### Ambiguity Theory

#### Posted by David Corfield

This paper – Ambiguity theory, old and new – is rather fun and would be good to understand thoroughly if we hope to get 2-Galois to do anything important. It’s by Yves André of the ENS, and refers to a comment made by Galois that he was working with a *théorie de l’ambiguïté*. Good to see Albert Lautman receiving a mention.

For those who want something less introductory, on the same day André has deposited Galois theory, motives and transcendental numbers. Lots there about Kontsevich and Zagier’s Periods, described in their article of that name in *Mathematics Unlimited – 2001 and beyond*, pages 771-808, unfortunately now no longer available on the Web.

## Re: Ambiguity Theory

Yes those two papers by Andre are

veryhelpful to see the bigger picture and motivate algebro-geometric stuff.As for the Periods paper of Kontsevich and Zagier parts are available on google books, it’s a shame the preprint isn’t online. This idea of finding algebraically investigable yet transcendental numbers is great indeed.