Recorded 18 April 2024. Jehanne Dousse of the Université de Genève presents "The Andrews-Gordon partition identities and commutative algebra" at IPAM's Integrability and Algebraic Combinatorics Workshop. Abstract: A partition of a positive integer n is a non-increasing sequence of positive integers, called parts, whose sum is n. A partition identity is a theorem stating that for all n, the number of partitions of n satisfying some conditions (often congruence conditions on the parts) equals the number of partitions of n satisfying some other conditions (often difference conditions between the parts). The Andrews-Gordon identities, which generalize the Rogers-Ramanujan identities, are among the most famous and widely studied partition identities. Using techniques from commutative algebra, Pooneh Afsharijoo conjectured in 2020 a companion to these identities (i.e. a partition identity with the same congruence conditions but other difference conditions). In this talk, we will explain the origins of this conjecture, and give a proof using new combinatorial dissections of Young diagrams and q-series identities. This is joint work with Pooneh Afsharijoo, Frédéric Jouhet and Hussein Mourtada. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-ii-integrability-and-algebraic-combinatorics/