3 problems

Newelski's conjecture. In good circumstances, for example when $T$ is an NIP theory, the canonical epimorphism

Henselianity conjecture. The valuation ring $\mathcal{O}$ is henselian.

Generic compact domination conjecture. For $h$-almost every coset $gG^{00}$ of $G^{00}$, the set $S\cap gG^{00}$ lies either entirely inside $X$ or entirely outside $X$.