Border Rank of Kronecker Square of a Small Coppersmith Winograd Tensor

I will discuss a refined border apolarity method that we used to determine the kronecker square of the small Coppersmith Winograd tensor when q=2. This tensor is also isomorphic to 3 X 3 permanents viewed as a tensor. This tensor is not subject to any known barrier for determining the exponent of matrix multiplication. I will review a little about the border apolarity method, which is one of the few known methods that are possible to distinguish cactus rank and border rank, and the difficulty it faces if the symmetry group of the tensor is too small. And I will explain how do we resolve the problem by putting a "Flag Condition" on border apolarity method that is enough for us to determine the border rank of 3X3 permanent tensor.

This seminar is part of the Problems in Algebraic Geometry Coming from Complexity Theory series.