If we are given a compact Lie group G acting on a space X, a powerful tool in "approximately" decomposing the G-action on functions on X is the orbit method. I will describe this method and how it sometimes refines to an exact algebraic statement which involves a "dual" group G^ and dual space X^. This is part of a joint work with David Ben-Zvi and Yiannis Sakellaridis about duality in the relative Langlands program, and I will explain that viewpoint at the end and how it connects to lecture 2. I will do my best to make a large part of the talk comprehensible without familiarity with the framework of the Langlands program. Speaker(s): Akshay Venkatesh (Institute for Advanced Study)