28 problems

Flow-closedness conjecture. If $\mu_c$ is a complex moment map associated to a linear action by a compact group $G$ on a vector space, then $|\mu_c|^2$ is flow-closed.

Flag Hilbert scheme conjecture. The following hold:

Moment-mapping conjecture. If the geometric quantization is suitably normalized, then the restriction of the moment mapping to the intersection of the unit sphere with the space of…

Moment-map fiber dimension conjecture. One has

Symplectic-singularities conjecture. Every fiber $Y$ of $\widetilde{\psi}_{G,X}/\!/G$ has symplectic singularities.

Nilpotent-model irreducibility conjecture. If $X=M_G(H,\eta,V)$, where $\eta$ is nilpotent, then $X$ satisfies (Irr).

Irreducibility conjecture. Every conical irreducible Hamiltonian $G$-variety $X$ satisfies (Irr).

Let a Hamiltonian $G$-manifold have $G$-moment map $\mu\colon M\to\mathfrak{g}^*$. The double commutator conjecture. The centralizer of the algebra of $G$-invariant functions on…

Let $G=K\exp\mathfrak p$ be a compatible subgroup of a complex Lie group acting holomorphically on a space $Z$, with moment map and associated semistable set…

Let $Q$ be a quiver with doubled quiver $\overline{Q}$, let ${\alpha}$ be a dimension vector, and let ${\lambda}\in\mathbb{C}^I$. Write…

Let $r$ be the rank parameter, let $V$ be a symplectic vector space, and let ${\mathfrak s}{\mathfrak l}_r$ be the Lie algebra of traceless $r\times r$ matrices, so that … The mome…

Let $Q'$ be an extended Dynkin quiver with minimal imaginary root $4\delta=(d_1,\ldots,d_k)4$, let $Q$ be obtained by adjoining a vertex and an arrow to an extending vertex, and le…

Let a compact group act in a finite-dimensional setting with moment map, and let the flow be the gradient flow of a convex function of that moment map. Conjecture on convex moment-…

Lagrangian conjecture. The subvariety $\Lambda_{{\mathscr{X}}}\subseteq {\mathscr{X}}$ is Lagrangian. This conjecture concerns the geometry of the moment-map fiber associated with…

Quadratic norm conjecture. The norm squared

Let $Q$ be a 2-connected quiver, and define … … Wyss's asymptotic relation conjecture. The limits $A_Q$ and $B_{\mu_Q}$ are directly related. The source says this relation is impli…

Uniformity conjecture. There exists a rational function $W\in\mathbb{Q}(T)$ such that, for almost all primes $p$ and every finite field $\mathbb{F}_{q}$ of characteristic $p$,

Properness conjecture. The moment map $\bm\mu$ is proper.

Let $\ngo$ be a nilpotent Lie algebra. Consider the space of diagonalizable derivations of $\ngo$ for which the corresponding one-dimensional solvable extension admits a left-invar…

Let the Hitchin-cscK system be considered in complex dimension greater than one, and let the Biquard–Gauduchon function be the function used in the higher-dimensional analogue of t…

Compatibility conjecture. The following diagram commutes:

Generation conjecture. The polynomials $f_J$, $g_J$, $h_{\iota}$, $k_{n,J}$, and $l_{J,1}$ generate the $B$-invariant subalgebra $\mathbb{C}[T^*(\mathfrak{b}\times\mathbb{C}^n)]^B$…

Let $\mathfrak{n}$ be a nilpotent Lie algebra, let $\mathfrak{t}(\mathfrak{n})$ be a maximal torus of diagonalizable derivations, let $\mathfrak{t}(\mathfrak{n})_{\mathrm{srn}}$ be…

Let $\pi:X\to B$ be a holomorphic fibration equipped with the optimal symplectic connection condition. Moment-map conjecture. The optimal symplectic connection condition arises fro…

Let $tau=rho{ u}^{(r)}$ denote the irreducible $mathfrak{S}r$-representation indexed by a partition $u$ of $r$, let $rho{ u}^{(r)}$ be the corresponding Specht representation, and…