8 problems

Homotopical constancy conjecture. If the isolated singularity $(X_0,f_0)$ does not split, then the Milnor fibration of the isolated singularity of $(X_t,f_t)$ is homotopically cons…

Let $(V,p)$ be a normal isolated surface singularity with rational homology $3$-sphere link, and let it have a smoothing with Milnor fiber $M$ and monodromy $\psi$. Suppose that…

Let $V = \{f = 0\}$ be a $2$-dimensional weighted-homogeneous isolated hypersurface singularity with rational homology $3$-sphere link $Y$, Milnor fiber $M$, and monodromy $\psi$ o…

Let $G:({\mathbb R}^{m},0)\to({\mathbb R}^{p},0)$ be a nice analytic map germ with $m>p\geq2$ and radial discriminant, and suppose that $\Psi_G$ is $\rho$-regular. Assume that the…

Milnor vector field conjecture. If both fibrations exist under these conditions, then they are equivalent.

Let ${\mathcal{A}}$ and ${\mathcal{A}}'$ be central arrangements in $\mathbb{C}^3$, let $F({\mathcal{A}})$ denote the Milnor fiber, and let…

Combinatorial monodromy conjecture. The characteristic polynomial is determined by this formula. The preceding results establish the formula in several cases, including arrangement…

Let $\psi=(f_1,\ldots,f_k):\mathbb{R}^n\to\mathbb{R}^k$ be a polynomial mapping with an isolated singularity at the origin. Compose $\psi$ with the projection…