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Séminaire Motifs et intégrales de Feynman

École polytechnique – Centre de Mathématiques Laurent Schwartz

 

14h30 – Oliver Schlotterer (Uppsala)

"The number theory of string amplitudes"

resume: In this talk, scattering amplitudes in string theory are explored as a laboratory for modern number-theoretic concepts including multiple zeta values and their elliptic generalizations.

String amplitudes are computed from moduli-space integrals over punctured Riemann surfaces. Since open strings give rise to surfaces with punctures ordered along their boundaries, one is naturally led to the iterated-integral representation of (elliptic) multiple zeta values. Closed strings in turn are associated with integrals over the sphere, the torus as well as higher-genus surfaces. In case of the sphere, one obtains the so-called ``single-valued’' subset of multiple zeta values. The modular invariant integrals over tori involve what is proposed to be an elliptic analogue of single-valued multiple zeta values.