Harmonic Analysis and Partial Differential Operators

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Harmonic Analysis has played an important role in the study of partial differential equations, operator theory, function spaces with wide applications. This project aims to study partial differential equations with non-smooth coefficients on domains with rough boundaries and on general metric spaces. The proposed problems are at the frontier of harmonic analysis and spectral analysis. Expected outcomes are solutions to a number of key long-standing open problems in harmonic analysis, new original ideas and new techniques with wide scopes of applications in mathematical research.