Austin Conner

activity

20182021

most citedNew lower bounds for matrix multiplication and the 3x3 determinant

12 citations · 14 across the 2 of their papers we have counts for

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4 papers · 1 filter

math.AG2021

Characteristic numbers and chromatic polynomial of a tensor

Austin Conner, Mateusz Michałek

We introduce the characteristic numbers and the chromatic polynomial of a tensor. Our approach generalizes and unifies the chromatic polynomial of a graph and of a matroid, charact…

math.AG2020★ 2 cited

Bad and good news for Strassen's laser method: Border rank of the 3x3 permanent and strict submultiplicativity

Austin Conner, Hang Huang, J. M. Landsberg

We determine the border ranks of tensors that could potentially advance the known upper bound for the exponent $ω$ of matrix multiplication. The Kronecker square of the small $q = 2$ …

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.AG2018

Towards a Geometric Approach to Strassen's Asymptotic Rank Conjecture

Austin Conner, Fulvio Gesmundo, Joseph M. Landsberg +2

We make a first geometric study of three varieties in $C^{m} \otimes C^{m} \otimes C^{m}$ (for each $m$ ), including the Zariski closure of the set of tight ten…