Abstract: Let \(\Gamma_{0,n}(p)\subset SL_n (\mathbb Z)\) be the congruence subgroup of level \(p\) whose first column is congruent to \((*,0,\dots,0)^t \mod p\). The cohomology of this subgroup has connections to problems in algebraic K-theory and number theory. Borel and Serre (1973) showed that the cohomology of \(\Gamma_{0,n}(p)\) vanishes above degree \(\binom{n}{2}\). We prove that the top-dimensional cohomology group $$ H^{\binom{n}{2}}(\Gamma_{0,n}(p);\mathbb Q )$$ vanishes for all \(p\in \{2,3,5,7,13\}\) when \(n \ge 3\), as well as for all primes \(p \leq 6n-11\). We also reprove the known non-vanishing result that this group is nonzero for \(n=2\) for every prime \(p\), and we establish a new non-vanishing for \(n=3\) for all primes \(p \notin \{2,3,5,7,13\}\). In this talk, I will outline the ideas behind these results and briefly survey what is known about the top cohomology of related congruence subgroups.