8 problems

Let $G$ be a simply-connected reductive group, let $\\g\in\mathfrak{g}((t))$ be topologically nilpotent, and let $A_{\g}$ denote the component-group action on the affine Springer f…

Let $G$ be a semisimple group over $\mathbb{C}$, let $\mathcal{M}^{\circ}_G$ be the neutral component of the affine Toda moduli space, and let $J^G_{G^{\mathrm{sc}}}$ be the associ…

Let $M_{r,\chi}$ be the moduli space of one-dimensional stable sheaves on $\mathbb{P}^2$ with support in the class $[rH]$ and Euler characteristic $\chi$, where $H$ is the hyperpla…

Let $C$ be a complex smooth projective curve of genus $g$, with divisor $D=p_1+\dots+p_k+rp$, where the points are distinct and $p$ has multiplicity $r$. Let ${\bm \mu}$ be a $k$-t…

Let $\bm{\mu}$ be the multipartition encoding the parabolic data of $M_B(n)$, let $k$ be as defined in the paper, and let $\mathbb{H}_{\bm{mu}}$ be the function defined in Section…

Let $M_D(n)$ be one of the five families of Hitchin moduli spaces, let $M_B(n)$ be the corresponding character variety, and let the perverse numbers of $M_D(n)$ be the dimensions o…

Let $X$ be a smooth complex projective variety and $G$ an algebraic reductive group. Let $M_D$ be the moduli space of Higgs $G$-bundles, with proper Hitchin map, and let $M_B$ be t…

Let $\mathcal{M}_\Dol$ be the Dolbeault moduli space and $\mathcal{M}_\B$ the corresponding Betti character variety. Let $P_\bullet$ be the perverse filtration on…