3 problems

Let $f\colon\left\{0,1\right\}^{n}\to\left\{0,1\right\}$ be a Boolean function, write $\mu=\mathbb{E}[f]$, and let $I(f)$ denote its total influence. A function $g$ is a Junta if i…

Let $f=(f_1,\ldots,f_m):\mathbb{Z}_k^n\to\mathbb{Z}_l^m$ be $\alpha$-Lipschitz with respect to the $L^1$ norm. Coordinatewise junta conjecture. For every $\delta,\epsilon>0$, at le…

Let $f:\mathbb{Z}_k^n\to\mathbb{Z}_l$ satisfy … Here $|\cdot|'$ is the source's normalized difference notation. Junta-size conjecture. The function $f$ is $\epsilon$-close to an…