Amy Huang, Auburn University
"Matrix Multiplication Complexity: Tensor Geometry and Commutative Algebra"
Tensors are just multi-dimensional arrays. 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 matrix multiplication complexity and classification of special tensors. The first result computes the border rank of 3 X 3 permanent, which is important in the theory of matrix multiplication complexity. The second result classifies linear spaces of matrices of bounded rank 4, making progress on an old problem that has been open for decades in linear algebra society. I will also briefly discuss how the role of commutative algebra, algebraic geometry, and representation theory comes into the picture.
Zoom link: https://uwaterloo.zoom.us/j/2433704471?pwd=aXJoSDh0NDF0aFREbkthSnFBOUI4UT09