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The Banff International Research Station will host the "Topology and Measure in Dynamics and Operator Algebras" workshop in Banff from September 8, 2019 to September 13, 2019. The theory of operator algebras was conceived by von Neumann in the 1920s as a rigorous framework for quantum mechanics and the idea of continuous dimensionality. Since that time the subject has enjoyed a rich and multifaceted relationship with both measurable and topological dynamics, which classically study the time evolution of physical systems and provide coordinate systems for understanding operator-algebraic structure. Recent advances in all of these areas have called for deeper and more coordinated investigations into the relations between measure and topology, and the workshop will provide a dedicated occasion for the pursuit of this program. 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).