7 problems

Let $\mathcal{F}$ be a $\mathcal{C}$-formal type of slope $r/h$, and let $\mathscr{O}\subset\operatorname{\mathfrak{g}}$ be a nilpotent orbit. Write…

Sabbah's conjecture. There is a finite sequence of point blow-ups

Let $\mathbf{S}=(S_i)_{i=1,\ldots,d}$ be a collection of abstract spectral types. A collection is irreducibly realizable if it is the spectral type of an irreducible meromorphic…

Jimbo–Miwa–Ueno differential conjecture. One has

Abate and Tovena's conjecture. There is a neighborhood $U$ of $p_0$ such that every geodesic ray which enters into $U$ tends to $p_0$. The two rays of any geodesic which stays in…

Let $S^o=\mathbb{P}^1(\mathbb{C})\setminus\{p_0,p_1,\dots,p_r\}$, where $p_0,p_1,\dots,p_r$ are the poles of a meromorphic connection $\nabla$ on $\mathbb{P}^1(\mathbb{C})$. Let…

Let $(M,t^0)$ be an irreducible germ of a generically semisimple F-manifold. A generically semisimple F-manifold structure conjecture. The existence and parametrization assertions…