Naslov
Geometry of numbers - Delaunay polytopes in lattices

Autori
Dutour Sikirić, Mathieu ; Schurmann, Achill ; Vallentin, Frank

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Seminar za teoriju brojeva i algebru, PMF Mathematicki odjel Zagreb / - , 2005

Skup
Seminar za teoriju brojeva i algebru, PMF Mathematicki odjel Zagreb

Mjesto i datum
Zagreb, Hrvatska, 09.03.2005

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Domaća recenzija

Ključne riječi
Lattice; polytope; covering; semidefinite programming

Sažetak
Given a lattice L, a polytope P is called a Delaunay polytope if the set of its vertices is S inter L with S being an empty sphere. The set of lattices of R^n correspond to the cone of positive definite symmetric matrices. If one prescribe the Delaunay polytopes of the lattice, then the corresponding set of matrices is a polyhedral cone called a L-type. A lattice covering is a set of balls x+B(0, R) with x belonging to a lattice L and such that every point belongs to at least one ball. The optimization of the covering density (also called inhomogeneous minimum) of lattice belonging to a fixed L-type is a semidefinite programming problem. We introduce an equivariant setting for that theory, i.e. we see what happens when one considers lattices invariant under a fixed symmetry group. Using this theory, we find good coverings in dimension 6 and above.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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