Stochastic and Multiscale Modeling and Computation Seminar by Robert Pego: Breaking Glass Optimally and Minkowski's Problem for Polytopes

Speaker: Robert Pego, Carnegie Mellon University

Title: Breaking Glass Optimally and Minkowski's Problem for Polytopes

Abstract: Motivated by a study of least-action incompressible flows, we study all the ways that a given convex body in Euclidean space can break into countably many pieces that move away from each other rigidly at constant velocity, following geodesic motions in the sense of optimal transport theory. These we classify in terms of a countable version of Minkowski's geometric problem of determining convex polytopes by their face areas and normals. Illustrations involve a number of curious examples both fractal and paradoxical, including Apollonian packings and other types of full packings by smooth balls.

 

Stochastic and Multiscale Modeling and Computation