Naslov
Lattice Sphere Packings

Autori
Dutour Sikirić, Mathieu

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, pp prezentacija, znanstveni

Izvornik
Seminar of computational homology and applications, National university of Ireland, Galway / - , 2007

Skup
Seminar of computational homology and applications, National university of Ireland, Galway

Mjesto i datum
Galway, Irska, 24.09.2007

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
lattice; packing; perfect form

Sažetak
A sphere packings is a family of balls of the same radius, whose interior do not overlap. A lattice sphere packing is a sphere packing, whose ball centers belong to a lattice v_1 Z+ .... + v_n Z. The lattice sphere packing problem is to find the lattice sphere packings of highest density. It is solved in dimensions 1, 2, 3, 4, 5, 6, 7, 8 and 24. I will present extensively the Gram matrix formalism, which allows us to replace lattices by positive definite matrices. Then I will present extensively the Voronoi algorithm, which gives a GL_n(Z) invariant tesselation of the cone S^n_{; ; ; ; >0}; ; ; ; of positive definite matrices. This algorithm works up to dimension 8. Next, as a side dish, I will present the alternative theories of Korkine Zolotarev and Cohn-Elkies, which allow to get dimension 24.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA