Ben Richert,
The betti numbers of finite length modules.
An important invariant of a finite length module is its betti numbers (or
graded betti numbers). There seems be some mysterious structure which
determines which sets of betti numbers actually occur and under what
circumstances -- especially in the graded case. In this expository talk,
we will consider several relevant results about betti numbers, and explore
some of the questions of current interest to researchers in the field.