20 problems

Let $G/H$ be a homogeneous space in the reductive setting, let $\mathfrak g$ and $\mathfrak h$ be the Lie algebras of $G$ and $H$, and let $\mathfrak h^{\perp}\subset\mathfrak g^*$…

Let $\mathcal M(\Sigma,t)$ be the moduli space associated with a surface $\Sigma$ and parameter $t$. In the higher-genus setting, model $\mathcal M(\Sigma,t)$ by a toric manifold,…

Let $\pi:{\mathfrak X}\to S[[h]]$ and the quantization sheaf $\operatorname{\cal O}_h$ satisfy the assumptions of Theorem. Consider the global sections functor … from sheaves of fi…

Poisson-normalizer extension conjecture. Every integrable irreducible representation of $\wp({\cal B})$ can be extended to a quantization of

Dense basic-set existence conjecture. There exists a nontrivial quantization of

Groenewold–Van Hove conjecture. There is no nontrivial strong quantization of

Let $(N,\omega)$ be a compact symplectic manifold, and let $\hbar>0$. The Dirac quantization condition is … A contactification of $(N,\omega)$ is a contact-geometric lift as define…

Let ${\bf M}$ be a complete Kähler manifold satisfying the condition of Proposition as a Riemannian manifold, and let its Kähler form be the symplectic form. Assume that ${\bf M}$…

Let $(M,\omega)$ be a closed symplectic manifold, and let $\{T_k:C^\infty(M)\to\mathcal{L}(H_k)\}_{k\in\mathbb{N}}$ be a geometric quantization satisfying the trace axiom and star…

Let $(M,\omega)$ be a closed symplectic manifold. A geometric quantization is a sequence of maps $\{T_k:C^\infty(M)\to\mathcal{L}(H_k)\}_{k\in\mathbb{N}}$ satisfying the geometric…

Let $(M,Z,\omega,\mu)$ be a compact connected Hamiltonian $G$-space, where $G$ is compact and connected, $M$ is prequantizable, and $Q_G(M,Z,\omega)\in R(G)$ is its equivariant qua…

Let $M$ be a $2n$-dimensional Poisson manifold with a real polarization $P$ and two integrable systems given by Lagrangian fibrations $\pi_i:M\to B_i$, with generically transverse…

Let $(X,L)$ be a polarized compact Kähler manifold, with $L$ a pre-quantum bundle, and let $\pi:X\rightarrow B$ be a Lagrangian torus fibration. Let $\Gamma_{X/B}(X,L)$ denote the…

Let $M$ be a closed symplectic manifold equipped with a non-degenerate integrable system whose singularities have any corank and Williamson type $(k_e,k_h,h_f)$, with $k_h<2$,…

Let $M$ be a $2m$-dimensional closed almost toric manifold with singularities of any corank and of Williamson type $(k_e,0,k_f)$, where $k_f<2$. Let $BS_r$ and $BS_{f-r}$ be the im…

Let $M$ be an integral $b$-symplectic manifold equipped with a Hamiltonian $T$-action with nonzero modular weight, and let $Q(M)$ denote its formal geometric quantization. Fredholm…

Nonexistence conjecture. There do not exist regulators of the first type for singular polarizations ${\mathcal P}$ such that there exist points $x\in M$ for which ${\mathcal P}_x$…

Let $t=(t_1,\ldots,t_n)$ be a family in $([0,\pi]\cap\mathbb{Q}\pi)^n$, let $D$ be the common denominator of the rational numbers $t_j/\pi$, and let…

Let $G_{\mathbb C}$ be a complex group with real form $G_{\mathbb R}$, and let $\mathfrak C_{\mathbb C}$ be a unipotent conjugacy class, or a semisimple conjugacy class obtained by…

Let $M$ be the moduli space, let ${\mathcal T}$ be the parameter space, and let $P$ be a formal trivialization of the formal Hitchin connection, with expansion…