Codes and Expansions (CodEx) Seminar
Bernhard Bodmann (University of Houston)
Polynomial embeddings as cheat codes for a real Game of Sloanes
This talk is concerned with optimal line packings associated with highly redundant real unit-norm frames. If the number of vectors in the frame becomes too large to admit equiangular arrangements, other geometric optimality criteria need to be found. Conway, Hardin and Sloane identified a quadratic embedding which maps equiangular lines to a simplex in a real Euclidean space and slightly larger sets of vectors forming an optimal packing to an orthoplex. A joint work with John Haas presented higher degree polynomial maps that embed certain unit-norm frames to simplices in high-dimensional Euclidean spaces. This talk first reviews the strategy used by Conway, Hardin and Sloane to establish some optimal packings and then studies a quartic embedding and its consequences.