The quantum mechanical nature of electrons is indispensable in explaining certain macroscopic properties of quantum materials. For instance, the electronic ground state of a crystal could have anomalous surface states due to the presence of robust many-body quantum entanglement in the bulk. These materials are called topological, since the impossibility to remove the entanglement could be traced to a topological obstruction. A direct certification of the presence of such entanglement in real-world materials is, however, a very challenging task. In this talk, we will discuss how one can leverage the interplay between symmetry and locality to diagnose topologically nontrivial materials. More specifically, in the context of weakly correlated electronic systems, we will introduce the theory of symmetry indicators for band topology, which has enabled the the discovery of topological materials candidates on an unprecedented scale. We will also discuss how an alternative use of topology leads to strong constraints on the possible phases that emerging in strongly correlated quantum spin systems.
 

Hoi Chun (Adrian) Po is a condensed matter theorist interested in a broad range of topics, like topological crystalline phases of matter and non-equilibrium quantum dynamics. Adrian grew up in Hong Kong and obtained his bachelor's degree from the Chinese University of Hong Kong in 2013. He began his postgraduate studies at the University of California, Berkeley, but transfered to  Harvard University in 2016 when his advisor moved. He got his Ph.D. from Harvard in 2018, and is currently a Pappalardo Postdoctoral Fellow at the Massachusetts Institute of Technology.