We have previously seen several different classes of singularities defined using the Frobenius map. But within a class, we sometimes want more fine-grained information. This is where numerical invariants come into play! In this talk, we will discuss both the F-signature, which measures "how" strongly F-regular a ring is, and the (relative) F-rational signature, which measures "how" F-rational a ring is. We will go over their key nice properties, and do a comparison of the two definitions.

This is the second in a series of two talks.