112 problems

Spectral-sequence collapse conjecture. For all $F,G\in\mathcal{P}$, this spectral sequence collapses at the second page. In particular, there is a graded isomorphism, not necessari…

The E2-degeneration conjecture. The spectral sequence degenerates at the $E_2$ page.

The critical-eigenspace conjecture. There is an isomorphism

Let $F$ be a field with $|\cdot F/\cdot F^2|=2^n$, so that $E=E_n\cong (\mathbb Z/2)^n$, and let ${\mathcal G}_F$ be the associated $W$-group. Let…

Let $\lambda\in\mathbb C$, let ${\mathfrak{gl}}(\lambda)$ be embedded in $\mathrm{Dif}_1$, and let … be the first page of the associated Feigin Serre–Hochschild spectral sequence.…

The $G^1$-degeneration conjecture. The spectral sequence $G^k_{p,q}$ for $H_*(X(\mathbb{R}))$ degenerates at the $G^1$ level.

Mokrane's spectral sequence conjecture. For all $r,w$, the map

Rapoport–Zink spectral sequence conjecture. For all $r,w$, the induced map on $E_2$-terms is an isomorphism

Spectral sequence differential conjecture. The spectral sequence collapses after the $E_3$ stage, and its differential

Let $\sigma$ be the simplicial resolution of the discriminant $\Sigma$ of the space of long knots, and let … be its natural filtration. Write $\bar\sigma_i$ and $\bar\sigma$ for th…

Vassiliev's stabilization conjecture. The spectral sequence associated with this filtration and computing the Borel–Moore homology groups of the resolution $\sigma$ stabilizes over…

Let $R$ be a ring spectrum and let $E$ be a commutative localized quotient of $R$. For a finite cell $R$-module $M$, let $\hat{\mathrm{L}}^R_E M$ denote the completed $E$-localizat…

Let $\mathrm{X}$ be a holomorphic symplectic manifold, and let $\mathscr{D}_\mathrm{L}$ and $\mathscr{D}_\mathrm{M}$ be quantised orientation modules associated to Lagrangian subma…

Let $Y$ be a closed, oriented $3$-manifold and $K\subset Y$ a knot. Let $HFK'_2(Y,K;\mathbb{C})$ be the homology of the mapping-cone complex … and let $I^\sharp(Y,K;\mathbb{C})$ de…

Let $F$ be a field of low cohomological dimension. Consider the motivic Adams spectral sequence based on $\operatorname{BPGL}\langle 2 \rangle$, and let $n$ be a positive integer.…

Let $\mathrm{HHH}_{S^n}(O_1)$ be the $S^n$-colored triply graded Khovanov–Rozansky homology of the unknot, with even generators $u_0,\ldots,u_{n-1}$ and odd generators…

Let $\phi$ be the flow under consideration, let $G_+$ be its associated graph, and let $SFC(\phi,\mathcal{C})$ and $CA(\phi)$ be the chain complexes described above, where…

Conjectured second-half description. The $\nu$ summands in the second half of $\mathcal{A}_k$ are $y_1^{2^{k-2}-2}M_{k+1}$ and all

Improved Adams-filtration bound. Then $x$ has Adams filtration at least $3n$.

Let $G$ be a 3D space group, and consider the standard Lyndon–Hochschild–Serre spectral sequence for its translation extension. At the $E_2$ page, examine the module structures in…

Let $A$ be an $\mathbb F_p$-algebra and let $X/A$ be a scheme. Consider the Hochschild-Kostant-Rosenberg spectral sequence for $X/A$, with differentials denoted by $d_r$. Power-of-…

Spectral-sequence non-collapse conjecture. There exists a strongly invertible knot $\widetilde{K}$ such that the spectral sequence of Theorem 1 collapses on the $E_k$ page for some…

Let $G$ be a compact $p$-adic Lie group, let $M$ be a $G$-module in the setting of the paper, and let $\mathrm{R}_{\mathrm{la}}^j(M)$ denote the $j$th derived functor of locally an…

Mixed-differential conjecture. There exists a $\tau^{2^n}$-periodic differential

Odd-prime transchromatic shearing conjecture. There is a shearing isomorphism