152 problems

Perry's noncommutative integral Hodge conjecture. The homomorphism

Quasi-bisymplecticity conjecture. The triple $({\mathcal{B}}(\Gamma_n),\Phi,\omega_n)$ is a quasi-bisymplectic algebra. Furthermore, the double quasi-Poisson bracket…

Let Equation … has a unique solution with a given appropriate boundary condition at infinity. This is an informal conjecture attributed to Nekrasov; the source does not specify the…

Let $\Gamma$ be a Fuchsian group with fundamental class $[\Gamma]$, let $\sigma$ be a multiplier on $\Gamma$ satisfying $\delta(\sigma)=0$, and define … Here a…

Multiplicity inequality. The following inequality holds:

Let $M$ be a compact complex manifold, let $obreaklambda$ be a line bundle on $M$, and let $boldsymbol1\lambda$ denote its identity differential operator. Write…

Let $C$ be a genus-$g$ Heegaard surface with fundamental group $\pi_1(C)$, let $X$ be the associated three-manifold, and let $L_+$ be one of the two lattices in the Heegaard splitt…

Let $R$ be the base algebra, let $A$ be a friendly Calabi–Yau $R$-algebra of dimension $3$, let $F$ be a smooth $R$-algebra, and let…

Let $(D,\omega,\xi)$ be the symplectic data used in the universal construction, and let $A$ be a friendly algebra satisfying the stated Calabi–Yau condition. Theorem main(ii) repre…

Let $\mathfrak{a}$ be a simple Lie algebra, let ${\mathbf d}\geq 1$, and let $\psi_{\mathbf d}$ be the real-valued polynomial obtained by restricting the potential $\Psi$ to the sp…

Kontsevich–Soibelman conjecture. For any saturated DG algebra $A^{\:\raisebox{3pt}{\text{\circle*{1.5}}}}$ over a field $K$ of characteristic $0$, the Hodge-to-de Rham spectral seq…

Formality conjecture. The Hochschild complex of the algebra $C^\infty(M)\rtimes G$ is a formal differential graded Lie algebra.

Let ${\mathcal F}$ be an arbitrary foliation on a compact Riemannian manifold. In the above notation, let $\Delta_F$ and $\Delta_H$ denote the leafwise and transverse Laplacians, r…

The coarse geometric Novikov conjecture. The map $Ind$ is injective.

Higher Cayley–Hamilton conjecture. On ${\cal L}_{{\hbar},q}^{\chi}$, the matrix $L_{(m)}$ satisfies

The q-index characteristic-polynomial conjecture. For every $m\ge 2$, the polynomial ${\cal CH^{\chi}}_{(m)}(t)$ has degree

Minimal noncommutative desingularization conjecture. The pair $(\operatorname{id}_X,\mathcal{E}nd(q_*\mathcal{O}_Y))$ is a minimal desingularization of $X$.

Projectivity conjecture. This union of schemes is actually a projective scheme.

Let $A^{\infty}$ be the smooth subalgebra of the group $C^*$-algebra associated with the dihedral group, and let $HC^n(A^{\infty})$ denote its cyclic cohomology in degree $n$. Cycl…

Flag-tuple parametrization conjecture. The tuple $T^\mathrm{DJ}$ is the flag tuple associated to $\OqG$; equivalently, $E^\mathrm{DJ}$ parametrizes all flag modules of the shape al…

Geometric reconstruction conjecture. The tuple $T^\mathrm{DJ}$ is a braided tuple, and

Let $\cA=C^\infty(\mathbb{T}^2)\rtimes\mathbb{R}$, with generators $u_1,u_2$ for the torus part and $v_t$ for the crossed-product action, and let $D$ be the Dirac-type operator def…

Cartesian–Klein–Lie conjecture. The combination of Cartesian and Klein–Lie approaches based on the assumption that coordinates are often a representation space for a group action i…

Let ${\cal C}^A$ be the cyclic $A_\infty$-category obtained from Fukaya's $A_\infty$-category $(V^F,\eta^F,{\frak m}^F)$ by suspension, and let ${\cal C}^B$ be the cyclic…

Let $\mathcal{A}_1=\mathcal{D}_{L^2}(\mathbb{R}^{2N})$ be the algebra of Moyal multipliers acting on the relevant Hilbert space, let $\mathcal{B}(\mathbb{R}^{2N})$ denote the propo…