15 problems

Jet-point counting conjecture. Then there exists a constant $D$ such that

Consider bifiltered affine schemes associated with four-dimensional $\mathcal{N}=2$ superconformal field theories having non-trivial Higgs branches, and let the jet scheme of such…

Let $k$ be an algebraically closed field of characteristic $0$, let $f\in k[[x_{1},...,x_{n}]]$ define an isolated singularity at $0$, and let $J(f)$ be the Jacobian ideal of $f$.…

Let $k$ be an algebraically closed field of characteristic $0$, let $R=k[[x_{1},...,x_{n}]]$ with maximal ideal $\mathbf{m}$, and let $f\in R$ be a weighted homogeneous polynomial.…

Shellability and Hilbert-series conjecture. The abstract simplicial complex corresponding to $\tilde{I^{m,n}_{r,k}}$ is shellable, and the Hilbert series of the principal component…

Let $G$ be a very well-covered graph, and let $\mathcal{J}_s(G)$ denote its graph of $s$-jets. Galetto–Helmick–Walsh conjecture. The graph $\mathcal{J}_s(G)$ is very well-covered f…

Uniformity conjecture. There exists a rational function $W\in\mathbb{Q}(T)$ such that, for almost all primes $p$ and every finite field $\mathbb{F}_{q}$ of characteristic $p$,

Let $f$ and $Z$ be as in the paper's notation, let ${\mathcal O}$ be the coefficient ring, and let $K\supset {\mathcal O}$ be a number field. For each local field $L$, write $k_L$…

Let $n\in\mathbb N$, let $I\subset(x_1,\dots,x_{n+c})$ define the $n$-dimensional variety $X=\operatorname{Spec}k[x_1,\dots,x_{n+c}]/I$, and let $s_m(0;X)$ be the jet-scheme invari…

The semicontinuity conjecture for minimal log discrepancies. The function

Let $r$ and $k$ be positive integers, and let $I^{2r+1,k}_r$ denote the jet pfaffian ideal associated with the ideal of size-$2r$ pfaffians of a generic $(2r+1)\times(2r+1)$ skew-s…

Let $X$ be a $d$-dimensional variety, let $x\in X$ be a closed point, and let $s_m(X,x)=(m+1)d-\dim X_m(x)$, where $X_m(x)$ is the local $m$-jet scheme at $x$. Let $\delta$ be an i…

Let $X$ be a variety of dimension $d$, let $x$ be a closed point of $X$, and define … where $X_m(x)$ is the local $m$-jet scheme of $X$ at $x$. Finite determination conjecture. For…

Uniform finite jet characterization conjecture. There exists a number $N_d$ depending only on $d$ such that

Finite jet detection conjecture. There is a number $N_{\delta,d}$ depending only on $\delta$ and $d$ such that, if