15 problems

Let $X$ be a variety over a perfect field $k$. Write $\operatorname{Der}_{\mathbb{C}}(\mathcal{O}_X)$ for the module of derivations of $\mathcal{O}_X$ over $\mathbb{C}$. Zariski–Li…

Smoothness conjecture for $D_k$. The curve $D_k$ is smooth if and only if the polynomial $x^7+kx^5+1$ has no zeros in $\mathbb{F}_q$. This is proposed as the even-characteristic co…

Let $f:M\rightarrow B$ be a generic special Lagrangian fibration of an almost Calabi–Yau $3$-fold, including fibres with singularities, where generic' has the meaning specified in…

Let $I_\Psi$ be the exponential functional of a potentially killed Lévy process with Lévy measure tail $\overline{\Pi}(0)$ and Gaussian coefficient $\sigma^2$. Infinite differentia…

Residuality conjecture. Residuality with exponent $\alpha\in(2,3)$ refers to the Hölder continuity of the second derivative.

Smoothness detection conjecture for $C_{k,r}$. There exists an integer $s=s(r)$ such that, for every finite field $\mathbb{F}_q$ of characteristic not dividing $r$ and every…

Existence conjecture for $C_{k,r}$. There exists an integer $m=m(r)$ such that, for every finite field $\mathbb{F}_q$ with $q>m$ and characteristic not dividing $r$, there is some…

Let $W^{(q)}$ be the $q$-scale function of a spectrally negative Lévy process, and let the process have jump measure $Pi$. Doney's conjecture. The smoothness of the scale functions…

Let $N_{\infty}(\delta,\mathcal{S}_{\gamma+1})$ denote the covering number of the smooth-function class $\mathcal{S}_{\gamma+1}$ at accuracy $\delta$, and let the lower bound in eq…

Let $S_{n+1}$ be the symmetric group, let ${\mathbf W}_n$ be the set of words, and let $\operatorname{inv}(\sigma)$ denote the inversion number of $\sigma$. For a nonidentity permu…

The nonlinear subdivision schemes $S_\epsilon$ and $T_{2,2}$ generate limit functions from the initial data considered in Figures 2 and 3, and the smoothness exponent is estimated…

Let $\Psi$ be a Laplace exponent in the class considered in the paper, and let $f_\Psi$ denote the density associated with the exponential functional $I_\Psi$. Assume that either t…

Let $0$ be the origin of $\Bbb R^{m+1}$, let $y$ be its $(m+1)$-st coordinate, and let $h\in C^k(\Bbb R^{m+1})$ satisfy … for some $s\le k$. Write $C^k(\Bbb R^{m+1})_{(0)}$ for the…

Smoothness conjecture. Any complete marginal log-linear parameterization is smooth.

Let $\mathbb{K}$ be a field, and consider the notions of simplicial smoothness and cubical smoothness for maps defined using simplicial and cubic divided differences, respectively.…