演講公告

演講主題：Equiangular lines and spherical designs
主講人：俞韋亘教授 (密西根州立大學)
演講日期：2015年10月20日(星期二) 14:00 - 15:00
演講地點：(光復校區) 科學一館223室
茶會時間：當天下午1:30 (科學一館205室)
摘要內容：
A set of lines in Rn 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 Rn, using semidefinite programming to improve the upper bounds on this quantity. Improvements are obtained in dimensions 24≤n≤136. In particular, we show that the maximum number of equiangular lines in Rn is 276 for all 24≤n≤41 and is 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.
相關檔案：演講1041020.doc

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