Conference: Geometry of Measures and Free Boundaries

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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.