The Triply Punctured Projective Line

Lenny Taelman (University of Groningen)

Behind this title lies an entire branch of mathematics that has as its goal a combinatorial description of the absolute Galois group of the field of rational numbers Q. This is a very difficult problem and it is not surprising that little progress has been made.

In a remarkable paper, Deligne starts with a much more modest goal and ends up relating this to certain classical formulae such as Euler's

1 + ¹/4 + ¹/9 + ... = ¹/6 π².
In this lecture I shall give an introduction to this beautiful part of mathematics, assuming only some familiarity with elementary Group Theory and Complex Analysis in one variable.

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