in this talk, i will explain some similar results and interaction between locally symmetric spaces and moduli spaces of riemann surfaces. for example, let $m_g$ be the moduli space of riemann of genus $g$, and $a_g$ be the moduli space of principally polarized abelian varieties of dimension $g$, i.e., the quotient of the siegel upper space by $sp(2g, z)$. then there is a jacobian map $j: m_g \to a_g$, by associating to each riemann surface its jacobian. the celebrated schottky problem is to characterize the image $j(m_g).$ buser and sarnak viewed $a_g$ as a complete metric space and showed that $j(m_g)$ lies in a very small neighborhood of the boundary of $a_g$ as $g$ goes to infinity. motivated by this, farb formulated the coarse schottky problem: determine the image of $j(m_g)$ in the asymptotic cone (or tangent space at infinity) $c_\infty(a_g)$ of $a_g$, as defined by gromov in large scale geometry. in a joint work with enrico leuzinger, we showed that $j(m_g)$ is $c$-dense in $a_g$ for some constant $c=c(g)$ and hence its image in the asymptotic cone $c_\infty(a_g)$ is equal to the whole cone. another example is that the symmetric space $sl(n,r)/so(n)$ admits several important equivariant cell decompositions with respect to the arithmetic group $sl(n, z)$ and hence a cell decomposition of the locally symmetric space $sl(n, z)/sl(n, r)/so(n)$. one such decomposition comes from the minkowski reduction of quadratic forms (or marked lattices). we generalize the minkowski reduction to marked hyperbolic riemann surfaces and obtain a solution to a folklore problem: an intrinsic equivariant cell decomposition of the teichmuller space $t_g$ with respect to the mapping class groups $mod_g$, which induces a cell decomposition of the moduli space $m_g$. if time permits, i will also discuss other results on similarities between the two classes of spaces and groups.