Colloquium: Monday, December 18, 4 pm. Speaker: Avner Segal (UBC). Title: “L-functions and the Failure of the Local-Global Principle for G_2”.

A common question in mathematics is “Can global questions be answered by local means?”, this is usually referred to as the “local-global principle”. A famous example is the Hasse-Minkowski theorem on quadratic forms. On the other and, it is also known that the Hasse-Minkowski theorem cannot be extended to cubic forms. In this talk, I will present the local-global principle for automorphic represntations, describe its success in the cuspidal spectrum of the group GL_n and its failure in the cuspidal spectrum of the exceptional group of type G_2.