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The problem of how densely solid objects can pack in space has been a source of fascination since the dawn of civilization. The dense packing of objects is intimately related to the arrangement of molecules in condensed states of matter and to the best way to transmit encoded messages over a noisy channel. Considerable progress has been made with the dense ordered packing of hard spheres, notably Hales’ proof of the famous Kepler conjecture. Similarly, the random packing of hard spheres now occupies a canonical position in granular physics with deep connections to jamming, thermodynamics and the glass transition. However, over the last two decades the field of packing problems has broadened considerably to encompass the packing of anisotropic particles (e.g. ellipsoids and polyhedra) and the packing of soft “squishy” particles. This has been driven in part by the rise of soft condensed matter physics - which is ever producing new building blocks (to play) or pack with – as well as advances in computer hardware/software enabling the ready simulation of anisotropic particles.
This workshop will take a broad view of recent advances within the context of the previous work on hard spheres. Particular questions that will be addressed include: what can proofs of hard sphere packings tell us about constructing proofs of the densest packings of anisotropic particles? Can packings of soft objects be given a rigorous mathematical definition? What do packing problems tell us about morphogenesis in biological systems – to which there are many similarities.
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