Shilin Lai, a mathematician at the University of Michigan, presents a Joint IAS/Princeton Number Theory seminar on constructing Euler systems in an arithmetic setting where a key simplifying assumption, local multiplicity one, fails to hold. He describes joint work with Li Cai and Yangyu Fan building the tame part of a split anticyclotomic Euler system tied to the twisted Friedberg-Jacquet setting, a framework used to study periods of automorphic forms and their connections to L-functions. Rather than the standard zeta integral method for producing the required test vectors, Lai introduces a new approach based on the unramified Plancherel formula, a tool from harmonic analysis on p-adic groups. The talk is aimed at researchers already fluent in automorphic representations and Galois cohomology, walking through the construction and the obstacles the multiplicity failure creates. It runs just over an hour, delivered at the Institute for Advanced Study's Simonyi Hall.