6 problems

Birbrair–Gabrielov conjecture. If $(X_0,0)$ and $(X_1,0)$ are ambient topologically equivalent and outer bi-Lipschitz equivalent, then $X_0$ and $X_1$ are ambient bi-Lipschitz equi…

Let $X\subset\mathbb{C}^n$ be a pure $d$-dimensional entire complex analytic subset. Suppose that there exists a sequence $T=\{t_j\}_{j\in\mathbb{N}}$ of real positive numbers such…

Sharpness conjecture for Lipschitz nice dimensions. If $(n,p)$ lies in the complement of the nice dimensions or in their boundary, then $\mathrm{S}^{Lip}(N,P)$ is not dense in…

Lipschitz nice-dimensions conjecture. The Lipschitz nice dimensions contain Mather's nice dimensions and their boundary.

Neumann–Pichon's conjecture. $X$ is metrically conical at $0$ if and only if $X$ is locally metrically conical at $0$.

Let $(S_0,0)$ and $(S_1,0)$ be two normally embedded real semialgebraic surface germs. They are normally embedded when their inner and outer metrics are bi-Lipschitz equivalent; fo…