Explore the mathematical intricacies of Eisenstein series and the cubic moment for PGL(2) in this advanced number theory seminar presented by Paul Nelson from ETH Zürich at the Institute for Advanced Study. Delve into the origins, applications, and proof sketches of Eisenstein series, examining concepts such as the Rankin-Selberg integral and spectral expansion. Investigate the distribution of credit, hypergeometric functions, and local integrals while learning how to achieve arbitrary weights using this method. Gain insights into improved bounds and practical applications of these mathematical concepts in this comprehensive lecture, suitable for graduate-level mathematicians and researchers in the field of number theory.