10 problems

Let $S$ denote the multiset of ordinates of the nontrivial zeros of the Riemann zeta function. For $a>0$, define the continuous function $H_a:\mathbb{R}_{>0}\to\mathbb{C}$ by … whe…

Independent-Bernoulli approximation conjecture. For large $m$, $\mathrm{SUM}'_{1,m}$ can be approximated by $\mathrm{SUM}”_{1,m}$, where the variables $Z'(\boldsymbol{k})$ are samp…

Let $H$ be a non-negative strongly convex drift function such that $H(0)=0$, and let the $\mathbf{slGCM}$ distribution denote the limiting distribution associated with the least co…

Let $\mathbb{X}$ and $\mathbb{Y}$ be independent infinite-dimensional matrices with independent standard normal entries. Let $p$ be a sequence of integers depending on $n$ such tha…

Let $B,C>0$, let $0<\delta<1$, and let $X=(X_{ij})$ be sampled uniformly from $\mathcal M_{n,\delta}(B,C)$. Let $B_c$ denote the critical value. Phase-transition conjecture. There…

Let $X\subseteq\mathbb{R}^m$ be compact with positive Lebesgue measure, and let $\mu$ be Lebesgue measure restricted to $X$ and rescaled to have total mass one. Let…

Let $X\subseteq\mathbb{R}^m$ be compact, let $\mu$ be a probability measure on $X$ absolutely continuous with respect to Lebesgue measure, and let $\hat{F}^{(i)}_n$ be the empirica…

Let $k\geq2$, let $M_k(x)$ denote the error in the counting function of $k$-free numbers, and let $C_k>0$ be a constant depending on $k$. Maximum-order conjecture. For every…

Let $k\geq2$, and let $\nu=\nu_k$ be the limiting distribution of $e^{-y/(2k)}M_k(e^y)$, where $M_k(x)$ is the error in the counting function of $k$-free numbers. Assume the Rieman…

Edge-probability conjecture. This condition can be weakened to