Explore a comprehensive lecture on quotient symmetry protected topological phenomena and quantum criticality delivered by Frank Pollmann from PCS Institute for Basic Science. Delve into the intriguing world of topological phenomena, examining their stability in parameter space even within trivial phases of matter. Investigate symmetry-protected topological phases and their trivialization through symmetry group extension. Discover how a quotient group emerging as a low-energy symmetry can stabilize a direct continuous quantum phase transition. Throughout the 48-minute talk, navigate through topics including general background, two Hamiltonians, different phases of matter, spin rotation symmetry, phase trivialization, the ionic Hubbard model, phase diagrams, string water parameters, generalizations, and quantum criticality. Gain valuable insights into this complex subject matter, drawing parallels to practical scenarios such as the distinction between liquid water and vapor.