Sug-Woo Shin, a mathematician at UC Berkeley, presents this joint IAS/Princeton Number Theory seminar on the local intertwining relation, an identity describing how normalized intertwining operators act on parabolically induced representations. The relation sits at the center of Arthur's endoscopic classification program for quasi-split classical groups, and Shin walks through several of the seed theorems still needed to complete that program. He concentrates on one in particular: extending the local intertwining relation from the tempered case to non-tempered Arthur packets using Aubert duality, also known as the Aubert-Zelevinsky involution. The talk draws on joint work with Hiraku Atobe, Wee Teck Gan, Atsushi Ichino, Tasho Kaletha, and Alberto Minguez, and assumes familiarity with representation theory of p-adic groups and the Langlands program. Recorded at the Institute for Advanced Study's Simonyi Hall, the seminar runs just over an hour and is aimed squarely at working number theorists rather than general audiences.