天元讲堂: New bounds for equiangular lines and spherical two-distance sets


報告題目New bounds for equiangular lines and spherical two-distance sets

報告人:俞韋亘Wei-Hsuan Yu, National Central University

時間201967日(星期五)10:30—11:30

地點:蘇州大學本部精正樓(數學樓)307

 

摘要The set of points in a metric space is called an s-distance set if pairwise distances between these points admit only s distinct values. Two-distance spherical sets with the set of scalar products {α, -α}, α  [0,1), are called equiangular. The problem of determining the maximal size of s-distance sets in various spaces has a long history in mathematics. We determine a new method of bounding the size of an s-distance set in two-point homogeneous spaces via zonal spherical functions. This method allows us to prove that the maximum size of a spherical two-distance set in R^n is n(n+1)/2 with possible exceptions for some n=(2k+1)^2?3, kN. We also prove the universal upper bound : 2n/3 a^2 for equiangular sets with α=1/a and, employing this bound, prove a new upper bound on the size of equiangular sets in an arbitrary dimension. Finally, we classify all equiangular sets reaching this new bound.

 

報告人主頁 http://w2.math.ncu.edu.tw/member/full/65

 

 

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