12 problems

Deligne–Grothendieck conjecture. There is a unique natural transformation

Let $X\subset(0,\infty)\times\mathbb{R}^k$ be a subanalytic set, and let $F\colon X\to\mathbb{R}$ be a constructible, non-negative function, written $F(\varepsilon,\bm{x})$. A func…

Theorem concerns constructible functions with compact support and a distance controlled by the convolution distance. Extension conjecture. Theorem should continue to hold when the…

Let $X$ be an aspherical complex projective manifold. A constructible function on $X$ has an effective characteristic cycle when its characteristic cycle is effective. Uniform non-…

Let $X$ be an aspherical complex projective manifold and let $Z\subseteq X$ be a closed irreducible subvariety. Let $Eu_Z$ be MacPherson's local Euler obstruction function, let…

Let $K=\mathbb{C}$ and let $\Pi=\Pi(C,D)$. Define the support of a constructible function $f\colon \operatorname{nil}_E(\Pi,d)\to\mathbb{C}$ by … Let…

Let $X$ be a real-analytic smooth manifold, and let $f$ and $g$ be $\mathbb{C}$-valued constructible functions on $X$. Suppose that their supports, or more generally the constructi…

Let $\mathbf{k}=\mathbb{R}$ or $\mathbb{C}$, and let $K_0=K_0(\operatorname{sa}_\mathbb{R})$ when $\mathbf{k}=\mathbb{R}$ and $K_0=K_0(\operatorname{Var}_\mathbb{C})$ when…

Let $\mathrm{\mathbf{econv}}(\mathrm{Gr})_0$ be the subcategory of constructible-function convolutions generated by the relevant Satake-fibre functions, and let…

Let $R_\chi$ be the Radon transform associated with the Euler characteristic in the double-fibration setting above, and let the Khovanskii–Pukhlikov constructible functions be fini…

Let $X$ and $Y$ be smooth manifolds in a double fibration … where $q_1$ and $q_2$ are smooth submersions, $q_1\times q_2$ is a closed imbedding, and $q_2$ is proper. Let $R_\chi$ b…

Let $X$ be a Calabi–Yau $3$-fold over $\mathbb C$, and let $(\tau,G,\leqslant)$ be a generic Gieseker stability condition. For each $\alpha\in C(\operatorname{coh}(X))$, let…