4 problems

Let $T\in\operatorname{SSYT}(k,[n])$ be a tableau whose distinct entries are $a_1<\ldots<a_r$. Let $n'\ge n$ and let $f:\{a_1,\ldots,a_r\}\to[n']$ satisfy $f(a_1)<\ldots<f(a_r)$; w…

Tilde-theta evacuation conjecture. For every $T\in\operatorname{SSYT}(k,[n])$,

Evacuation conjecture. For every $T\in\operatorname{SSYT}(k,[n])$,

Promotion conjecture. For any tableau $T\in\operatorname{SSYT}(k,[n])$ without frozen factors,