Topological and geometrical properties of wave functions are becoming an indispensable tool with which to understand quantum phenomena in materials. By thinking about these properties, condensed matter physicists are uncovering a surprisingly rich set phenomena with overarching principles. These are relevant to numerous fields including optics, electronics, metamaterials, superconductivity and even quantum computation. However, the field is somewhat biased, and perhaps limited, by the tempting assumption of perfect crystalline symmetry. The advent of new material platforms, such as twisted heterostructures, amorphous solids, quasicrystals, and disordered systems, calls for a generalization of topological and geometrical properties to systems where crystalline symmetries are either absent, approximately satisfied, or only satisfied on average. In this talk I will give examples of the importance of geometry and topology to these fields, and how we aim to bridge the gap between the communities studying them.
Alexander Balatsky, Ivan Khaymovich, Dhruba Mitra, Florian Niedermann