All what I wanted to know about Langlands program and was afraid to ask

Abstract

These notes are very informal notes on the Langlands program. I had some pleasure in daring to ask colleagues to explain to me the importance of some of the recent results on Langlands program, so I thought I will record (to the best of my understanding) these conversations, and then share them with other mathematicians. These notes are intended for non specialists. Myself, I am not a specialist on this particular theme. I tried to give motivations and a few simple examples.

These notes are very informal and not intended to be published in any journal. They are based on pleasurable conversations with colleagues, that I recorded at the level of my understanding. Any comment will be welcomed