QLunch: Jeong-Hoon Ju

Speaker: Jeong-Hoon Ju

Title: The Border Rank of 4 x 4 Determinant Tensor is 12

Abstract: For a given tensor, its tensor rank is defined as the smallest number of decomposable tensors required to express the tensor as the sum of them, and its border rank is defined as the smallest number such that the tensor can be expressed as the limit of tensors of tensor rank at most the number. Both are natural generalizations of matrix rank, but finding these ranks for a given tensor is regarded as a challenging problem, because the methods to determine the matrix rank have not been generalized to the tensor and border ranks yet. Even for fundamental tensors such as matrix multiplication, determinant, and permanent tensors, their tensor rank and border rank remain only partially understood. In this talk, I determine the border rank of the 4 × 4 determinant tensor to be twelve.
This is joint work with Jong In Han and Yeongrak Kim.