6 problems

Dominance conjecture for higher Albanese maps. The map

CDY's virtual nilpotence conjecture. The group $\pi_1(X)$ is virtually nilpotent.

Let $S \subset K \subset \mathbb R^n$ be a bounded definable set with a monotone family of compact sets $\{S_\delta\}_{\delta>0}$ satisfying $S=\bigcup_\delta S_\delta$. Suppose th…

Let $K \subset \mathbb R^n$ be a definable bounded set in an o-minimal structure over $\mathbb R$, with a fixed linear order of the coordinates. A cylindrical decomposition of…

Let $K \subset {\mathbb R}^n$ be a compact definable set in an o-minimal structure over $\mathbb R$, and let $\{S_\delta\}_{\delta>0}$ be a monotone family of compact subsets of…

Let $f:K\to\mathbb{R}$ be a definable function on a compact definable set $K\subset\mathbb{R}^m$. A definable triangulation of $K$ is a definable triangulation whose open simplices…