The Mathematics of Monge-Kantorovich Optimal Transport
PIMS-IFDS-NSF Summer School, Seattle, Washington, USA, June 19-July 1, 2022
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Beschreibung
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.
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.
Gathers written notes from three lecture series Provides a lively introduction to the mathematical theory of Monge-Kantorovich optimal transport and applications Is not readily accessible outside of research papers
Autor*in
Young-Heon Kim
Themen in »The Mathematics of Monge-Kantorovich Optimal Transport«
optimal transport quadratic optimal transport harmonic approximation seminal regularity theory Euler-Lagrange equation Monge-Ampere equation variational regularity theory Neumann problem equilibrium transport substitutability Jacobi algorithm M-functions trajectory of cells developmental biology RNA transcripts