distance, Monge-Kantorovich problem, Wasserstein distance) has witnessed a lot of applications: Theory (Brenier, Gangbo, Villani, Figalli, et.al.); Gradient flows (Otto, Villani, Maas, Miekle, et.al.); Proximal methods (Jordan, Kinderlehrer, Otto et.al.); Physics: GENERICs/Pre-GENERICs (Grmela and Ottinger, Doung et.al.), Flux-gradient flows (Li, Liu, Osher); Mean field games (Larsy, Lions et.al.); Population games; Evolutionary game theory (Degond, Liu, Li, et.al.); Image processing (Rubner et.al. 2000, Tannenbaum, Georgiou, et.al.); Inverse problems (Stuart, Li, Osher, et.al.); Scientific computing: (Benamou, Brenier, Carillo, Oberman, Peyre, Osher, et. al.) AI and Machine learning: See NIPS, ICLR, ICML 2015– 2023. Minimal surfaces in Wasserstein spaces (Li, Georgiou); Wasserstein common noises (Li); 10