7 problems

Matrix Spencer conjecture. There exists a universal constant $C$ such that

Optimal estimation rate conjecture. The computationally optimal error rate is

Weak variance conjecture. The expected spectral norm satisfies

Fix $n\in\mathord{\mathbb N}$ with $2<n$, and let ${\cal S}\in\mathrm{S}^d\mathord{\mathbb C}^n$ be nonsingular. Let $\mathbf H$ denote the polynomial map whose fixed points are us…

Let $X$ be the $d\times d$ symmetric random matrix with entries $X_{ij}=b_{ij}g_{ij}$, where $\{g_{ij}:i\ge j\}$ are independent standard Gaussian random variables and…

For a Boolean function $f:\{0,1\}^n\to\{\pm1\}$, let $\|\widehat f\|_{1,\epsilon}$ be the smallest spectral norm of a function $g$ satisfying … The function $f$ is symmetric when i…

Let $(M,\omega)$ be a symplectic manifold, let $\operatorname{Symp}_0(M,\omega)$ be its identity component, and let $\operatorname{Ham}(M,\omega)$ be the Hamiltonian subgroup. Let…