6 problems

Representations of the fundamental group form an algebraic variety, called the character variety. In higher dimensions, good formal structures for Stokes data can fail before modif…

The Fourier-transform construction gives isomorphisms between wild character varieties, and for an irregular class $\mathit{\Theta}$ let $\widehat{\Theta}$ denote its formal Fourie…

Twistor Riemann–Hilbert conjecture. The iteration converges, and the spectral coordinates of $\nabla^\mathrm{H}_w(R,\zeta)$ satisfy

Fix $w\in {\mathcal B}'$ and let $\Gamma'=\{\gamma\in\Gamma\mid\Omega(w,\gamma)\neq0\}$, which is finite in the examples considered. Let…

Fix $w\in {\mathcal B}'$ and let $\hbar\in{\mathbb C}^\times$. Let $X_\gamma(\hbar)$ be the spectral coordinate associated to the oper connection $\nabla_w^\mathrm{op}(\hbar)$, and…

Consider the wild character varieties in the case $g=0$, $k=0$, $m=1$, and $r=r_1\in\mathbb{Z}_{>0}$, together with the more general wild character varieties discussed by the cited…