## Speaker:

Carmelo Interlando

## Speaker Link:

## Institution:

San Diego State University

## Time:

Tuesday, May 9, 2017 - 2:00pm to 3:00pm

## Host:

## Location:

RH 340P

In this talk a lattice will mean a discrete subgroup Λ of *n*-dimensional Euclidean space; the sphere packing associated to Λ is the arrangement of congruent spheres of radius equal to one half the minimum distance of Λ and centered at the lattice points. The main parameter under consideration will be the packing density of the arrangement of spheres. With this in mind, a family of *p*-dimensional lattices will be constructed from submodules *M* of the ring of integers of a cyclic number filed *L *of degree *p*, where *p* is an odd unramified prime in *L/ Q*. The density of the associated sphere packing will be determined in terms of the nonzero minimum of the trace form in

*M*and the discriminant of

*L*.