20 citations · 43 across the 10 of their papers we have counts for
5 papers · 1 filter
Polynomials and the exponent of matrix multiplication
Luca Chiantini, Jonathan D. Hauenstein, Christian Ikenmeyer +2
We define tensors, corresponding to cubic polynomials, which have the same exponent as the matrix multiplication tensor. In particular, we study the symmetrized matrix multipli…
Permanent v. determinant: an exponential lower bound assumingsymmetry and a potential path towards Valiant's conjecture
Joseph M. Landsberg, Nicolas Ressayre
We initiate a study of determinantal representations with symmetry. We show that Grenet's determinantal representation for the permanent is optimal among determinantal representati…
Connections between conjectures of Alon-Tarsi, Hadamard-Howe, and integrals over the special unitary group
Shrawan Kumar, J. M. Landsberg
We show the Alon-Tarsi conjecture on Latin squares is equivalent to a very special case of a conjecture made independently by Hadamard and Howe, and to the non-vanishing of some in…
Padded polynomials, their cousins, and geometric complexity theory
Harlan Kadish, J. M. Landsberg
We establish basic facts about the varieties of homogeneous polynomials divisible by powers of linear forms, and explain consequences for geometric complexity theory. This includes…
P versus NP and geometry
J. M. Landsberg
I describe three geometric approaches to resolving variants of P v. NP, present several results that illustrate the role of group actions in complexity theory, and make a first ste…