4 problems

Gotsman–Linial conjecture. The extremal examples among degree-$d$ polynomial threshold functions for total influence are symmetric polynomials whose signs alternate around the midd…

Talagrand's conjecture. For every fixed $\tau>0$, there is a constant $C_\tau$ such that, uniformly in the dimension and over all $f\geq 0$,

For a Boolean function $F:\{-1,1\}^{n}\to\{-1,1\}$, define its $i$-th influence by … Its total influence is $\operatorname{Inf}(F)=\sum_{i=1}^{n}\operatorname{Inf}_{i}(F)$. For a p…

Friedgut–Kalai conjecture. There is an absolute constant $c$ such that, if $up^n(P)epsilon$, then