Modular Graph Functions and Non Holomorphic Modular Forms

Explore the intricacies of modular graph functions and non-holomorphic modular forms in this lecture from the Hausdorff Trimester Program on Periods in Number Theory, Algebraic Geometry and Physics. Delve into the study of non-holomorphic modular forms arising from string perturbation theory in genus 1, as investigated by Green, Russo, Vanhove, Zagier, and Zerbini. Learn about the conjectured properties of these functions and discover a new approach to constructing non-holomorphic modular forms using real and imaginary parts of iterated integrals of Eisenstein series regularized at tangential base points. Examine how these modular forms are associated with mixed (Tate) motives and gain insights into a novel class of 'non-abelian' L-functions linked to universal mixed elliptic motives.