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Explore G-causal optimal transport theory in this 32-minute conference lecture that extends classical optimal transport by incorporating causality restrictions defined by directed graphs. Learn how this framework generalizes both traditional optimal transport and causal optimal transport problems, where transportation plans are constrained by graph-based causality conditions rather than temporal flow. Examine fundamental properties of G-causal optimal transport and the induced G-Wasserstein distance, with particular emphasis on identifying graph structures that preserve the triangle inequality—a key open problem in the field. Discover the introduction of lifted G-Wasserstein distances, which maintain metric properties and align with standard G-Wasserstein distances for measures with continuous disintegration kernels. Gain insights into this advanced mathematical framework that bridges optimal transport theory with graph-theoretic causality constraints, presented as part of the Workshop on Probabilistic Mass Transport at the Erwin Schrödinger International Institute for Mathematics and Physics.
