90 citations · 333 across the 51 of their papers we have counts for
50 papers
On Linear spaces of of matrices bounded rank
Hang Huang, J. M. Landsberg
Motivated by questions in theoretical computer science and quantum information theory, we study the classical problem of determining linear spaces of matrices of bounded rank. Spac…
Equivariant spaces of matrices of constant rank
J. M. Landsberg, L. Manivel
We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symple…
Secant varieties and the complexity of matrix multiplication
J. M. Landsberg
This is a survey primarily about determining the border rank of tensors, especially those relevant for the study of the complexity of matrix multiplication. This is a subject that…
Algebraic Geometry and Representation theory in the study of matrix multiplication complexity and other problems in theoretical computer science
J. M. Landsberg
Many fundamental questions in theoretical computer science are naturally expressed as special cases of the following problem: Let be a complex reductive group, let be a …
Towards finding hay in a haystack: explicit tensors of border rank greater than in
J. M. Landsberg, Mateusz Michałek
We write down an explicit sequence of tensors in , for all sufficiently large, having border rank at least , overcoming a longstanding barrier…
New lower bounds for matrix multiplication and the 3x3 determinant
Austin Conner, Alicia Harper, J. M. Landsberg
Let denote the matrix multiplication tensor (and write ) and let $det_3\in ( C^9)^{\o…