Tutte seminar - Aidan Roy

Complex spherical codes and designs

Abstract:

Real spherical designs have been shown by Delsarte, Goethals, and Seidel to give rise to association schemes when the strength of the design is high compared to its degree as a code. In contrast, designs on the complex unit sphere remain relatively uninvestigated, despite their importance in numerous applications. In this talk, I will first give an introduction to spherical designs and explain their usefulness and connections to other combinatorial structures such as block designs, binary codes, and regular polytopes. I will then introduce a new type of complex design which, in contrast with real spherical designs and projective designs, gives rise to nonsymmetric association schemes. This talk is based on joint work with Sho Suda.