18 problems

The $e_m$-overkiller conjecture. For $3\leq m\leq k$,

The exact $e_m$-killer conjecture. For $1\leq m\leq k$,

The filtration-saturation conjecture. For $1\leq m\leq k$,

The filtered Hilbert-series conjecture. For $m\geq 0$,

Let $X$ be a quasi-projective surface. For each $n$, let $H^*(X^{[n]})$ be expressed in the Heisenberg monomial basis $(\mathfrak h_\mu(n))$. Constant Conjecture. The structure con…

Cohomology-ring presentation conjecture. The de Rham cohomology ring is

Let $\mathcal{M}$ be the moduli space above, let $H_I^*(\mathcal{M})\subset H^*(\mathcal{M})^\Gamma$ be the subring generated by the universal classes $\alpha_{\mathcal{M}}$,…

Multiplicative splitting conjecture. There exists such a splitting that is multiplicative under cup product:

Let $M_{d,c7}$ be the moduli space of one-dimensional sheaves on $\mathbb{P}^2$ with degree $d$ and Euler characteristic $\chi$, and let $P_\bullet H^*(M_{d,\chi},\mathbb{Q})$ and…

Complete homogeneous basis conjecture. For $1\leq m\leq\min(\ell,k)$,

Let $X$ and $Y$ be toric Fano manifolds, and let $H^*(X)$ and $H^*(Y)$ denote their cohomology rings. A cohomology ring isomorphism preserves their first Chern classes when it maps…

Let $h$ be a Hessenberg function and let $\operatorname{Hess}(N,h)$ be the associated regular nilpotent Hessenberg variety. For a Hessenberg function $h'\subset h$, write…

Let $X_0$ be an irreducible nodal curve with exactly one node, and let $U_{X_0}(2,\mathcal{L}_0)$ be the moduli space of rank-two semistable sheaves on $X_0$ with determinant…

Let $\textup{Sp}_{q/p}$ be the affine-flag Springer fiber, and let $\epsilon,\xi_1,\ldots,\xi_p,e_2,\ldots,e_p$ be the equivariant classes and parameters defined in the source. Let…

Let $C_{q/p}$ be the plane curve under consideration, let $J_{q/p}$ be its compactified Jacobian, and let $P$ be the perverse filtration on $\textup{H}^{*}(J_{q/p})$. Let…

Let $n$ be odd, and let $X_n=X_{\mathbb{A}_n}^{\mathtt{generic}}$ be the generic fiber associated with the linear tree $\mathbb{A}_n$. Write $\operatorname{WP}$ for the distinguish…

Ozsváth–Szabó's conjecture. The differential $d_3$ is given by

Presentation conjecture. The quotient