| Résume | Transporting the action of complex conjugation from Betti to de Rham cohomology via the Betti-de Rham comparison isomorphism, one obtains a pairing between differential forms and dual differential forms which takes real values. These values, introduced by F. Brown and called single-valued periods, form a subalgebra of the algebra of Kontsevich-Zagier periods, and were recently found to play an important role in particle physics. More specifically, it is conjectured that they appear in the perturbative expansion of scattering amplitudes of closed strings, and that they yield a cohomological interpretation of relations observed between open and closed strings, and therefore between gauge theories and quantum gravity. We will give an overview of the current state of the art without assuming any previous knowledge in physics, and we will report on recent progress in collaboration with K. Baune and J. Broedel. |
