Let R be a ring of integers in a number field. In this talk, I will discuss what is known about the question: What is the largest number i such that H^i(SL_n(R);Q) \neq 0? Surprisingly, the nicer the ring, the less is known. I will discuss some recent progress on the case R=Z, Z[i], or Z[\frac{1+i \sqrt 3}{2}]. This is joint with Kupers, Patzt, and Wilson. Speaker(s): Jeremy Miller (Purdue University)