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In recent years there have been exciting new developments at the interface between elliptic integrable systems, special functions and quantum field theory. The aim of this workshop is to obtain a better understanding of the emerging links between these topics and to help bring out further unexpected connections in the future. This will be achieved by bringing together researchers from diverse areas in mathematics and physics, for a week of lectures and informal discussions. The workshop is the continuation of a series (Kyoto 2004, Bonn 2008, Leiden 2013, Vienna 2017). It is a satellite meeting of String Math 2019, which takes place on Uppsala 1-5 July. The main themes of the meeting are: Elliptic integrable systems, Elliptic hypergeometric functions, Elliptic and classical Painlevé equations, and New special functions emerging from quantum field theory