📔 Optimal Transport
Graduate Course, UCSB, 2022
📌 Logistics: These notes are from Math 260J: Optimal Transport (Winter 2022), taught by Prof. Katy Craig at UC Santa Barbara (course page), which I worked through on my own.
- Lec-1: Introduction to OT
- Lec-2: The Monge problem
- Lec-3: From transport maps to transport plans
- Lec-4: The Kantorovich problem
- Lec-5: Compactness in the narrow topology
- Lec-6: Lower semicontinuity in the narrow topology
- Lec-7: Narrow vs wide topology and intro to convex analysis
- Lec-8: The subdifferential and duality
- Lec-9: Equiv of primal and dual optimization problems
- Lec-10: Equiv of primal and dual Kantorovich problems I
- Lec-11: Optimal plans: the Knott-Smith criterion
- Lec-12: Optimal maps: Brenier’s characterization
- Lec-13: Definition of Wasserstein metric
- Lec-14: Approximation of measures by convolution
- Lec-15: Wasserstein metric: triangle inequality and topology
- Lec-16: Curves in the space of probability measures
- Lec-17: Duality again: Benamou Brenier
- Lec-18: The continuity equation and Wasserstein geodesics
- Lec-19: Characterization of absolutely continuous curves (part 1)
- Lec-20: Characterization of absolutely continuous curves (part 2)