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We want to bring together both leading experts and active researchers of the three areas involved to explain their latest results, new ideas and open problems on the subject, and always addressing their talks to a wide and diverse audience. Our list of speakers already covers a wide range of topics: Commutative and noncommutative cluster theory, the interplay between homotopy theory, K-theory and algebraic geometry, algebraic symbolic dynamics, infinite dimensional representation theory are some of the topics that are already represented in the conference.