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Rezakhani, Ali Sharif University of Technology Title: Symmetry frcationalization and identification of topological phases Abstract: Identification of phases of quantum matter is an important problem in strongly correlated systems. Symmetry fractionalization is a symmetry-based method that helps characterize topological phases in one-dimensional systems. I will rview this method briefly, and show how this method can be used to conclusively identify quantum phases of some interesting Hamiltonians.