The Mathematics of Monge-Kantorovich Optimal Transport

This book gathers written notes from three lecture series presented at the PIMS–IFDS–NSF Summer School on Optimal Transport, held at the University of Washington in June 2022. The summer school was the first major event organized by the Kantorovich Initiative, a nascent research consortium linking several universities in the Pacific Northwest and dedicated to advancing the mathematics of Monge–Kantorovich transport problems and their many applications. The mini-courses offered during the summer school—and the lecture notes collected here—are poised to have a substantial impact on the next generation of optimal transport researchers. The range of topics included in this volume reflects the remarkable breadth of contemporary research in the field. Felix Otto and Lukas Koch’s contribution, based on Otto’s mini-course, presents a variational perspective on the regularity theory of optimal transport. Alfred Galichon and Antoine Jacquet’s notes, drawn from Galichon’s mini-course, explore the links between optimal transport and matching models in economics. Finally, Geoffrey Schiebinger’s notes survey his mini-course on applications of optimal transport in developmental biology.