Schur decompositions and related problems in operator theory

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This project aims to solve some famous problems concerning eigenvalue decompositions in operator theory through new collaborations and by connecting new areas of mathematics. Eigenvalue decomposition is a central concept in mathematics with many applications in science and engineering. One hundred years since its development, however, it is still not known how to decompose certain important operators that arise in analysis and geometry. The project is expected to provide new technology to achieve this, promising new understanding and new applications.