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The Banff International Research Station will host the "Probing the Earth and the Universe with Microlocal Analysis" workshop in Banff from April 14, 2019 to April 19, 2019. We use mathematics to model problems arising in seismic imaging and cosmological tomography. The workshop will gather researchers in who study this problem from different perspectives. This synergy will lead to progress and discovery of further areas of research. 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).