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1 Lecture 1: Preliminary notions and the Monge problem |
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2 Lecture 2: The Kantorovich problem |
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3 Lecture 3: The Kantorovich - Rubinstein duality |
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4 Lecture 4: Necessary and sufficient optimality conditions |
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5 Lecture 5: Existence of optimal maps and applications |
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6 Lecture 6: A proof of the Isoperimetric inequality and stability in Optimal Transport |
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7 Lecture 7: The Monge-Ampére equation and Optimal Transport on Riemannian manifolds |
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8 Lecture 8: The metric side of Optimal Transport |
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9 Lecture 9: Analysis on metric spaces and the dynamic formulation of Optimal Transport |
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10 Lecture 10: Wasserstein geodesics, nonbranching and curvature |
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11 Lecture 11: Gradient flows: an introduction |
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12 Lecture 12: Gradient flows: the Brézis-Komura theorem |
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13 Lecture 13: Examples of gradient flows in PDEs |
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14 Lecture 14: Gradient flows: the EDE and EDI formulations |
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15 Lecture 15: Semicontinuity and convexity of energies in the Wasserstein space |
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16 Lecture 16: The Continuity Equation and the Hopf-Lax semigroup |
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17 Lecture 17: The Benamou-Brenier formula |
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18 Lecture 18: An introduction to Otto’s calculus |
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19 Lecture 19: Heat flow, Optimal Transport and Ricci curvature |
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1 Lecture 1: Preliminary notions and the Monge problem |
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2 Lecture 2: The Kantorovich problem |
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3 Lecture 3: The Kantorovich - Rubinstein duality |
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