组合数学讨论班

报告题目: Maximal determinants of roots of unity matrices

报 告 人: Dr Guillermo Ponasso (Tohoku University)

时      间: 11:00-12:00, September 26, 2025

地      点：820 Haina Complex Building 2

摘      要: Hadamard posed the question of determining the maximal determinant of a +/-1 matrix of any given order. A special family of matrices maximizing the determinant are Hadamard matrices, but these can only exist at orders n a multiple of 4, when n>2. Hadamard matrices are very interesting mathematically, but also for its wide range of practical applications. Much work has been done in maximizing the determinant of +/-1 matrices when the order n is odd or when it is even, but not divisible by 4.  More recently, complex Hadamard matrices, and in particular Hadamard matrices with roots of unity entries, have drawn many people's attention, also because of practical applications. But much less is known about general (non-Hadamard case) maximal determinant matrices over the roots of unity. In this talk I will give an account of three special cases: the classical +/-1 problem, the problem over the third roots of unity, and the problem over the fourth roots.