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New mathematical insights and experimental techniques have led to a renewed interest in the rich phenomenology exhibited by flexible sheets. This has led to both a deeper understanding of thin elastic films and fluid membranes, and to the development of new structured surfaces that harness mechanical instabilities to control their properties. Examples include the fabrication of woven or fibrous sheets, the manipulation of internal order in liquid crystal elastomers, tailored nonuniform growth and buckling, and the coupling between electronic states and graphene buckling. The goal of the program is to bring together a diverse set of experts whose primary interests range from field theory, statistical mechanics, geometry, thermodynamics, and mechanical instabilities of thin soft materials. The program will explore potential links and address contemporary problems in biology and innovative material science.