Collection

Special Issue: Information Geometry and Optimal Transport

Optimal transport is an interdisciplinary field of mathematics at the intersection of probability, analysis, and geometry. Originally conceived by Monge in 1781 as a problem of finding the most efficient transportation of resources, the modern framework was developed by Kantorovich and others in the early 1900s as a problem of finding optimal coupling between two probability measures characterizing the transported resource. In recent decades, the field of optimal transport has flourished due to its deep connections with many different areas of mathematics and ever expanding applications in other fields.

Connections between the geometry of optimal transport (Wasserstein geometry) and information geometry have also started to emerge. The aim of this Collection is to explore some of these developments and their applications of this promising area of research.

Editors

  • Jun Zhang

    Jun Zhang is a Professor of Psychology and Professor of Statistics at the University of Michigan, Ann Arbor, USA.

    His main research in information geometry has been on divergence functions, embedding functions, deformation models, embedding functions, and linking statistical structure to symplectic, (para-)Hermitian, and (para-)Kahler geometry. He is also interested in application of information geometry to theoretical physics (geometric mechanics, thermodynamics, and quantum information), and to neural-cognitive and machine learning systems.

  • Gabriel Khan

    Assistant Professor, Department of Mathematics, Iowa State University

Articles (9 in this collection)