6 problems

Let $f$ be a singular complex analytic germ at $0\in\mathbb{C}^{n}$ with $f(0)=0$, and let $\varphi$ be a Schwarz function on $\mathbb{C}^{n}$ with sufficiently small support and…

Demailly–Kollár's conjecture. The set $\mathcal{C}(n)$ satisfies the ascending chain condition: every ascending sequence in $\mathcal{C}(n)$ eventually stabilizes.

Let $X \subset \mathbb{C}^N$ be a variety of dimension $n$ with a normal isolated singularity at $0$. For sufficiently small $\epsilon>0$, let $L_{X,\epsilon}$ be its link, and let…

Let $X \subset \mathbb{C}^N$ be a complex variety of dimension $n$ with a normal isolated singularity at $0$. Its link $L_X$ carries a strongly pseudoconvex CR structure, and cohom…

A nonlinear dispersive equation has a dispersionless solution whose shocks are surrounded by regions of modulated oscillations. Complex-singularity conjecture. These regions can be…

Let $Re$ denote the Reynolds number, let $t_s$ be the time at which Prandtl's solution develops its separation singularity, and let $\delta_{NS}$ be the width of the analyticity st…