[There will be a pre-seminar for students starting at 13:30. For zoom link please email s.nagyATqmul.ac.uk] The relation between the physics of the bulk and that of a boundary plays an important role in quantum field theories, quantum gravity and condensed matter physics. In this talk, I will review a manifestation of this relation that can be summarized as a short statement: "the bulk is the center of a boundary". I will explain the meaning of "center" and provide a formal proof of this statement (arXiv:1702.00673). By including higher codimensional domain walls between boundaries, the boundary-bulk relation can be formulated mathematically as a higher functor. In lower dimensional cases, it becomes precise mathematical theorems. In the end, I will discuss the significances of this relation in the study of topological orders and topological phase transitions.