11 papers
Meromorphic higher-genus integration kernels via convolution over homology cycles
Eric D'Hoker, Oliver Schlotterer
Polylogarithms on arbitrary higher-genus Riemann surfaces can be constructed from meromorphic integration kernels with at most simple poles, whose definition was given by Enriquez…
Degenerations of flat connections on Riemann surfaces
Mattia Biancotto, Eric D'Hoker, Axel Kleinschmidt +2
The integration kernels for polylogarithm functions on a compact Riemann surface of arbitrary genus are shown to close as the surface undergoes a non-separating degeneration to…
Towards Motivic Coactions at Genus One from Zeta Generators
Axel Kleinschmidt, Franziska Porkert, Oliver Schlotterer
The motivic coaction of multiple zeta values and multiple polylogarithms encodes both structural insights on and computational methods for scattering amplitudes in a variety of qua…
Deriving motivic coactions and single-valued maps at genus zero from zeta generators
Hadleigh Frost, Martijn Hidding, Deepak Kamlesh +3
Multiple polylogarithms are equipped with rich algebraic structures including the motivic coaction and the single-valued map which both found fruitful applications in high-energy p…
Equivalence of flat connections and Fay identities on arbitrary Riemann surfaces
Eric D'Hoker, Oliver Schlotterer
A flat connection on a Riemann surface with values in an infinite dimensional Lie algebra provides a systematic and effective tool for generating an infinite family of polylogarith…
Fay identities for polylogarithms on higher-genus Riemann surfaces
Eric D'Hoker, Oliver Schlotterer
A recent construction of polylogarithms on Riemann surfaces of arbitrary genus in arXiv:2306.08644 is based on a flat connection assembled from single-valued non-holomorphic integr…