17 problems

Let ${\mathcal{M}}_\B^{{\bm \mu},{\bf r}}$ be the generic wild character variety, let $d_{{\bm \mu},{\bf r}}$ be its dimension, and let…

Let $n$ be an even integer. An elementary wild character variety is a wild character variety arising from an elementary connection, considered up to isomorphism. Finiteness conject…

Let $\mathcal{X}$ be a wild character variety associated with a Painlevé equation, and consider an unfolding map from the wild character variety for a more irregular singularity to…

Let $\mathcal{M}_{\rm B}^{{\bm\mu},{\bf r}}$ be a generic wild character variety and let $\mathcal{M}_{{\bm\mu},{\bf r}}^*$ be the corresponding open de Rham space. Let…

Let $\mathcal{M}_{\rm B}^{{\bm\mu},{\bf r}}$ be a generic wild character variety of type $({\bm\mu},{\bf r})$ with genus $g=0$. Let $\mathbb H_{\widetilde{{\bm\mu}},r}(z,w)$ be the…

Irregular purity conjecture. The map $\nu$ induces

Wild character-variety conjecture. The weighted Poincaré polynomial satisfies

P=W conjecture. The weight filtration on the cohomology of the character variety is identified with the perverse Leray filtration on the cohomology of the corresponding Hitchin sys…

Let $\mu\in\mathcal{P}_n$, let $\mu'$ be the partition obtained by deleting the first part of $\mu$, and let $n'=n-\mu_1$. Set … Assuming the notation and the wild-to-tame correspo…

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…

Let ${\mathcal{M}}_\B^{{\bm \mu},{\bf r}}$ be the generic wild character variety, let $d_{{\bm \mu},{\bf r}}$ be its dimension, and let…

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 $C$ be a complex smooth projective curve, let $D=p_1+cdocdots+p_k+rp$, and let ${\mathcal{M}}_\Dol^{{\bm \mu},r}$ be the corresponding moduli space of stable twisted parabolic…

Let $C$ be a locally planar rational curve with a unique singularity, and let $\Lambda$ be a rainbow closure of a positive braid such that the topological knot underlying $\Lambda$…

Let a braid closure be the link of a singular plane curve, and let its associated moduli space be the moduli space of constructible sheaves with singular support in the correspondi…

Choose a marking of each conjugacy class $\breve{\mathcal{C}}_i\subset \operatorname{GL}(V_i)$ for all $i\in I$. Gluing legs to obtain a supernova graph $\widehat{\Gamma}$ with nod…

Let $\Gamma$ be a simply-laced supernova graph with monochromatic core, and let $\mathcal{M}^{st}(\Gamma,q,d)$ be the associated stable multiplicative quiver variety, which is a hy…