28 problems

Let $L$ be a $(-2)$-symplectic space, viewed as a $(-1)$-Lagrangian of a point, and assume the Joyce–Safronov conjecture supplies a functor inducing a homomorphism … Here…

Let $M$ be a $(-1)$-symplectic space and let $L\to M$ be a $(-1)$-Lagrangian. Let $\operatorname{MF}(M)$ denote the category of matrix factorisations associated with $M$, and let ……

Let $M$ be a $(-1)$-symplectic space, meaning a space equipped with a $(-1)$-symplectic structure. For example, if $M$ is the critical locus of a function $f$ on a smooth space $U$…

Let $M$ be a Seifert-fibred $3$-manifold, let $G$ be a semisimple group, and for $n>0$ let $\Sigma_{\mathrm{orb},M}^{[n]}$ be the quotient of $M$ by the $S^1$-action composed with…

Let $X$ be a Calabi--Yau $3$-fold over a field $k$ of characteristic $p>2$, and let $\operatorname{Map}_{k}(X,\operatorname{\underline{Perf}})$ carry the de Rham $(-1)$-shifted sym…

Coisotropic reduction conjecture. The space of $n$-shifted coisotropic structures on $f$ is equivalent to the space of such diagrams, where $\pi_Y$ is an $(n+1)$-shifted Lagrangian…

Let … be a $(-1)$-shifted exact oriented Lagrangian correspondence. Here $\phi_M$ and $\phi_N$ are the perverse sheaves of vanishing cycles associated with the oriented $(-1)$-shif…

Let $M$ be a manifold. Let $\mathrm{LocSysCat}(M)$ denote the $(\infty,2)$-category of local systems of categories on $M$, and let $^{2}\mathrm{Fuk}(\mathrm{T}^{*}[1]M)$ denote the…

Let $B$ be a base manifold, and let $\mathrm{T}^{*}[1]B$ denote its $1$-shifted cotangent bundle. A schober on $B$ is a categorified local system with allowed singularities. Schobe…

Let $U$ be a smooth $\mathbb{C}$-scheme and let $\phi\colon U\to\mathbb{C}$ be a regular function. Let $\mathbf{M}\to\mathbf{Crit}(\phi)$ be a $(-1)$-shifted Lagrangian such that…

Let $X$ be a generalized complex manifold, let $T_X^*\to X$ be its Poisson Lie algebroid, and let $\mathcal{X}=[X/T_X^*]$ be the corresponding quotient stack. The stack…

Joyce's conjecture. There is a natural morphism

Let $X$ be the nonsingular quasiprojective variety considered in the construction, let $R$ be the corresponding relation algebra, and let … be the derived affine scheme equipped wi…

Let $X$ be a smooth projective threefold with holomorphic $2$-form $\theta$, and let the moduli stack of Pandharipande–Thomas stable pairs on $X$ carry the $(-1)$-shifted $1$-form…

Let $\boldsymbol{Y}$ be an oriented $-2$-shifted symplectic derived scheme, set $Y=t_0(\boldsymbol{Y})$, and suppose the dimensional reduction conjecture holds. Let…

Let $\boldsymbol{Y}$ be a $-2$-shifted symplectic derived scheme over $\operatorname{Spec}{\mathbb C}$, equipped with an orientation, and set $Y=t_0(\boldsymbol{Y})$. Let…

Let $\boldsymbol{\tau} \colon \boldsymbol{L} \to \boldsymbol{X}$ be an oriented Lagrangian of an oriented $-1$-shifted symplectic derived Artin stack. Write…

Perverse-sheaf and BV-quantization conjecture. There is a canonical BV quantization $\Delta_\hbar$ of $\det(\mathbb{L}_\mathsf{X})^{\frac12}$ and a quasi-isomorphism

Shifted-symplectic determination conjecture. The $(-1)$-shifted symplectic structure on $f^{-1}(0)\times\mathbb{C}$ should be sufficient to determine the wrapped Fukaya category of…

Compatibility conjecture. This isomorphism is compatible with the $(n-2)$-shifted symplectic structures on both sides. The mapping stack $\mathrm{Map}(C_{\mathrm{dR}},X)$ is known…

Suppose $C$ is either an elliptic curve or $\mathbb{CP}^1$ with a fixed framing at $\infty$. Let $G$ be the group used to define the moduli stacks, and let $\Lambda_i$ be the stabi…

Filtered shifted-structure conjecture. There exists a relative $n$-shifted symplectic structure $\widetilde{\omega}$ on $\widetilde{Y}_f$ over $[\mathbb{A}^1/\mathbb{G}_m]$ such th…

Polyvector-field conjecture. The resulting $\mathbb{P}_{n+1}^{gr}$-algebra structure on $\Gamma\big(X,S(\mathbb{T}_X[-n])\big)$ is equivalent to the $\mathbb{P}_{n+1}^{gr}$-algebra…

Joyce's conjecture. There should exist a morphism of constructible sheaves

Joyce's conjecture. Lagrangians in $X$ should define sections of the sheaf $\mathcal{P}_X$.