6 problems

The random Turán conjecture. With high probability,

A $k$-uniform hypergraph $H$ has no exponent when there is no real number $\alpha$ such that its Turán function satisfies $\operatorname{ex}(n,H)=\Theta(n^\alpha)$. The Turán funct…

Let $D\subset\mathbb{R}^{n}$ be the domain in the spatial Turán problem, and let $a_{\mathbb{R}^{n}}(D)$ denote the supremum of $\widehat{h}(0)$ over admissible functions $h$ suppo…

Fon-der-Flaass conjecture.

Let $\Omega\subseteq{\mathbb R}^d$ be a symmetric convex body, and let $\chi_{\frac12\Omega}$ denote the characteristic function of its half-body. Its convolution square is the fun…

Let $G$ be either ${\mathbb R}$ or ${\mathbb T}$, and let $\Omega\subseteq G$ be a measurable set of fixed measure $|\Omega|=m$. A set is zero-symmetric when it is symmetric about…