Quadratic fusion categories: A frontier in subfactor theory

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This project aims to investigate the quantum symmetries of the quadratic fusion categories. Fusion categories are mathematical structures that generalise the symmetries of finite groups. These structures arise as invariants of subfactors in operator algebras and in mathematical models of conformal field theory. The quadratic fusion categories encompass most known subfactors that do not come from finite or quantum groups and form a vast frontier about which little is known. By uncovering the symmetries of the quadratic fusion categories, the project will advance subfactor theory and provide new models for conformal field theory. Progress in these fields will have applications to the emerging technology of quantum computing.