Ratner's non-divergence conjecture for unipotent flows

Let $G$ be a Lie group, let $\Gamma$ be a discrete subgroup of $G$, let $\{u_t\}_{t\in\mathbb{R}}\subseteq G$ be a unipotent one-parameter subgroup, and let $x=g\Gamma\in G/\Gamma$. For a neighborhood $N$ of the identity in $G$, consider the set of times at which the conjugated subgroup intersects $N$ nontrivially. Ratner's non-divergence conjecture. For any point $x=g\Gamma\in G/\Gamma$, there exists a neighborhood $N$ of the identity in $G$ such that

$$\frac{1}{T}m\bigl(\{t\in[0,T]:N\cap(u_tg)\Gamma(u_tg)^{-1}\neq\{e\}\}\bigr)<\epsilon$$

for all large $T>0$, where $m$ is Lebesgue measure on $\mathbb{R}$. This conjecture asks for quantitative non-divergence of unipotent flows for arbitrary discrete subgroups, extending the known results for lattices and related settings; its resolution is not specified in the source.