Codes and Expansions (CodEx) Seminar

Lenny Fukshansky (Claremont McKenna College)
On lattices generated by frames

Tight frames in Euclidean spaces are widely used generalizations of orthonormal bases. Some particularly nice classes of such frames are irreducible group frames and equiangular tight frames (ETFs). Integer spans of rational tight frames often form Euclidean lattices with some notable geometric properties. We discuss constructions of such lattices, focusing on an especially interesting infinite family in arbitrarily large dimensions, which comes from vertex transitive graphs. We demonstrate several examples of lattices from graphs with particularly nice geometric properties. We also discuss some remarkable lattices generated by ETFs.