A Sampler of Combinatorial Problems on Spheres
|Speaker:||William J. Martin|
|Affiliation:||Worcester Ploytechnic Institute|
|Room:||Mathematics 3 (M3) 3103|
In my first month as a graduate student at the University of Waterloo, I somehow selected an advisor (and that is a story entirely of its own) and asked him to give me a paper to read. Chris Godsil gave me a paper in which he proved that, aside from complete multipartite graphs, there are finitely many distance-regular graphs having an eigenvalue of any given multiplicity $m\ge 3$.
This exploration, and a visit to Waterloo by Jaap Seidel in May 1989, had a lasting impact on me. Ever since, I have been regularly interested in
problems involving finite point sets on the unit sphere. In this talk, I will survey a few of these problems.
I will start with some of the more famous problems such as the kissing number problem and the equiangular lines problem. Then I will mention
a few problems from my own work, including a minimum distance bound for error-correcting codes, the dual Bannai-Ito Conjecture, real mutually unbiased bases, and systems of almost orthogonal vectors. Various applications will appear throughout the talk.
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