What is a gapped (fracton) phase of matter?

Abstract: Over the past 15 years, there has been a remarkable amount of progress understanding gapped phases of quantum matter.  However, work on fracton phases makes it clear that we still have a lot to learn about gapped phases.  In fact, somewhat surprisingly, even the basic question of how to define gapped phases is more subtle and less understood than previously recognized.  In this talk, I will review a few key ideas in the theory of fracton systems, and will then sketch a single definition of gapped phases that behaves nicely for both fracton and topological systems.