15 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 $f=(f_1,\ldots,f_p):(\mathbb{R}^n,0)\to(\mathbb{R}^p,0)$ be an analytic map germ with $n>p\geq 2$, where $p$ is odd, and let … be its nonempty link. Let … be the associated Mil…

Let $f:(\mathbb{R}^n,0)\to(\mathbb{R}^p,0)$ be an analytic map germ admitting a Milnor fibration … Here $0<\eta\ll\epsilon\leq\epsilon_0$, where $\epsilon_0$ is a Milnor radius for…

Let $f:(M,D)\to(\mathbb C,0)$ be a resolved singularity, and for each nonempty subset $J$ of the irreducible-component index set $I$, let $(M,D)^{\mathrm{mot}}_{|D_J^\circ}$ be the…

Finer Grothendieck-ring conjecture. The equivalences given in Section 4 should be much stronger and should imply the existence of the motivic Milnor fibre in a much finer Grothendi…

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…

Let ${\mathcal{A}}$ be a generic arrangement of $n$ planes in $\mathbb{C}^3$, and let ${\partial{{\overline{F}}}}$ be the boundary of its Milnor fiber. Suciu's torsion conjecture.…

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

Let $f$ be a homogeneous polynomial that is a product of distinct linear forms, so that $f=0$ defines a hyperplane arrangement, and let $F=f^{-1}(1)$ be its Milnor fiber. The homol…

Let $f$ and $g$ be holomorphic function-germs on a holomorphic germ of a complex analytic space $X$, with no common irreducible components. Suppose that the real analytic map-germ…

Let $Y$ be the Milnor fibre compactification equipped with the product-type metric described above, and let $D$ be its signature operator. Denote by $D_{I-P_{Y_0}}$ the operator wi…