5 problems

Topological mirror symmetry in degree zero. For every $\kappa\in\hat{\Gamma}$, with $\gamma=w(\kappa)$,

Let $\mathcal{M}_{\B}^d$ be the $\operatorname{GL}_n$ character variety with central monodromy $\zeta_n^d I_n$, and let $\hat{\mathcal{M}}_{\B}^e$ be the corresponding…

Let $n$ be a positive integer, let $d,e$ be integers satisfying $(d,n)=(e,n)=1$, and let $\mathcal{M}_{\Dol}^d$ and $\hat{\mathcal{M}}_{\Dol}^e$ denote the corresponding Dolbeault…

Perverse topological mirror symmetry.

Let $\Gamma=H^1(C,\mathbb{Z}_n)$ act on the relevant Hitchin moduli space $\mathcal{M}^d$, and let $\hat\Gamma$ be its character group. Write $E_\kappa(\mathcal{M}^d;u,v)$ for the…