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)
• 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

• Geodesics and generalized geodesics; Santambrogio (202-207), Ambrosio, Gilgi, Savaré (158-160)
• 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)
• Formal Riemannian Structure of the Wasserstein metric; Villani (245-247, 250-251); Ambrosio, Gigli, Savaré (189-191)

Numerical Methods for Optimal Transport

• Semidiscrete Optimal Transport (for $c(x,y)=|x-y|^{2}$); Santambrogio (242-248); Peyré Cuturi (85-89)
• Computing OT via Benamou-Brenier; Santambrogio (220-225); Peyré, Cuturi (102-108)
• Sliced Wasserstein Distance; Santambrogio (214-215); Peyré, Cuturi (166-169)
• Wasserstein Barycenters; Santambrogio (215-218); Peyré, Cuturi (138-144)

Applications of Optimal Transport

• Machine Learning Kolouri, et al, Optimal Mass Transport: Signal processing and machine-learning applications

Mathematical Foundations: Optimization

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

Mathematical Foundations: Differential Equations

• Gradient flows in metric spaces; Santambrogio (285-290) more refs