Explore a 53-minute lecture on the Andrews-Gordon partition identities and their connection to commutative algebra, presented by Jehanne Dousse from the Université de Genève at IPAM's Integrability and Algebraic Combinatorics Workshop. Delve into the world of partition identities, focusing on the famous Andrews-Gordon identities that generalize the Rogers-Ramanujan identities. Discover Pooneh Afsharijoo's 2020 conjecture of a companion to these identities, and learn about the proof involving new combinatorial dissections of Young diagrams and q-series identities. Gain insights into the origins of this conjecture and its implications in the field of algebraic combinatorics. This talk, based on joint work with Pooneh Afsharijoo, Frédéric Jouhet, and Hussein Mourtada, offers a deep dive into advanced mathematical concepts at the intersection of number theory and algebra.