No dia 17 de maio, pelas 17h30, László Szabó, da Universidade Eötvös Loránd, Hungria, apresenta uma talk subordinada ao tema “12-neighbour packings of unit balls in E³”, na sala E.4.7.
A packing of unit balls in E³ is said to be a 12-neighbour packing if each ball is touched by 12 others. A 12-neighbour packing of unit balls can be constructed as follows. Consider a horizontal hexagonal layer of unit balls in which the centres of the balls are coplanar and each ball is touched by six others. Put on the top of this layer a second horizontal hexagonal layer of unit balls so that each ball of the first layer touches three balls of the second layer. The translation which carries the first layer into the second one, carries the second layer into a third one, and repeated translations of the same kind in both directions produce a packing of unit balls in which each ball has 12 neighbours. László Fejes Tóth conjectured that any 12-neighbour packing of unit balls in E³ is composed of such hexagonal layers. The aim of this talk is to give a proof of this conjecture.
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