Modular Forms, Elliptic Polylogarithms and Feynman Integrals

Explore advanced mathematical concepts in this lecture on modular forms, elliptic polylogarithms, and Feynman integrals. Delve into the intricacies of solving Feynman integrals using epsilon-form differential equations, even when they don't evaluate to multiple polylogarithms. Discover how a non-algebraic change of basis for master integrals can achieve this result. Examine specific cases like the sunrise and kite integrals, learning how they lead to iterated integrals of modular forms and homogeneous epsilon-expansions. Investigate the implications of different period choices for elliptic curves with the same periodicity lattice. Gain insights into cutting-edge research connecting number theory, algebraic geometry, and physics through this in-depth presentation from the Hausdorff Trimester Program.

Stefan Weinzierl: Modular forms, elliptic polylogarithms and Feynman integrals