I will discuss recent work, with Prakash Belkale, where we show the section ring for the pair (Bun, D) is finitely generated, for D the determinant of cohomology line bundle on the stack Bun = Bun_{SL(r)}(C) parameterizing principal SL(r)-bundles on a singular stable curve C.  I'll define these things, put the result into some historical perspective, and give two applications.