15 problems

Mirror-duality conjecture. The diagram

Let $L$ be a link, let $m(L)$ denote its mirror, and let $\mathcal{X}_\mathit{Kh}^j(L)$ denote its Khovanov homotopy type in quantum grading $j$. Mirror duality conjecture. The spa…

Let $\lambda$ be a $\mathbf T$-regular partition. Let $s(\lambda)$ be its spike monomial, let $v(\lambda)$ be the polynomial associated with $\lambda$, and let $\gamma$ be the part…

Let $p$ be a prime, let $\lambda$ be a partition, and let $d_c(\lambda)$ denote the first degree in which the irreducible module $L(\lambda)$ occurs as a composition factor of the…

Morán's conjecture. The operations $\mathfrak{sq}^n$ coincide with the Steenrod squares $\operatorname{Sq}^n$ for all $n$. The operations $\mathfrak{sq}^0$ and $\mathfrak{sq}^1$ ar…

Let $\Gmr$ be a finite group and let $p$ be a prime. For each $i$, let $\Ecal^{(p^i)}_{\Gmr,p}$ be the collection of integral $\uprho_{\Gmr}$-stable $\Hmr\underline{\FF}_p$-Euleria…

Schütz's conjecture. The operations $\operatorname{Sq}_0^2$ and $\operatorname{Sq}_1^2$ arise from the $\operatorname{Sq}^2$ operations on the odd Khovanov spectra…

Let $F$ be a field. Write $\mathcal{A}^{\star,\star}_{F}$ for the algebra of motivic Steenrod operations and $H\mathbb{F}_{p,F}^{\star,\star}H\mathbb{F}_{p,F}$ for the correspondin…

p-curvature conjecture. The equivariant quantum Steenrod operator satisfies

Steenrod-operation polynomiality conjecture. $H^{\star}(K_{r\sigma+s})$ is a polynomial algebra on certain classes

Let $k$ be the base field, let $H\mathbb{F}^{k}_{p}$ denote the motivic Eilenberg–MacLane spectrum, and let … be the split monomorphism indexed by finite sequences…

Fix $m$ and let … and … Here the $a_{m,2,k'}$ are the invariants introduced for the $n=2$ case, and Steenrod operations act on them. Steenrod-generation conjecture. Every element o…

Dual Steenrod operation criterion. If every element in the reduced homology of $X$ is either in the source or the target of a nontrivial dual Steenrod operation, then $X$ might be…

Let $\phi$ be a symplectic automorphism for which the relevant Floer stable homotopy type exists, and let … be the degree-doubling map obtained by composing the quantum Steenrod op…

Podkorytov's conjecture. Conversely, the ${\mathscr A}_p$-module $H^*(X)$ determines the diagonal morphism d^p_{X\,#} up to coherent quasi-isomorphisms.