Conference: Geometry of Measures and Free Boundaries

该奖项为措施和自由边界的几何形状的国际研究会议提供支持，将于2024年7月22日至26日在西雅图的华盛顿大学举行。会议在于变分法，几何测量理论，调和分析和偏微分方程的交叉点。该活动将包括会前介绍博士生的迷你课程，将于2024年7月20日至21日举行。该奖项的资金将用于支持非本地演讲者和其他与会者参加会议和小型课程的差旅费，并优先支持博士生，博士后和研究人员，而无需获得其他资金来源。几何测量理论的主题包括一系列用于描述具有几何风味的集合的大小和结构的分析工具，自由边界问题的理论解决了表征遵循特定约束的未知界面的挑战，这些约束通常由偏微分方程描述。自由边界问题出现在纯数学之外的几个学科中，包括物理学，金融学和生物学。度量空间中的当代几何测度理论与大型数据集中流形结构识别问题的应用研究是并行的。会议的两个主要议题是通过一系列的概念，低阶和高阶正则集。通过召集几何测量理论，自由边界问题以及几何和调和分析相关领域的当前从业者分享他们的观点并报告最新进展，会议旨在加强学科之间的联系，阐明共同的原则，并促进长期问题的新解决方案。会议网站是https://sites.google.com/view/gmfbseattle2024/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 support for an international research conference on the geometry of measures and free boundaries, to take place July 22–26, 2024 at the University of Washington, Seattle. The conference lies at the intersection of calculus of variations, geometric measure theory, harmonic analysis, and partial differential equations. The event will include pre-conference introductory minicourses for PhD students, to be held July 20–21, 2024. Funding from this award will support travel expenses for non-local speakers and other participants in the conference and the minicourses, with priority for participant support given to PhD students, postdocs, and researchers without access to other sources of funding.The subject of Geometric Measure Theory encompasses a range of analytical tools used to describe the size and structure of sets with a geometric flavor, and the theory of Free Boundary Problems addresses the challenge of characterizing unknown interfaces that adhere to specified constraints, often described by a partial differential equation. Free Boundary Problems arise in several disciplines outside of pure mathematics, including physics, finance, and biology. Contemporary geometric measure theory in metric spaces is parallel to applied research on the problem of identifying manifold structure in large data sets. The two main topics of the conference are linked through a spectrum of notions of lower-order and higher-order regularity of sets. By convening current practitioners in geometric measure theory, free boundary problems, and related areas of geometric and harmonic analysis to share their perspectives and report on the latest advances, the conference seeks to strengthen the connections between the subjects, to shed light on shared principles, and to facilitate novel solutions to longstanding problems. The conference website is https://sites.google.com/view/gmfbseattle2024/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.