7 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 \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 $\mathfrak{M}_{Dol}(r,0)$ 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…

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…