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The Banff International Research Station will host the "Classification Problems in von Neumann Algebras" workshop in Banff from September 29, 2019 to October 4, 2019. Von Neumann algebras are certain collections of infinite matrices, which were originally introduced as a tool to understand quantum mechanics, and representation theory of groups. They arise naturally in various contexts, notably from groups and their actions on measure spaces. A fundamental problem is: how much structure does a von Neumann algebra remember about the group or group action it was constructed from? The workshop will focus on this and related classification problems. This is a very active and broad research program, which has deep and fruitful connections with other areas of mathematics, including ergodic theory, group theory, and logic. The workshop will take advantage of these connections and capitalize on the spectacular breakthroughs made in the past few years to stimulate further progress and interaction. 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).