10 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…

Generic cohomology conjecture. For all $F,G\in\mathcal{P}$, there is a graded isomorphism, natural in $F$ and $G$,

An $N=2$ super-Riemann surface with genus-zero compact body is an $N=2$ super-Riemann surface whose underlying compact body has genus zero. The $N=2$ super-Riemann sphere is denote…

Let $Q_1\in SK(m)$ and $Q_2\in SK(n)$ be supergeometric data of the forms … and … Here $SK(k)$ denotes the space of supergeometric configurations with $k$ tubes, and $\Gamma$ and…

Let $X = \operatorname{\mathbf{Flag}}(p_1|q_1, \dots, p_t|q_t;\;V)$ be a flag supervariety of type $\tau$, and let $Y$ be the variety associated to $X$ by the construction in the p…

Let ${\mathcal Y}$ be a projective smooth superscheme of dimension $r|s$, with bosonic reduction $Y$, and let $\beta_0\in A_1(Y)$. Let…

Let $(E,\nabla)$ be a homogeneity manifold, and let a vector bundle structure on $E$ have Euler vector field $\nabla_E$. Compatibility means that this vector bundle structure is co…

Let $\mathbb{F}$ be either $\mathbb{R}$ or an algebraically closed field of characteristic $0$, and consider the morphism $\phi$ of the affine superspace $\mathbb{A}^{m|n}$ over…

Let supercohomology be the cohomological invariant under consideration, let the Jacobian ring encode the relevant algebraic data, let gaps refer to gaps in the associated categoric…

Consider supermanifolds, their Hodge numbers, and the associated categories of singularities. A gap is a missing interval in the generation-time spectrum of such a category, and a…