13 problems

Higher BV quantization conjecture. There is a natural equivalence

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…

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 $M$ 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 $U$ 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…

Joyce's conjecture. There is a natural morphism

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…

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

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…