New article ideas

Below, you can find a list of new article ideas and suggested references. (Feel free to incorporate additional references! Please list all references you use at the bottom of your article.) If you choose to write about one of these ideas, remove it from the list below and create a new link on the main page.

Want to write about something that's not listed here? Email me!

The Optimal Transport Problem

• Optimal transport in one dimension; Villani (73-78); Santambrogio (59-67)

Variants of Optimal Transport Problems

• Multi-marginal optimal transport and density functional theory (perhaps discussing applications in economics or density functional theory); Figalli-Glaudo(105-106); Santambriogio (48-51)
• Entropic optimal transport and the Schrödinger bridge problem [1][2]

The 2-Wasserstein Metric

• Benamou-Brenier dynamic characterization of W2; Santambrogio (187-198); Villani (238-249) (make sure to cite existing wiki article on Geodesics and generalized geodesics)
• Displacement convexity; Santambrogio (249-251,271-276); Villani (150-154) (make sure to cite existing wiki article on Geodesics and generalized geodesics)
• 2-Wasserstein metric and Ricci curvature; Figalli-Glaudo (112-114); [3]

Numerical Methods for Optimal Transport

• Computing OT via Benamou-Brenier; Santambrogio (220-225); Peyré, Cuturi (102-108)
• Wasserstein Barycenters; Santambrogio (215-218); Peyré, Cuturi (138-144)

Mathematical Foundations:

• Gradient flows in metric spaces; Figalli-Glaudo (107-108); Santambrogio, 'OT for Applied Mathematicians' (285-290); Santambrogio, 'Euclidean, Metric, and Wasserstein GFs' (90-107; don't need to cover all topics, just what interests you)

Applications:

• Wasserstein Generative Adversarial Networks [4], [5]
• Optimal transport methods in economics; see introduction of book by Galichon (I have a copy you can borrow) and [6]
• Quantization and Lloyd's algorithm [7], [8], [9]