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The Banff International Research Station will host the "Geometry of Real Polynomials, Convexity and Optimization" workshop in Banff from May 26, 2019 to May 31, 2019. On the one hand, a systematic study of nonnegative polynomials already appeared in Minkowski-s early work in the 19th century. Then, Hilbert, in his famous address at the International Congress of Mathematicians in 1900, asked for characterizations of nonnegative polynomials, including this question in his research agenda setting list of foundational problems. On the other hand, researchers like Petrovksy in the classical area of partial differential equations were laying the foundations for the theory of hyperbolic polynomials. By the beginning of the 21st century, these two areas started interacting deeply with optimization as well as theoretical computer science. This interaction recently led to solutions of many important open problems, new breakthroughs and applications. This workshop will bring together established experts and young researchers from the areas of real algebraic geometry, the geometry of polynomials, and convex and polynomial optimization, to review the most recent significant discoveries and strive to forge new connections. 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).