27 problems

The classical Grassmannian carries an action of the Virasoro algebra, and the moduli space of curves is considered with respect to this action. In the super setting, one analogousl…

Leites's conjecture. In a suitable category, there should exist an object called purely odd projective superspace, namely the factor of

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…

Conjecture on the $G(2)$-structure. The tensors $V(\mathfrak{g}_i)$ might be related to the $G(2)$-structure on a purely odd superspace.

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 $WSP(1,\ldots,1|m)$ denote the weighted superprojective space with $m$ bosonic weights equal to $1$ and fermionic weight $m$. The super Calabi–Yau conjecture. For $m>2$,…

Let $\mathfrak{ns}$ be the Neveu–Schwarz algebra, let $\rho_{h,c}$ be a highest weight representation of $\mathfrak{ns}$, and let $\EuScript H_\infty[\EuScript A]$ be the correspon…

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 a physical description use commuting coordinates for Bose particles and anticommuting indeterminates for Fermi particles. Berezin's conjecture. To describe Bose and Fermi parti…

Let $x\colon X\to B$ be a smooth proper map with connected base $B$, write $X_b=x^{-1}(b)$, and let $\beta_b\in H_2^+(X_b)$ vary locally constantly. Deformation axiom. The super Gr…

For $k\geq3$, let $SGW_{0,k}^{X,\beta}$ denote the super Gromov--Witten classes, let $f\colon\overline{M}_{0,k+1}\to\overline{M}_{0,k}$ forget the last marked point, let $[X]$ be t…

Let $X$ be a convex non-super scheme, and let $\beta\in H_2^+(X)$. Denote by $\overline{\mathcal{M}}_{0,k}(X,\beta)$ the moduli stack of super stable maps of genus zero with $k$ Ne…

The moduli stack of stable spin curves is denoted by $\overline{M}^{spin}_{0,k}$, and for a stable spin curve $c\colon C\to B$ of genus zero with $k$ marked points and fixed tree t…

Superoper–Gaudin conjecture. Under certain nondegeneracy conditions, $Z$-twisted Miura–Plücker opers are $Z$-twisted Miura opers for certain choices of ${L_i(z)}_{i\in I_g}$. Moreo…

Bäcklund–Bethe correspondence conjecture. Satisfying these Bäcklund transformations under certain nondegeneracy conditions should impose enough constraints on the $qq$-system to pu…

Let ${\mathpzc{X}}$ be a complex supermanifold, and let ${\text{\sffamily{\emph{T}}}}_{\mathpzc{X}}$ denote its tangent bundle. The super Atiyah class is the Atiyah class of this t…

Let $B$ be a Ramond boundary component of the moduli space $\overline{{\mathcal S}}$ of stable supercurves, with gluing map $iota:B\tooverline{{\mathcal S}}$, and let…

The paper develops a functorial approach to differential calculus over a commutative base ring, using functors from a category of topological algebras to sets and natural transform…

Let $\mathrm{Hol}_x$ be the supergroup functor constructed from holonomy at an $S$-point $x$, and let $\mathrm{Hol}_x^{\mathrm{Gal}}$ denote the functor of points of Galaev's holon…

For a given type II world sheet $\mathbf{\Sigma}$, consider metrics satisfying the condition that every non-trivial supercircle has length at least $2\pi$. Minimal area uniqueness…

A supermanifold is a local ringed space modeled on open domains of $\mathbb R^{p}$ endowed with the $\mathbb Z_{2}$-graded algebra … The coordinate description uses local charts an…

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…