We prove the non-left-orderability of the fundamental group of the $n$-th fold cyclic branched cover of the pretzel knot $P(3,-3,-2k-1)$ for all integers $k$ and $n\geq 1$. These 3-manifolds are $L$-spaces discovered by Issa and Turner.

We consider the Laplace-Beltrami operator $\Delta_{g}$ on a smooth, compact Riemannian manifold $(M,g)$ and the determinantal point process $\mathcal{X}_{\lambda}$ on $M$ associated with the spectral projection of $-\Delta_{g}$ onto the subspace corresponding to the eigenvalues up to $\lambda^{2}$. We show that the pull-back of $\mathcal{X}_{\lambda}$ by the exponential map $\exp_{p} : T_{p}^{*}M \to M$ under a suitable scaling converges weakly to the universal determinantal point process on $T_{p}^{*} M$ as $\lambda \to \infty$.

Denote by $\mathbf{G}(k,n)$ the Grassmannian of linear subspaces of dimension $k$ in $\mathbf{P}^{n}$. We show that if $n>m$ then every morphism $\varphi: \mathbf{G}(k,n) \to \mathbf{G}(l,m)$ is constant.