Besides being interesting in their own right, algebraic lattices have proven immensely useful in wireless communications. This project studies a certain useful property of such lattices, called well-roundedness, which helps the transmission when the signal quality is low as well as in the presence of an eavesdropper. On the more theoretical side, we connect this lattice property to long-standing open conjectures in number theory known as the Minkowski and Woods conjectures. The employed tools mainly come from algebraic number theory, lattice theory, and communications theory.

2022

2026