Sean McCurdy
Overview
My research is in Geometric Measure Theory (GMT). Broadly speaking, GMT is the study of the relationship between the geometry of sets and measures and their measuretheoretic properties. It often works at the intersection of Calculus of Variations, Partial Differential Equations, Geometric Analysis, Harmonic Analysis, and Metric Analysis.
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GMT is the natural home for many geometric problems in the Calculus of Variations such as Minimal Surfaces, Isoperimetric problems, Brakke Mean Curvature Flow, and Freeboundary problems. It also has a 'pure' branch which does fundamental research into the geometry of sets and measures. This fundamental research has found applications in many branches of Analysis.
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Here is a recent article describing some of the history and recent applications of GMT.
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Currently, my research touches upon several branches of GMT.
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Here in Taiwan, I am engaged in the study of varifold regularity under the mentorship of Ulrich Menne (National Taiwan Normal University). Varifolds are a generalization of surfaces. See this article for a brief introduction to the concept of varifolds.
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I also have a collaboration with KuanTing Yeh (University of Washington, Seattle) studying symmetrization inequalities, Isoperimetric problems, and the fine properties of Ehrhard symmetrization when the underlying measure is not an isotropic Gaussian function.
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I also have a longstanding interest in the structure of singular sets arising from Free boundary problems. As a graduate student, I studied twophase freeboundary problems for harmonic measure. Later as a PostDoctoral Fellow at Carnegie Mellon University, I studied the singular structure of local minimizers of degenerate AltCaffarelli functionals inspired by the theory of water waves.

Here are some slides from a talk I gave summarizing some of my work on these degenerate AltCaffarelli functionals.â€‹

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I also have an ongoing collaboration with Matthew Badger (University of Connecticut, Storrs) studying the quantitative geometry of rectifiable curves in Banach spaces.