Amorphous packings of hard objects are familiar in everyday life—seen in piles of grains, sand, cement, or even prescription pills. Their ubiquity may make them seem mundane, yet the underlying physics is anything but. The problem of particle packing is an ancient puzzle in physics and mathematics that has attracted sustained attention over the last millennium. Researchers have also long sought to uncover packing geometries and to use them as a route toward understanding the behavior of liquids and amorphous materials.
Hard-sphere systems, in particular, provide a powerful model for studying liquid–glass–crystal transitions. Extending the study to amorphous hyperspheres in higher-dimensional spaces not only deepens our understanding of glass formation in three dimensions but also connects the problem to fields such as signal digitization and error-correcting codes. Yet real-world systems often go beyond the idealization of hard spheres: they may be soft, polydisperse, or anisotropic in shape. Packing principles therefore also illuminate the structure and dynamics of foams, colloids, granular materials, emulsions, biological assemblies, and even protein folding.
Despite extensive research and reviews over the past quarter century, some of the most fundamental questions about packing remain unsettled. Even for the simplest particle models—frictionless hard spheres—the relationship between preparation methods and achievable packing density continues to generate debate. For more complex systems, new challenges emerge in linking microscopic interactions and particle shapes to large-scale organization.
This conference will present the latest physical and mathematical insights into the broad and enduring problem of particle packing, spanning systems from idealized hard spheres to the diverse packings found in nature and technology.