Sphere Packings, Lattices, Groups, and Infinite Dimensional Algebra

  title={Sphere Packings, Lattices, Groups, and Infinite Dimensional Algebra},
  author={Lisa Carbone},
The problem of packing identical spheres as densely as possible in Euclidean space has a 400 year history, having been initiated by Johannes Kepler in 1611 [Ke]. Though the problem is unsolved in general today, attempts to solve it have led to the discovery of a wealth of mathematics. Most of the densest known sphere packings are lattice packings. A lattice in R is an additive subgroup L ⊂ R which is generated by some basis for the real vector space R. A lattice packing in R is then a sphere… CONTINUE READING
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