Stefan van Zwam: Properties of Lattices; a Semidefinite Programming Approach

Lattices and quadratic forms have been studied for hundreds of years. We concentrate on the notion of Korkin--Zolotarev (KZ)-reduced lattice bases, and show how a characterization of such bases in terms of quadratic forms can be relaxed to a semidefinite programming problem. We apply a branch-and-bound approach to this formulation to compute several intrinsic properties of low-dimensional KZ-reduced forms.