8 problems

Let $k$ be a non-Archimedean complete valued field that is nontrivially valued and algebraically closed, and let $X$ be a smooth compact boundaryless $k$-analytic space. An entire…

Let $p_{cr}\ge 2$ and let $\Gamma$ be a compact analytic hypersurface. Let $M_\Gamma$ denote its associated maximal operator, let $\mu$ be the measure on $\Gamma$, and let…

Let $X$ be a pure $d$-dimensional $\mathbb{K}$-analytic set, where $\mathbb{K}$ is $\mathbb{C}$ or $\mathbb{R}$, and let $\mathcal{N}(X)$ denote its Nash transformation. A Nash–Sem…

Let $k$ be a complete non-Archimedean valued field, and let $f:X\rightarrow S$ be a quasi-finite morphism of quasi-compacted, separated $k$-analytic spaces. We seek a factorization…

Whitney's fibering conjecture. Every analytic subvariety $V\subset U$ has a stratification such that each point $p_0\in V$ has a neighborhood $U_0$ with a semi-analytic fibration.

Let $d\geq 2$, let $V$ be a periodic potential, and let $F_{\lambda}(V)$ denote the Fermi variety at energy $\lambda$. An analytic set is irreducible if it cannot be represented as…

Let $V$ be a periodic potential and let $B(V)$ denote its Bloch variety. An analytic set is irreducible if it cannot be represented as the union of two nonempty proper analytic sub…

Let $V$ be an analytic variety in $\mathbb C^n$ and let $X$ be a stratum of an analytic stratification of $V$. For every point $p\in X$, there should exist a neighborhood $U$ of…