Emil Claasen (MPI, Potsdam)
Abstract: Modular Graph Forms (MGFs) are a class of modular forms represented by lattice sums associated to directed simple graphs. They originated from the calculation of graviton amplitudes in type II string theory. MGFs have remarkable mathematical properties such as an intricate network of algebraic and differential relations or the appearance of (conjecturally single-valued) multiple zeta values in their Fourier expansion. In particular, they are conjectured to arise as expansion coefficients of certain generating series dubbed equivariant iterated Eisenstein integrals. In this first of two talks, I will introduce the MGFs, talk about their appearance in string theory, and set the stage for their systematic conversion into their iterated integral representations.
More specifically, in this second part, among other things Emiel plans to report on sections 2 and 3 of the paper https://arxiv.org/pdf/2209.06772 and to discuss iterated integrals.
FYI, Emiel mentioned two papers by Francis Brown https://arxiv.org/pdf/1707.01230 and https://arxiv.org/pdf/1708.03354. For an introduction to modular forms, Emiel recommends sections 3.1 and 3.3 in https://arxiv.org/ftp/arxiv/papers/2011/2011.08647.pdf.
