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Explore the fascinating world of flatbands in this comprehensive lecture by Alexei Andreanov. Delve into the construction of dispersionless single particle bands in various tight-binding settings and examine how their properties change when subjected to perturbations such as disorder or interactions. Learn about the potential of flatbands as hosts for unconventional and exotic phases of matter due to their quenched kinetic energy. Discover the emergence of non-perturbative metal-insulator transitions and ergodicity breaking, including many-body localization and many-body flatband localization, with connections to percolation transitions. Gain insights into weak ergodicity breaking and understand the implications of these phenomena in the context of flatband systems.
