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The Banff International Research Station will host the "Advances in Dispersive Equations: Challenges & Perspectives" workshop in Banff from June 30, 2019 to July 5, 2019. This workshop provides a forum for international experts in the mathematical analysis of nonlinear dispersive partial differential equations — a type of equation which models wave-like behaviour in such diverse physical settings as water waves, Bose-Einstein condensates, gravitation, lasers, and ferromagnets — to survey the state-of-the art, and exchange ideas on promising future directions of research. The main themes include global dynamics and soliton resolution; wave turbulence and KAM theory; stochastic waves; and numerical methods for dispersive equations. The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada-s Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta-s Advanced Education and Technology, and Mexico-s Consejo Nacional de Ciencia y Tecnología (CONACYT).