Algebra and Combinatorics Seminar

Date: February 10, 2017

Time: 3:00PM - 3:50PM

Location: BLOC 628

Speaker: Xiaoxian Tang, Texas A&M University

Title: Computing bounds for equiangular lines in Euclidean spaces

Abstract: Determining the maximum number of equiangular lines in a r-dimensional Euclidean vector space is an open problem in combinatorics, frame theory, graph theory, linear algebra and many related areas. So far the exact maximum number is only known for a few small dimensions. In this talk, we compute the upper bound of number of equiangular lines by combing the classical pillar decomposition and the semi-definite programming (SDP) method. Our computational results show an explicit bound, which is strictly less than the well-known Gerzon's bound for the dimensions between 44 and 400. Particularly, when the angles is arccos(1/5) or arccos(1/7), we dramatically improve the known SDP bounds.