Quantum algebra has become an important direction in mathematical research in recent years. It is a natural combination and extension of theories such as representation theory, Hopf algebra theory, tensor category theory, and Lie theory. It has also gained widespread attention due to its profound connections with low-dimensional topology, rational conformal field theory, and topological field theory. In recent years, the field of quantum algebra has developed rapidly, with a series of outstanding works and progress emerging.

To enhance communication and discussions among experts in quantum algebra, showcase cutting-edge work from various directions within the field, and promote cross-disciplinary collaborations, we organize the Advances in Quantum Algebra conference in February 2025. The conference focuses on several core directions of quantum algebra, including tensor categories, Hopf algebras, vertex operator algebras, subfactor theory, topological order, topological quantum field theory, and low-dimensional topology, among others.

The conference aims to gather experts’ views and suggestions on core issues in the field, providing valuable references for young scholars in this area. Through the display of cutting-edge work across various directions of quantum algebra, this conference seeks to stimulate intellectual exchange among the experts, providing an excellent platform for cross-disciplinary and cross-field collaboration, while further advancing the development of quantum algebra.