Single Valued Elliptic Multizetas and String theory

Modular invariance is ubiquitous in string theory.   This is the symmetry of genus-one amplitudes, as well as the non-perturbative duality symmetry of type IIb superstring in ten dimensions.  The alpha’ expansion of string theory amplitudes leads to interesting new modular forms. In this talk we will describe the properties of the new modular forms. We will explain that the modular forms entering the alpha’ expansion of genus one type-II superstring amplitude are naturally expressed as particular values of single valued elliptic multiple polylogarithm.  They are natural modular generalization of the single valued elliptic multiple-zeta introduced by Francis Brown.