The title is motivated from the well-known Global Differential Geometry but has a slightly different meaning. Condensed matter theorists usually begin their studies from a concrete quantum many-body system (a lattice model with a concrete Hamiltonian). In this talk, I will explain a wave of new ideas of studying all/many quantum many-body systems at the same time. More precisely, we will study the categories of all gapped/gapless quantum liquid phases. For this reason, I will call this line of ideas "a Global Condensed Matter Theory". Some universal features of quantum liquid phases are emergent from this study.  I will briefly outline them and discuss their consequences. As we will see, a new mathematical framework unifying all quantum liquid phases, including topological orders, SPT/SET orders, symmetry-breaking phases and gapless liquid phases, are emerging.

Affiliation: Shenzhen Institute for Quantum Science and Engineering, SUSTech