J. Landsberg

activity

19952023

most citedRanks of tensors and a generalization of secant varieties

90 citations · 333 across the 51 of their papers we have counts for

collaborators

Showing 2019Show all

4 papers · 1 filter

cs.CC2019★ 2 cited

Towards finding hay in a haystack: explicit tensors of border rank greater than $2.02 m$ in $C^{m} \otimes C^{m} \otimes C^{m}$

J. M. Landsberg, Mateusz Michałek

We write down an explicit sequence of tensors in $C^{m} \otimes C^{m} \otimes C^{m}$ , for all $m$ sufficiently large, having border rank at least $2.02 m$ , overcoming a longstanding barrier…

math.AG2019★ 12 cited

New lower bounds for matrix multiplication and the 3x3 determinant

Austin Conner, Alicia Harper, J. M. Landsberg

Let $M_{⟨ u, v, w ⟩} \in C^{uv} \otimes C^{v w} \otimes C^{w u}$ denote the matrix multiplication tensor (and write $M_{n} = M_{⟨ n, n, n ⟩}$ ) and let $det_3\in ( C^9)^{\o…

math.RT2019★ 8 cited

Tensors with maximal symmetries

Austin Conner, Fulvio Gesmundo, Joseph M. Landsberg +1

We classify tensors with maximal and next to maximal dimensional symmetry groups under a natural genericity assumption (1-genericity), in dimensions greater than 7. In other words,…

cs.CC2019★ 13 cited

Rank and border rank of Kronecker powers of tensors and Strassen's laser method

Austin Conner, Fulvio Gesmundo, Joseph M. Landsberg +1

We prove that the border rank of the Kronecker square of the little Coppersmith-Winograd tensor $T_{c w, q}$ is the square of its border rank for $q > 2$ and that the border rank of…

Towards finding hay in a haystack: explicit tensors of border rank greater than 2.02m in Cm⊗Cm⊗Cm

New lower bounds for matrix multiplication and the 3x3 determinant

Tensors with maximal symmetries

Rank and border rank of Kronecker powers of tensors and Strassen's laser method

Towards finding hay in a haystack: explicit tensors of border rank greater than $2.02 m$ in $C^{m} \otimes C^{m} \otimes C^{m}$