Commutative algebra seminar Tuesday, 11 October 2022 Time: 3.30 pm-4.45 pm Venue: Ramanujan Hall Speaker: H. Ananthnarayan Title: Boij-Soderberg Conjectures and the Multiplicity Conjecture-II Abstract: In an article published in 2008, Boij and Soderberg introduced the notion of a cone related to the graded Betti numbers of a graded module over the polynomial ring over a field, and stated a couple of conjectures related to the extremal rays of this cone. They also showed that a positive answer to these conjectures resolves the Multiplicity conjecture. Eisenbud-Schreyer (2009) show that the Boij-Soderberg conjectures are true. In these talks, we will introduce the multiplicity conjectures, indicate their connection to the Boij-Soderberg conjectures, and give an idea of how Eisenbud-Schreyer resolve the latter conjectures. We explore similar results over other standard graded rings.