Voronoi diagrams and manifold learning

Abstract:

Voronoi diagrams can be observed in nature from the microscopic to the astronomical scale. They have been described by Descartes, reinvented many times, and are now used in almost all disciplines, including physics, biology, medecine, human sciences, and even in art.  The talk will emphasize the algorithmic side of the subject and focus on the application of Voronoi diagrams and Delaunay triangulations, their dual structures, to represent, discretize and learn the geometry of curved spaces of possibly high dimensions. These questions are ubiquitous in science and have become an essential part of scientific computing and data analysis.