Well-rounded lattices from algebraic constructions

09/16/2014 - 12:15pm
09/16/2014 - 1:10pm
Lenny Fukshansky (CMC)

Well-rounded lattices are vital in extremal lattice theory, since the classical optimization problems can usually be reduced to them. On the other hand, many of the important constructions of Euclidean lattices with good properties come from diferent algebraic settings. This prompts a natural question: which of the lattices coming from algebraic constructions are well-rounded? We consider three such well known algebraic constructions: ideal lattices from number fields, cyclic lattices from quotient polynomial rings, and function field lattices from curves over finite fields. In each of these cases, we provide a partial answer to the above question, as well as discuss some generalizations and directions for future research.

Mudd Science Library 126, Pomona College