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Algorithmic study of elliptic modular graph forms

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NC2W02 - Crossing the bridge: New connections in number theory and physics

Elliptic modular graph forms (eMGFs) are a string-theory motivated approach to construct higher-depth generalizations of Siegel’s / Zagier’s single-valued elliptic polylogarithms. They are generalizations of modular graph forms (a class of non-holomorphic modular forms appearing in genus-one closed string amplitudes), which depend on additional unintegrated punctures. For example, eMGFs emerge in the non-separating degeneration limit of building blocks of genus two string amplitudes. In this talk, we proceed from an algorithmic perspective and focus on general strategies to express eMGFs in terms of a canonical function space which exposes their algebraic / differential relations and their expansion around the cusp. The function space consists of iterated integrals denoted by beta^sv, which are obtained through a confluence of generating-series methods and a generalized Sieve algorithm that extends from the case of MGFs. We exemplify at fixed modular / transcendental weight how our organization of eMGFs implies the counting of their independent representatives.   Axel Kleinschmidt (AEI Potsdam), Oliver Schlotterer (Uppsala University), Bram Verbeek (Uppsala University)

This talk is part of the Isaac Newton Institute Seminar Series series.

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