Hi, this is my first question (of many). I am blogging for the Fields Medal Symposium and would like to get into the mathematics involved with our program.

In an attempt to sort through the articles and through all the conversations that I've been having in and around the Fields Institute, I'm having trouble seeing how all these concepts relate to each other.

In particular, the Langlands Program began with an aim to discover quadratic reciprocity laws, for which methods of representation theory of automorphic forms were applied. How and when do orbital integrals come into the picture and why is stability important?