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A common intuition in dynamical systems is that systems with low complexity should have some sort of structure, while systems with high complexity should exhibit more randomness. We explore this notion in various settings, particularly focussing on recent developments in ergodic theory and symbolic dynamics that are related to combinatorial, number theoretic, and algebraic problems. Fine properties of sequences of numbers can be studied via dynamics, relating the complexity of the sequence to hidden structures it contains. The proposed meeting will cover such recent evelopments, bringing together mathematicians from a variety of fields, including ergodic theory, symbolic dynamics, number theory, and group theory to discuss on long-standing open problems that have implications for these fields.