This will be my first Valentine's Day talk in seminar. We'll move along to Chapter 3, focusing on the proof of the Main Theorem 3.8. After invoking Menger's characterization of k-connected graphs and Lemma 2.12, the authors' strategy for the final paragraph depends Gorenstein Liaison Theory (as covered in Migliore's book) and the regularity result of Derksen-Sidman. If time permits, I might motivate a statement of the main result Thm 1.4 of the "Regularity of Line Configurations" paper, whose proof also depends on Liaison Theorem and the definition of regularity in terms of Tor. Speaker(s): Robert Walker (University of Michigan)