报告题目：New bounds for equiangular lines and spherical two-distance sets
报告人：俞韋亘（Wei-Hsuan Yu, National Central University）
时间：2019年6月7日（星期五）10:30—11:30
地点：苏州大学本部精正楼（数学楼）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, k∈N. 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.
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