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Explore the mathematical concept of the directed landscape in this conference talk that delves into one of the most significant developments in probability theory and integrable systems. Learn about this universal object that emerges as the scaling limit of various discrete models in the Kardar-Parisi-Zhang universality class, including last passage percolation, TASEP, and random matrix theory. Discover how the directed landscape provides a unified framework for understanding fluctuations in growth processes and interface dynamics. Examine the construction of this random field through Airy processes and understand its remarkable geometric and probabilistic properties. Gain insights into the connections between the directed landscape and other areas of mathematics, including representation theory and algebraic geometry, while exploring recent breakthroughs in understanding its structure and applications to solving long-standing problems in probability theory.
