While the relationship between periods and mirror symmetry has been studied for some time, it has been receiving new inputs in recent years from diverse fields such as homological mirror symmetry, tropical geometry, string theory, and (noncommutative) topological K-theory. The workshop brought together experts from these fields bringing complementary expertise to a topic of mutual interest, which is ripe for collaboration. The prospect of bringing Kontsevich’s powerful homological mirror symmetry conjecture to bear on the study of periods is particularly timely, in view of the rapid developments in HMS in recent years. One concrete objective motivating the workshop was to establish the connection between HMS and periods, by proving that the topological K-theory of the Fukaya category corresponds to the Gamma integral structure. The recently-developed string-theoretic understanding of the Gamma integral structure may play an important role here.