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.  Assuming they satisfy a least-action principle from optimal transport theory, we classify them 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.

Bio-Sketch: Robert Pego received his Ph.D. in Applied Mathematics from UC Berkeley in 1982.Since 2004 he has been a professor at Carnegie Mellon University, becoming emeritus in 2022. His research focuses on dynamics in infinite-dimensional systems, especially stability of solitary waves and dynamics of clusteringand phase transitions. He was named a SIAM Fellow in 2009, an AMS Fellow in 2016, and received a Simons Fellowship for 2017. In 2017 he delivered the Lipshitz Lectures at the University of Bonn. He served SIAM as editor-in-chief of the SIAM Journal on Mathematical Analysis and chaired the activity group on Analysis of PDE.