13 problems

Let $M\subset\mathbb C^N$ be a real analytic generic submanifold and let $p\in M$ be a point of finite type. Let $M'\subset\mathbb C^{N'}$ be a real analytic set containing no nont…

Let $M$ and $M'$ be connected real analytic hypersurfaces through $0$ in $\mathbb C^2$, and suppose that $M$ is of finite type at some point. Let…

Let $M\subset\mathbb C^N$ be a real analytic CR submanifold. Let $p\in M$, let $M'\subset\mathbb C^N$ be a real analytic submanifold with $\dim_{\mathbb R}M=\dim_{\mathbb R}M'$, an…

Let $M\subset\mathbb C^N$ be a real analytic CR submanifold, let $p\in M$ be a point of finite type, and let $K$ be a positive integer. Let $M'\subset\mathbb C^{N'}$ be a real anal…

Let ${\mathcal P}$ be the domain of a Noetherian chain and let $P_1,\ldots,P_n:{\mathcal P}\to\mathbb C$ be Noetherian functions of format ${\mathscr F}$. Khovanskii's format-bound…

Let $X,Y\subset\mathbb{R}^n$ be two germs at the origin of irreducible real analytic subsets. Let $h\colon(\mathbb{R}^n,0)\to(\mathbb{R}^n,0)$ be a germ of a subanalytic, arc-analy…

Let $f$ be a real analytic function on an open set $U\subset\mathbb{R}^n$, and let $x(t)$ be a gradient flow line of $f$ with a limit point $x_0\in U$. Arnold–Thom conjecture. If…

Milnor vector field conjecture. If both fibrations exist under these conditions, then they are equivalent.

Let $f$ be an analytic function and let $x(t)$ be a gradient flow line of $f$. Suppose that $x(t)$ has a limit point $x_{\infty}$ as $t\to\infty$. Stronger Arnold-Thom conjecture.…

Let $G$ be the group under consideration, and call a real-analytic subset of $G$ simple if it is contained in a finite union of sets of the form … with $\chi\in\widehat G$ and…

Let $w\subset\mathbb{R}^d$ be a bounded closed connected set with non-empty interior, and suppose that its boundary is a real-analytic submanifold of $\mathbb{R}^d$. The real-analy…

Ebenfelt–Huang analyticity conjecture. Any $C^{\infty}$-smooth CR (local) diffeomorphism

Let $M$ be a real-analytic symplectic manifold of dimension $2n$, and consider a Hamiltonian system … Assume that the system is completely integrable by an infinitely dimensional n…