Prof. Liu Zhengwei’s team is engaged in the research on operator theory, quantum topology, quantum symmetries and on mathematical aspects of quantum theory and its applications. In particular the team studies quantum complex systems, theoretical aspects of quantum complexity. At present, the team has established a new alterfold theory which provides a unified mathematical picture language based on operator theory, quantum topology, quantum algebra and other frontier mathematical theories. It extensively generalized the quon language and tensor networks and proposed new tools to study subfactors, quantum Fourier analysis, topological quantum field theory, topological orders, higher categories etc.. In the next three years, the team plans to apply the alterfold theory to unify various concepts and remarkable theories in related areas in a more fundamental, systematic and conceptual way, including rigorous mathematical formulations of physics concepts and new efficient computational tools. Many remarkable results become transparent in this approach.
The team is engaged in theoretical research. All results of this research are in the public domain.