5 problems

A Joyce structure on a moduli space of quadratic differentials with simple poles is a geometric structure of the type considered in the paper. The examples above admit a Killing ve…

Joyce–Tanaka generic uniqueness conjecture. For a generic point of $X^\#$ lying over a point $(C,Q_0)\in M$, there is a unique equation satisfying the stated pole and apparent-sing…

Let $M$ be the moduli space of pairs $(C,Q_0)$, let $\mathcal O=\mathcal O(g,m)$ be the space of data $(C,Q_0,Q_1,Q_2)$ described above, and let $X^\#$ be the space equipped with t…

Let $\mathcal O=\mathcal O(g,m)$ be the space of data $(C,Q_0,Q_1,Q_2)$ satisfying the prescribed pole, apparent-singularity, and residue conditions, and let $X^\#$ be the correspo…

Let projective connections on Riemann surfaces have apparent singularities, and consider their isomonodromic deformations. Bridgeland's Joyce-structure conjecture. These isomonodro…