9 problems

Majority is Stablest conjecture. The majority function is the most noise stable among functions which have low influences.

Let $\Sigma$ be a finite alphabet, let $k\in\mathbb{N}$, and let $\mu$ be a pairwise-connected distribution over $\Sigma^k$ in which every atom has mass at least $\alpha$. A functi…

Let $p:\{-1,1\}^n\to\mathbb{R}$ be a polynomial of degree at most $d$. Its Fourier completely bounded $d$-norm is denoted by $\|p\|_{\operatorname{fcb},d}$, and…

Let $p:\{-1,1\}^n\to\mathbb{R}$ be a polynomial of degree at most $d$, with supremum norm $\|p\|_\infty\leq 1$. A variable $i$ has influence $\operatorname{Inf}_i(p)$, and…

Let $f$ be a homogeneous polynomial of degree $d$ in $n$ variables. Write $\operatorname{Var}[f]$ for its variance, $\operatorname{Inf}_i[f]$ for the influence of the $i$-th variab…

Let $\rho$ satisfy $0\leq\rho\leq1$, let $b1\in[1,9]$, and let $\mathbf{MaxStab}_{\alpha}(1/2)$ denote the maximal asymmetric $b1$-stability at mean $1/2$. A dictator function is a…

Let $\rho\textsuperscript{}$ be the noise parameter, let $\boldsymbol{\operatorname{MaxStab}}_{\alpha}$ denote the maximal asymmetric $b1$-stability, and let dictator functions be…

Let $0<p\leq 1/2$ and let $f\colon\binom{[n]}{pn}\to\{0,1\}$ satisfy … where the norm is with respect to the uniform measure on the slice. The authors of Filmus, Ihringer, Kindler,…

Linear-error conjecture for the Kindler–Safra theorem. Theorem should hold with an error bound of $O_{p,k}(\epsilon)$ rather than $O_{p,k}(\epsilon^{1/C} + 1/n^{1/C})$.