DMS Colloquium: Dr. Amy Huang

Speaker: Dr. Amy Huang (Department of Mathematics, Texas A&M University)

Title: Tensor Ranks and Matrix Multiplication Complexity

Abstract: Tensors are just multi-dimensional arrays. Notions of rank and border rank abound in the literature. Tensor decomposition also has a lot of applications in data analysis, physics, and other areas of science. I will survey my recent two results about tensor rank and its application to matrix multiplication complexity. The first result relates different notions of tensor rank to polynomials of vanishing Hessian. The second one computes the border rank of 3 X 3 permanent, which is important in the theory of matrix multiplication complexity. I will also briefly discuss the newest technique we used to achieve our results: border apolarity. Furthermore, I will survey how this new technique helps us to compute/bound the border rank of a lot of tensors of interests that were considered to be inaccessible before.

Faculty Host: Ash Abebe