36 problems

Let $A=C^\infty(X)$ be the algebra of smooth functions on a smooth real manifold $X$, and let $C^\bullet=C^\bullet(A,A)[1]$ be the suspended local Hochschild complex, whose cohomol…

Let $R$ be a finitely generated smooth commutative algebra over $\mathbb Z$, let $P_{n,R}$ be the polynomial Poisson algebra, and let $A^{\hbar}_{n,R[\hbar]}$ be the algebra over…

Let $cmathfrak hto eqcmathfrak g$ be an inclusion of Lie algebras, let $Zto eq(cmathop{wedge}^3cmathfrak g)^{cmathfrak g}$, and let a formal classical dynamical $r$-matrix mean a f…

Quantizability conjecture. Any Lie bialgebroid is quantizable.

Let $L$ be an $ffrak{h}$-base manifold, let $P$ be an $ffrak{h}$-manifold, and let $pi$ be a Poisson dynamical bracket on $P$ over $L$. A quantization of the Poisson dynamical…

Free-action quantization conjecture. A quasi-Poisson manifold $X$ for $({\mathfrak{g}},Z)$ can be quantized if the ${\mathfrak{g}}$-action on $X$ is free, i.e. if $X$ is a principa…

Let $M$ be an algebraic symplectic manifold with a symplectic action of a finite group $G$, and let $X\to M/G$ be a smooth symplectic resolution. Choose deformation-quantizations…

Let $M$ be a symplectic manifold, let ${\cal W}$ be its Weyl algebra bundle, and let $(\Omega(M, {\cal W}), \nabla, R)$ be the associated $Q$-algebra. A finitely generated projecti…

Let $X$ be a symplectic manifold, let $F^{naive}(X,\omega)$ denote its naive Fukaya category, and let $D^b_{\infty}(hol(X))$ be the derived $A_{\infty}$-category of holonomic modul…

Compatibility conjecture. The diagram of curved $L_\infty$-morphisms

Let $\mzvswithhalf^n$ be the weight-$n$ component of the filtered ring generated by normalized multiple zeta values, with $\mzvswithhalf^n=\mzvs^n+\frac{1}{2}\mzvs^{n-1}$, where…

Let $G$) be a reductive group, let $\Sigma$ be a closed compact surface, and let $\mathrm{SkCat}_G(\Sigma)$ denote the $G$-skein category at a generic value of the quantization par…

Work over the complete topological $k\llbracket\hbar\rrbracket$-modules, with their symmetric monoidal structure, and let $\mathbbst{BD}_0$ and $\mathbbst{BD}_1$ denote the corresp…

Let $(M,\omega)$ be a symplectic manifold, and let $C^{\infty}_c(M)$ denote the compactly supported smooth functions on $M$. A strict deformation quantization is understood in the…

Let $M$ be a connected closed oriented $3$-manifold with a basepoint $x\in M$, and let $G$ be a reductive algebraic group equipped with the extra data described in the source. For…

Weinstein's conjecture. The dual $\mathfrak{g}^*$ admits a tangential star product if and only if there is a flat torsion-free affine connection on a neighborhood of the identity i…

Let $(M,\Omega_I)$ be holomorphic symplectic, set $\omega_u=\operatorname{Re}(u^{-1}\Omega_I)$ and $B_u=\operatorname{Im}(u^{-1}\Omega_I)$, and let $F(M,\omega_u,B_u)$ be the corre…

Let $G$ be a reductive algebraic group. Let $R_2=H^\bu(\mathbb{A}^2,\mathcal{O}_{\mathbb{A}^2}^{\mathrm{alg}})$, let $\mathfrak{g}$ be the Lie algebra of $G$, and let…

Let $A_{n,\mathbb{C}}$ be the Weyl algebra and let $P_{n,\mathbb{C}}$ be the commutative polynomial algebra equipped with its Poisson bracket. For an infinite prime $[p]$, let … be…

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 $W_n(\mathbb{Q})$ be the $n$-th Weyl algebra over $\mathbb{Q}$ and let $P_n(\mathbb{Q})$ be the polynomial Poisson algebra in $2n$ variables with its canonical Poisson structur…

Let $W_{n,\mathbb{C}}$ be the $n$-th Weyl algebra over $\mathbb{C}$, and let $P_{n,\mathbb{C}}$ be the $n$-th commutative Poisson algebra. Kontsevich's conjecture. The automorphism…

Let $c_n$ be the coefficients in the factorizing operator … where $w_\Gamma$ is the weight of a Leibniz graph $\Gamma$ and $\#\!\operatorname{Aut}(\Gamma)$ denotes the order of its…

Kontsevich–Kanel-Belov correspondence conjecture. The automorphism groups are isomorphic:

Let $\Sigma$ be an affine algebraic curve, and let $\operatorname{Diff}(\Sigma)$ be its algebra of polynomial differential operators. The five-dimensional quantum field theory on…