4 problems

Let $I_d(d,2d-1)$ be the ideal generated by the maximal permanents of the generic $d\times(2d-1)$ matrix $M_{d,2d-1}$ over a field $k$. Monomial conjecture for maximal permanents.…

Let $M_{m,n}=(x_{i,j})$ be a generic $m\times n$ matrix over a field $k$, and let $I_d(m,n)\subset k[x_{i,j}]$ be generated by the permanents of its $d\times d$ submatrices. A mini…

Let $X$ be a $3\times 4$ generic matrix of indeterminates, and let $\Bbbk$ be a field of characteristic $p>2$. F-purity conjecture for the $3\times4$ third permanental ideal. The q…

Let $X$ be an $m\times n$ generic, symmetric, or Hankel matrix, and let $\Bbbk$ be a field of characteristic $p\neq 2$. Write $P_t(X)$ for the ideal generated by the $t\times t$ pe…