7 problems

Let $K\subset\mathbb{C}$ be compact and connected, with logarithmic capacity $\operatorname{cap}(K)=1$, $0\in K$, and conformal centroid at the origin. Let $\mu_K$ be the equilibri…

Let $K\subset\mathbb{C}$ be compact and connected, with logarithmic capacity $\operatorname{cap}(K)=1$, $0\in K$, and conformal centroid at the origin. Let $g$ be the Green's funct…

Let $p$ and $q$ be real-rooted polynomials of degree $d$, and let $\f$ be in $C^{4}(\mathbb{R})$ with $f^{(4)}\geq 0$. Write $\mu_p$ and $\mu_q$ for the probability measures assign…

Let $q>0$ be real, let $a_1,\dots,a_n$ be non-negative real numbers satisfying … and let $X_1,\dots,X_n$ be independent identically distributed standard exponential random variable…

The $q$-moment conjecture. If $\mu$ is an isotropic probability mass on $\mathbb{R}^k$, then

Let $d\geq 2$, let $(G_1,\ldots,G_d)$ be a $d$-dimensional real-valued centered Gaussian vector, and let $m\geq 1$ be an integer. Gaussian Product Conjecture. One has … This is an…

Comparable weak and strong moments conjecture. Every symmetric log-concave probability measure on $\mathbb R^n$ satisfies $\mathrm{CWSM}(C)$.