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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?

edited Sep 27 at 13:48

Richard Cerezo

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Richard, I gather that you are an aspiring mathematics journalist, which is laudable: the public understanding of what mathematicians do is poor, and we mathematicians could probably use some help from enthusiastic people who want to spread the word. But (even though my area is not very close to the Langlands Program), your question does not seem to have the requisite level or focus for this site. This is a site essentially for sharply focused research questions and answers between professionals, and the software is not really adapted to the type of discussion you seem to be after. Sorry. – Todd Trimble Sep 27 at 1:31

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While it's true that the question is not of the type desired for this site, I wonder where he COULD ask such a question. The people with the right level of understanding are the users of MO, not, say, StackExchange, I think. I don't know the answer.. Tom – Tom Dickens Sep 27 at 3:48

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Dear Richard, You can find a very basic introduction to the Langlands Programme in my Splitting Primes, available on the arXiv (arxiv.org/abs/1007.4426). On p.13, there are references to other expository articles, written by professionals such as Arthur, Gelbart, Knapp and Taylor. Best wishes, – Chandan Singh Dalawat Sep 27 at 5:23

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Perhaps the word "quadratic" should be removed from "quadratic reciprocity laws". – S. Carnahan♦ Sep 27 at 6:19

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One potential place for such an open-ended question / discussion would be in comments to an appropriate post on Richard Cerezo's blog itself (linked to in his profile); it might be a good approach to write to well-known math bloggers and have them advertise this blog so that interested parties can contribute. – jc Sep 27 at 16:28

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What do orbital integrals have to do with reciprocity?

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