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The field of colloidal semiconductor nanocrystals is flourishing at the frontiers of discovery in nanoscience and nanotechnology. Recent advances in synthesis have enabled unprecedented properties and phenomena in diverse materials systems, including novel perovskite, pnictide, and multinary nanocrystals. Atomistic understanding of surfaces, dopants, and defects is facilitating systems-level design and integration of nanocrystals with other materials for applications in displays, (opto)electronics, energy, catalysis, biology, medicine, and sensing. Innovations in assembly, oriented attachment, and surface chemistry herald high-performance nanocrystal solids and metamaterials with emergent collective properties. The 2020 GRC brings the community together to discuss major advances, pressing challenges, and new directions, build collaborations, and foster the next generation of scholars in this vibrant interdisciplinary field.