4 problems

Let $G$ be a reductive group with Langlands dual $G^\vee$, let $C$ be the underlying curve, and let $D=\{c_i\}$ be the parabolic divisor. Let $(E,\varphi,Q)$ be a smooth fixed poin…

Let $X$ be a compact Riemann surface with marked points and fixed parabolic parameters, and let the corresponding character variety parametrize representations of the fundamental g…

Let $X$ be a compact Riemann surface, let $D\subset X$ be a finite set of marked points, and fix corresponding parameters for filtered local systems and parabolic Higgs bundles of…

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…