并规划未来进展的方向。该活动网站是 https://event.mq.edu.au/harmonic-。分析.本次获奖通过使用基金会的智力价值和更广泛的影响审查标准进行评估，NSF 的法定使命被认为值得支持。