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.

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The Optimal Transport Problem

• Optimal Transport in one dimension; Villani (73-78); Santambrogio (59-67)
• 1-Wasserstein metric, duality, and measures with unequal mass; Piccoli, Rossi, and Tournus A Wasserstein norm for signed measures, with application to nonlocal transport equation with source term

The 2-Wasserstein Metric

• Displacement convexity; Santambrogio (249-251,271-276); Villani (150-154)
• Asymptotic equivalence of $W_{2}$ and ${\dot {H}}^{-1}$; Santambrogio (209-211); Villani (233-235)
• This article has been partially written, but further contributions are welcome: Gradient flows in metric spaces, 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)

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: Optimization

• Fenchel-Rockafellar and Linear Programming; Brezis (15-17); Rockafellar, Variational Analysis (505-507)