Symbols, coactions and single-valued (elliptic) polylogarithms

Abstract

Perturbative calculations in a variety of quantum field theories and in string theory exhibit striking stability properties under the motivic coaction of the contributing polylogarithms and transcendental numbers. However, for iterated integrals beyond the Riemann sphere such as elliptic polylogarithms, coaction formulae and the associated stability properties of amplitudes are less tractable. This talk introduces an alternative approach to determine coactions through the construction of single-valued versions of iterated integrals. At genus zero, the single-valued versions of polylogarithms are generated by similar types of series as their coactions. At genus one, an explicit construction of single-valued elliptic polylogarithms was recenty accomplished in joint work with Sohnle and Tao which will in the future be linked with coaction formulae.

The link to join the seminar online is https://meet.google.com/xup-zyyp-zvf