Optimal Transport on Discrete Domains Notes for AMS Short Course on Discrete Differential Geometry

Many tools from discrete differential geometry (DDG) were inspired by practical considerations in areas like computer graphics and vision. Disciplines like these require fine-grained understanding of geometric structure and the relationships between different shapes—problems for which the toolbox from smooth geometry can provide substantial insight. Indeed, a triumph of discrete differential geometry is its incorporation into a wide array of computational pipelines, affecting the way artists, engineers, and scientists approach problem-solving across geometry-adjacent disciplines.