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Francis Brown : Periods, Galois theory and particle physics: General introduction to periods

A period is a certain kind of complex number which can be written as an integral of algebraic quantities. Kontsevich and Zagier conjectured that all identities between periods can be obtained from the elementary rules of calculus. After discussing several examples I will focus on the case of multiple zeta values which were first introduced in a special case by Euler, and now occur in numerous branches of mathematics. They satisfy many families of relations which are the subject of several open conjectures.

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