15 problems

Let $V$ be a vector space, let $G\subset SL(V)$ be a finite subgroup, and set $X=V/G$. Assume that there is a proper smooth crepant resolution $\pi:Y\to X$. For each homomorphism…

Let $X^{{\mathcal P},{\mathcal Q}}_{c,d}$ be a generalized Steinberg variety, and let $e_c\in\mathbb{Q}W_P$ and $e_d\in\mathbb{Q}W_Q$ be primitive idempotents associated with the c…

A generalized Steinberg variety $X^{{\mathcal P},{\mathcal Q}}_{c,d}$ is associated with nilpotent adjoint orbits in $\operatorname{Lie}(P/U_P)$ and $\operatorname{Lie}(Q/U_Q)$, de…

Let $W$ be the Weyl group of $G$, equivalently of $G^{\vee}$. Set $\fX=T^*_{\psi}\fY$, let $\CB=G/B$ be the flag variety, and let … denote the zero fiber of the moment map for the…

Uncorrected Borel–Moore homology conjecture. The conjecture attributed to the cited work proposes an isomorphism of modules

Let $X=G/H$ be the symmetric space under consideration, let $M=T^*X$, let $M^\vee$ be its hyperspherical dual, and let … Write $sgn$ for the sign representation of the Weyl group…

Let \tilde{\frac?} be the tensor product variety associated with dominant weights $\lambda_1,\lambda_2$, and let $\omega^1,\omega^2$ be the corresponding framing data, with…

Let $\mathcal{J}_\ell$ be the moduli space of flags of modules associated with an algebraic knot, and let its geometric superpolynomial be defined using the Borel–Moore homology of…

Let $\mathfrak{M}_{Dol}(r,0)$ and $\mathfrak{M}_{B}(r,0)$ be the stacks of semistable Higgs bundles and semisimple representations, respectively. Let $W_\bullet$ be the weight filt…

Let $Q$ be the quiver, let $\mathbf{d}\in\mathbb{N}^{Q_0}$, and let $\mathfrak{N}_{\Pi_Q,\mathbf{d}}^{\mathcal{SSN}}$ be the seminilpotent stack, with irreducible components…

Let $X$ and $X'$ be the varieties in the induction diagram, with a map $g\relationships W\to X'$ and the induced map … where … Let…

Consider the symmetric pair $(\mathfrak{g},\mathfrak{k})$ of type AIII induced by the longest word of the Weyl group of type $A_{\text{odd}}$. Let $\mathfrak{Z}(\mathbf{w})$ be the…

Let $G$ be a complex reductive group, and let $\mathcal{Loc}_G(S)$ denote the character stack of a surface $S$. Its Borel–Moore homology carries both the naive Hodge filtration ari…

Purity conjecture. The Hodge structure on $H_i^{BM}(\mathcal{C}oh(X)_P^{H-\operatorname{ss}})$ is pure for any $H$, and, in general, $H_i^{BM}(\mathcal{X})$ is pure for any algebra…

Levine's comparison conjecture. The natural transformation $\vartheta_{{\operatorname{MGL}}'}$ is an isomorphism.