5 problems

Let $r$ denote the rank of the low-rank approximation used to evaluate the multi-dimensional Jacobi polynomial transform, with $n$ the transform size. Logarithmic-rank conjecture.…

Let $r$ be the rank of the augmented matrix used in the precomputation procedure for the fast Jacobi expansion algorithm, and let $n$ denote the number of discretization points. Ba…

Fastfood replacement conjecture. The Hadamard matrix $\mathbf{H}$ can be replaced by any matrix $\mathbf{T}$ such that $\mathbf{T}/\sqrt{n}$ is orthonormal, the maximum entry in…

The hierarchical interpolative factorization for integral equations (HIF-IE) is an approximate generalized LU decomposition for discretized elliptic operators in two and three dime…

Universal complexity conjecture. There are universal constants $c_1,c_2$ such that, for every group $G$,