2015-10-19 16:00 ~ 2015-10-19 17:00
Prof. Wei-Hsuan Yu (俞韋亘), Michigan State University
綜合三館4F Lectute Room B
學術演講-Equiangular lines and spherical designs
Abstract:
A set of lines in R^n is called equiangular if the angle between each pair
of lines is the same. We address the question of determining the maximum
size of equiangular line sets in R^n, using semidefinite programming to
improve the upper bounds on this quantity. Improvements are obtain in
dimensions 23<=n <=136. In particular, we show that the maximum number of
equiangular lines in R^n is 276 for all 24 <=n <=41 and 344 for n=43. This
provides a partial resolution of the conjecture set forth by Lemmens and
Seidel (1973). We also study the existence problem for tight spherical
designs of harmonic index T. We prove the nonexistence of tight {8,4}
designs by using the theory of elliptic diophantine equations, and the
semidefinite programming method of eliminating some 2-angular systems for small dimensions.
Tea Time: 3:30PM, R707
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