In the past three decades, a new class of highly entangled quantum matter have been intensively studied both theoretically and experimentally. A novel concept -  topological order was proposed to describe the essential physics behind highly entangled quantum matter. In particular, it has been realised that the entanglement pattern is the essential feature of topological phases. We define that a state only has "short-range entanglement" if and only if it can be transformed into an un-entangled state (i.e a direct product state) through a local unitary evolution; otherwise, it has "long-range entanglement". Thus, (intrinsic) topological orders can be defined as the equivalent classes of local unitary evolutions, or in other words, the patters of "long-range entanglement:. 

Very recently, the concept of many body quantum entanglement even leads to revolutionary impact in many other areas of modern physics, such as quantum computation and quantum geometry. In this lecture series, we will systematically describe the classification scheme and mathematical foundation of topological orders in interacting boson and fermion systems. Moreover, we will also provide very basic introductions of quantum computation and quantum geometry from the aspects of quantum entanglement.

More details please see: http://www.phy.cuhk.edu.hk/events/croucher-summer-course-2019/.