17 problems

Let $x\thicksim X$ be a symplectic singularity. Let $v_X$ be the valuation associated with $x$ in Theorem AGlc, and let $r(\xi)$ denote the rational rank associated with $\xi$ in T…

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

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

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 the Higgs and Coulomb branches of a 3d $\mathcal{N}=4$ supersymmetric gauge theory be mirror dual symplectic singularities, and let $\mathcal{O}$ denote the category associated…

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 $\mathcal{M}_{q,\theta}(Q,\alpha)$ denote a multiplicative quiver variety. A symplectic singularity is a normal singular variety whose smooth locus carries a symplectic form ex…

Let $Y$ be a conical symplectic singularity, let $\lambda,\lambda'\in\mathfrak{h}_Y^*$, and let $\overline{\operatorname{HC}}(\mathcal{A}_{\lambda'},\mathcal{A}_{\lambda})$ denote…

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

Let $\tilde{Y}^\lambda_\mu$ be the parameterized algebra obtained from $\tilde{Y}_\mu$ by base change along the map from the $r_i^{(s)}$ to the $c_i^{(s)}$ and imposing…