Although I am a mathematician or a mathematical physicist, most of my research works are motivated by physics and natural philosophy. My long term goal is to gain a deeper understanding of the following questions:
I am not entirely sure if they are different questions. My approach is mainly algebraic or representation-theoretical because the usual language of physics based on classical calculus is inadequate to describe the quantum world. I believe that we need to develop a quantum calculus or a new algebra geometry based on representation theory of certain quantum algebras. A proposal of such a new algebra geometry, called stringy algebraic geometry, was given in [arXiv:1107.3649].
One of the recurring themes of my works is the so-called boundary-bulk duality, which appears in both topological and conformal field theories. It plays the role of the defining property of the stringy algebraic geometry. This theme motivated me to explore many related problems in conformal field theories and topological orders (with or without symmetries).
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