16 problems

Cycle-removal conjecture. The Weyl star-product associated with ${\ast^K_\hbar}$ contains no cycles and is obtained from ${\ast^K_\hbar}$ by ignoring the graphs with cycles.

Let $\pi_n^{(\lambda)}$ denote the deformed quasiprobability associated with energy level $n$, parametrized by $\lambda$, and let $H>0$ be an energy value. Negativity conjecture. F…

A natural star product is a formal associative deformation of the pointwise product whose bidifferential operator at order $r$ differentiates each argument at most $r$ times. The g…

Let $M$ be a Kähler-Poisson manifold with Kähler-Poisson tensor $\eta$. A star-product with separation of variables on $M$ is a formal associative product whose bidifferential oper…

Let $\mathfrak g$ be one of the five exceptional simple Lie algebras, let $\mathcal O_{\mathrm{min}}$ be its minimal nilpotent orbit, and let $\Lambda^x$ denote the operator associ…

Consider a non-commutative quantum field theory formulated in terms of tempered ultrahyperfunctions, and let $\tilde\star$ denote the concrete type of star-product used in the form…

Let $\mathsf{V}=\mathbb{C}^n$ and let $\sigma$ be a quadratic Poisson bivector on $\mathsf{V}$. A canonical quantization of $\sigma$ is a star product obtained by Kontsevich's cano…

Let $n$ be the parameter defining a quantization of a Kleinian singularity of type $A_{n-1}$. A unitary short star-product is a unitary star-product satisfying the shortness condit…

Let $\mathfrak g$ be the Lie algebra under consideration, let $s$ denote the degree-sign involution, and let ${{\mathbf A}}_\lambda$ be the corresponding filtered quantization para…

Let $A={\mathcal O}(X)$ be the Poisson algebra of a Higgs or Coulomb branch $X$, and let ${{\mathbf A}}$ be a ${\mathbb Z}/2$-equivariant filtered quantization of $A$. An even filt…

Local transition-operator conjecture. In the more general coordinate-dependent case, the star product solving the transition equation is

Lone-star product conjecture. The structure constants of $\mathfrak{hs}[\lambda]$ are given by the commutator lone-star product.

Let $P^{ij}(x)$ be an arbitrary antisymmetric bi-vector, and let $\star$ be a Weyl star product quantizing the corresponding bracket. The product is Hermitian when … For functions…

Reduction conjecture. Most noncommutative spaces can be obtained by reduction of some sufficiently large noncommutative space with canonical noncommutativity.

Let $X$ be a measure space, and let a star-product on functions on $X$ be given by an associative product with a specified kernel. A quantizer and dequantizer are operator families…

Conjecture. There is no expression parameter such that