Guillermo Nuñez Ponasso (東北大学)「Maximal determinants of matrices with entries over the roots of unity」
Hadamard's maximal determinant problem involves finding the maximum possible determinant of a +/- 1 square matrix. In this talk we will extend this problem to matrices over the roots of unity, and focus on the especially interesting case of third roots of unity. In particular, we will derive determinantal upper and lower bounds, as well as techniques to find candidate maximal determinant matrices of small order, and certify their maximality.