Abstract: We will discuss the notion of a random cover of an undirected graph and averages one can calculate for such covers. While the definition we will give for a cover is likely to be familiar to anyone who has studied a bit of algebraic topology, we will not assume everyone in the audience has the background. The notion of random we will give is quite naive, but it leads to algebraic objects we regard as very interesting, e.g., d-matchings polynomials. I will explain some known properties of these geometric and algebraic, if time permits, point out open questions which I regard as interesting.

I intend for this talk to be accessible to graduate students and encourage anyone who thinks they might be interested to attend.