8 problems

Let $f:[0,1]^n\to\\{0,1\\}$ be a Boolean function, and let ${\tilde I}_f$ denote its total variational influence. Strong Friedgut conjecture. There exists a function…

Let $Y$ be a closed manifold and let $m$ be a positive integer. Write $Y^m$ for the $m$-fold Cartesian product of $Y$, and let $\operatorname{cat}$ denote Lusternik–Schnirelmann ca…

Abbe–Bengio–Cornacchia–Kleinberg–Lotfi–Raghu–Zhang extension conjecture. The lower bounds of Abbe, Bengio, Cornacchiam, Kleinberg, Lotfi, Raghu and Zhang should extend in a straigh…

Rectangle-atom conjecture. The product Hardy space $H^1(\mathbb{R}^{\vec n})$ can be represented by rectangle atoms. This was an initial conjecture in the development of product Ha…

Exchangeable-set reduction conjecture. This restriction to exchangeable sets should hold not only in this special convexity case, but also in any other cases.

Let $(X,\mathrm d_X,\mathfrak m_X)$ and $(Y,\mathrm d_Y,\mathfrak m_Y)$ be metric measure spaces, and let $X\times Y$ carry the product measure…

Let a space $X$ be normal-Frolík for normal $P$-spaces when $X\times Y$ is normal for every normal $P$-space $Y$. Morita's second conjecture. Metrizable spaces are exactly the norm…

Let $\mathfrak F(\mathrm{normal})$ denote the class of topological spaces $X$ such that $X\times Y$ is normal whenever $Y$ is normal. Morita's first conjecture. The class…