Optimal transport

Optimal transport is a mathematical theory linking probability to
geometry. Originally proposed in operations research and mathematical
theory, OT has experienced reinvigorated interest in machine learning,
computer vision, graphics, and other applied disciplines thanks to new
efficient algorithms and a variety of applications. In this tutorial,
I will summarize the basic constructions in optimal transport theory
as well as algorithms for evaluating transport distances in practice.
We will conclude by surveying a few of the many modern computational
applications of optimal transport and some open problems in this
discipline. Emphasis will be put on developing intuition rather than
formalism.