In the light bulb problem, one is given as input vectors x_1,...,x_n,y_1,...,y_n∈{-1,1\}^d which
are all uniformly random. They are all chosen independently except for a planted pair …

The asymptotic restriction problem for tensors s and t is to find the smallest β≥ 0 such that
the n th tensor power of t can be obtained from the (β n+ o (n)) th tensor power of s by …

We determine defining equations for the set of concise tensors of minimal border rank in C
m⊗ C m⊗ C m when m= 5 and the set of concise minimal border rank 1∗-generic tensors …

We review the open problems in the theory of deformations of zero-dimensional objects,
such as algebras, modules or tensors. We list both the well-known ones and some new ones …

|$2{\mathbf{n}}^2-{\text{log}}_2({\mathbf{n}})-1$| lower bound for the border rank of matrix
multiplication | International Mathematics Research Notices | Oxford Academic Skip to Main …

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 …

Let $ M_ {\langle u, v, w\rangle}\in C^{uv}\otimes C^{vw}\otimes C^{wu} $ denote the matrix
multiplication tensor (and write $ M_n= M_ {\langle n, n, n\rangle} $) and let $ det_3\in (C …

We prove that the border rank of the Kronecker square of the little Coppersmith–Winograd
tensor T_ cw, q T cw, q is the square of its border rank for q> 2 q> 2 and that the border rank …

Recent works of Costa-Dalai, Christandl-Gesmundo-Zuiddam, Blatter-Draisma-Rupniewski,
and Bri\" et-Christandl-Leigh-Shpilka-Zuiddam have investigated notions of discreteness …

We present scheme theoretic methods that apply to the study of secant varieties. This mainly
concerns finite schemes and their smoothability. The theory generalises to the base fields of …