3 problems

Minor nonvanishing conjecture. For each $d\ge2$ and $k\ge2$, each $1\le l\le k-1$, and each linear subspace $V\subset\mathbb{R}^n$ with dimension $\dim(V)$, the matrix…

For each integer $s\ge1$, let $J_{s,2,2}(N)$ denote the number of integral solutions with $1\le X_i,Y_i\le N$ to the quadratic Parsell–Vinogradov system consisting of the conservat…

Mean value decoupling conjecture. For every $\epsilon>0$,