报告主题：Classifying complex Hadamard matrices and Equiangular Tight Frames
报告人：Ferenc Szollosi Postdoctoral （Aalto University）
报告时间：2019年7月3日（周三）10:00
报告地点：校本部G507
邀请人： Mikio Nakahara
主办部门：太阳成集团tyc33455数学系
报告摘要：A complex Hadamard matrix of order n is an nxn matrix of complex unimodular entries with pairwise orthogonal rows. In this talk I will survey some results on the classification of complex Hadamard matrices of small orders. I will treat the case n=5 in detail, but I will also briefly touch upon higher order matrices. The main conceptual challenge is finding and describing the unimodular solutions of a system of polynomial equations. I will introduce several techniques to deal with these, including analytic tricks and general-purpose computational tools for computing a Groebner basis. These are frequently used in experimental mathematics for discovering new matrices.
As an application of this methodology, I will show how I leveraged on these ideas to fully classify all complex equiangular tight frames in dimension three. In particular, these methods led to a rigorous proof of the nonexistence of a complex equiangular tight frame formed by 8 unit vectors in dimension three.
I will conclude the talk with a list of pressing unresolved problems related to this research area.
欢迎教师、员工参加！
