Our understanding of quantum dynamics of many-body systems has been reshaped in the past two decades by new insights about the topology of quantum states. Recent theoretical and experimental progress on synthetic quantum systems, such as cold atoms in optical lattices, trapped ions, and solid-state heterostructures subject to periodic potentials in space and time, has ushered in a new era of engineered quantum matter in and out of equilibrium. A central theme of this progress is the exquisite in-situ control allowing the realization and study of novel quantum phases of matter and transitions among them. In this context, Professor Seradjeh will present recent and ongoing theoretical work on proposed realizations, detection, and applications of non-equilibrium topological phases of matter in synthetic quantum systems. These include Floquet topological phases with multiple bound states that follow a universal pattern, their efficient measurement in driven optical lattices, novel phases of graphene structures irradiated by circularly polarized lasers, higher-order topological phases that support fractionally charged corner and bulk bound states, and topological gauge pumps that can detect ground-state degeneracies and can be realized in driven trapped ions.
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