9 problems

Let $P_h$ be the polynomial algebra on $h$ variables over $\mathbb F_p$, equipped with the action of the Steenrod algebra $\mathscr A_p$. For a positive integer $n$, write its $p$-…

Let $P_k=\mathbb F_2[x_1,\ldots,x_k]$ be the polynomial algebra, let $Q P_k$ denote its quotient by the image of the positive-degree Steenrod algebra, and let … be Kameko's squarin…

Coinvariant-dimension conjecture. Its dimension is

Let $k=\mathbb Z_2$, let $P_4=k[x_1,x_2,x_3,x_4]$, and write $Q^{\otimes 4}=k\otimes_A P_4$. For a positive integer $s$, Kameko's squaring operation is the $kGL_4(k)$-module epimor…

Coinvariant-dimension conjecture. This space is trivial if $s=2$ and has dimension $1$ if $s\neq 2$.

Admissible-monomial prediction. If $\omega$ is a weight vector, then

Let $M_n$ be the mod $2$ motivic cohomology algebra of the classifying space of the elementary abelian $2$-group of rank $n$, and let $QM_n^{d,*}$ denote its degree-$(d,*)$ quotien…

Let $P_k$ be the polynomial algebra on $k$ generators over $\mathbb{F}_2$, let $QP_k$ denote its indecomposable quotient under the Steenrod algebra, and write $(QP_k)_n$ for its de…

Let $E^k$ be an elementary abelian $2$-group of rank $k$, let $BE^k$ be its classifying space, and set … Write $\mathbb F_2\underset{\mathcal A}\otimes P_k$ for the quotient of…