The attempts to resolve the Huneke-Herzog-Srinivasan Multiplicity Conjecture lead to the development of the Boij-Soderberg theory, and the study of Betti numbers of graded modules via the Betti cone. In this talk, we discuss the conjecture, the Boij-Soderberg conjectures, and how their resolution by Eisenbud-Schreyer resolves the original one. If time permits, we will discuss some related recent work. The definitions and results in the talk will be illustrated using examples.
