5 problems

Let $M$ be a three-manifold and let $G$ and $G^{\vee}$ be Langlands dual groups. Write $\mathfrak{M}_G(M)$ and $\mathfrak{M}_{G^{\vee}}(M)$ for the corresponding stacks of local sy…

Let $C$ be a smooth projective curve with underlying Riemann surface $\Sigma_g$. Let $\mathcal{H}^{\operatorname{Betti}}$ and $\mathcal{H}^{\operatorname{Dol}}$ be the graded BPS c…

Let $\Sigma$ be a compact oriented $2$-manifold and let $G$ be a semisimple group, with Langlands dual group $G^{\vee}$. Let…

Let $M$ be a Seifert-fibred $3$-manifold, let $G$ be a semisimple group, and for $n>0$ let $\Sigma_{\mathrm{orb},M}^{[n]}$ be the quotient of $M$ by the $S^1$-action composed with…

Let $S=\operatorname{Spec}\mathcal{O}_F$ where $\mathcal{O}_F$ is a local ring with finite residue field $k_F$. Let $D=K_\mathcal{C}$ and let $L\in\mathcal{P}ic^d(\mathcal{C})$ for…