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Explore the intricacies of Feynman integrals in this 55-minute lecture from the Hausdorff Trimester Program on Periods in Number Theory, Algebraic Geometry and Physics. Delve into the kite and sunrise integrals, which cannot be expressed using multiple polylogarithms, and discover recent developments in finding appropriate function classes for their computation. Examine the properties of these integrals through the lens of elliptic curve periods and the Picard-Lefschetz theorem. Learn about elliptic generalizations of polylogarithms and their applications in physics. Based on joint work with Schweitzer and Weinzierl, the lecture also touches on previous collaborations with Adams, providing a comprehensive overview of cutting-edge research in this field.
