12 problems

Morsification conjecture for topological exceptional collections. The ordered collection of vanishing cycles obtained from a topological exceptional collection of geometric vanishi…

The differential-value conjecture. For any element $\lambda\in\Lambda_C\setminus\Gamma_C$, the rational number $-\lambda/nm$ is a root of the Bernstein–Sato polynomial of $C$.

Let $f\in\mathbb{K}[[x,y]]$ be a reduced power series, and let $\mathcal{T}$ be a minimal tree of $f$. Let $\mathcal{V}$ be the set of vertices of $\mathcal{T}$, let…

Let $R$ be a plane curve germ over $\mathbb{C}$, and let $\widehat{\mathit{NZ}}_R(t)$ denote its completed numerator series. Modularity and topological invariance conjecture. There…

Topological monodromy conjecture. If $\theta$ is a pole of $Z_f^{\mathrm{top}}(s)$, then $\exp(2\pi i\theta)$ is an eigenvalue of the monodromy $M_x^{(q)}$ for some $q\in\mathbb N$…

Restricted Yano conjecture. The $b$-exponents $\{\tilde{\beta}_1,\ldots,\tilde{\beta}_\mu\}$ of a generic element of $\Sigma_\mu$ satisfy

An algebraic divide is a divide arising from a real morsification of a plane curve singularity. A divide is malleable when it is YB-equivalent to a scannable divide, where YB-equiv…

Let $D$ and $D'$ be link-equivalent scannable algebraic divides of the same minimal index. Let $\beta(D)$ and $\beta(D')$ be their associated positive braids; two positive braids a…

Let $(C,z)$ and $(C',z')$ be real isolated plane curve singularities, and choose real morsifications of them. Each morsification has an associated quiver; two quivers are mutation…

Existence conjecture. Every real plane curve singularity possesses a real morsification.

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 $X^n$ be the space of homogeneous binary forms of degree $n$, let ${\mathcal R}^n$ be the collection of invariant rational functions on $X^n$ obtained by evaluating absolute cl…