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The Banff International Research Station will host the "Workshop on Probabilistic and Extremal Combinatorics" workshop in Banff from September 1, 2019 to September 6, 2019. Combinatorics, sometimes also called Discrete Mathematics, is a branch of mathematics focusing on the study of discrete objects and their properties. Although Combinatorics is probably as old as the human ability to count, the field experienced tremendous growth during the last fifty years and is one of the most modern in today-s Mathematics, with numerous connections to different disciplines and various practical applications, ranging from designing VLSI chips to modeling complex social networks. Is it true that in any company of six people there are three who know each other, or alternatively are unfamiliar with each other? Can the countries of any planar map be colored with at most four colors so that no two countries that share a common boundary have the same color? In how many ways can one traverse all major cities of some country, visiting each city only once? If each link of a complex telephone network fails with probability p, what is the probability that Alice will not be to have a phone conversation with her friend Bob? Questions of this type are in the heart of modern Combinatorics, and especially two of its most central branches - Probabilistic and Extremal Combinatorics. The workshop will discuss some of latest developments in these fields, their connections and applications. 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).