28 problems

Kaledin's conjecture. Every symplectic singularity is formally isomorphic to a conical symplectic singularity.

Let $\mathcal M_C(\mu,\lambda)$ denote the Coulomb branch of a $3d$ $\mathcal N=4$ gauge theory, equivalently the moduli space of singular monopoles with magnetic charge $\mu$ and…

Symplectic singularities conjecture. For all $(V,G)$, the modified complex symplectic quotient has symplectic singularities and is graded Gorenstein.

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

Let $Y$ be a symplectic singularity, let $y\in Y$ be a closed point, and let $Y_{y,0}$ be the transversal symplectic slice in the formal product decomposition … A $\mathbb{G}_m$-ac…

Poisson-cohomology conjecture. There is an isomorphism of vector spaces

Namikawa's conjecture. The variety $W$ is smoothable by flat deformations if and only if it admits a symplectic resolution.

F.-N.'s conjecture. There are flat deformations

Namikawa's conjecture. For any two symplectic resolutions $f_i:X_i\to W$, $i=1,2$, there are deformations

A contact singularity is a singularity carrying the contact structure considered by Campana and Flenner. A symplectic singularity is a normal singularity whose smooth locus has a s…

Finiteness conjecture. Any symplectic singularity admits at most finitely many non-isomorphic symplectic resolutions.

Stronger deformation conjecture for symplectic resolutions. There exist deformations

Symplectic-resolution deformation-equivalence conjecture. Then $Z_1$ is deformation equivalent to $Z_2$.

Hyperkähler cone conjecture. Any conical symplectic singularity is a hyperkähler cone.

Bonnafé's conjecture. The normalization of the closure of any symplectic leaf on the associated Calogero–Moser variety is isomorphic to a Calogero–Moser variety for the group…

A generalized quiver is a triple $(V,A,K)$, where $V$ is finite, $A:V\times V\to\mathbb{Z}$, and $K:V\to\mathbb{Z}_{>0}$, satisfying the diagonal and symmetrizability conditions st…

Let $Q$ be a good 3d $\mathcal{N}=4$ quiver theory, let $\mathcal{M}_C(Q)$ denote its Coulomb branch, and let $\mathcal{L}$ be the set of decay and fission products of $Q$, ordered…

Let $G$ be a connected semisimple group, let $P$ be a parabolic subgroup of $G$, and let $U_P$ be its unipotent radical. Let $B$ be a Borel subgroup and set … as a homogeneous vect…

Let $G$ be a reductive linear algebraic group and let $U$ be a maximal unipotent subgroup. The affine closure $\overline{T^*(G/U)}$ is the variety whose coordinate ring is the ring…

Symplectic-duality conjecture. Nilpotent slices should be the symplectic duals of certain affinizations of covers of nilpotent orbits.

The Higgs branch is a symplectic singularity with a Hasse diagram of symplectic leaves. For generalized toric polygons with mutually non-local 7-branes, the T-brane data are expect…

Let $W$ be a complex reflection group, let $\tau$ be a finite-order element of the normalizer of $W$ in ${\mathrm{GL}}_{\mathbb{C}}(V)$, and let $c\in{\mathcal{C}}$ satisfy…

Let $G_c$ be the compact form of a gauge group, and let $mu$ and $lambda$ be coweights with $lambda$ dominant. For dominant $nu$ satisfying $mu\leqnu\leqlambda$, let…

Let $(Q,\mathbold{v},\mathbold{w})$ be a quiver with Coulomb branch $\mathcal{M}_C(Q,\mathbold{v},\mathbold{w})$. For generic deformation parameter $\mathfrak{d}$, let…

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…