Joint Theory Seminar: Kilian Bönisch

Title: Feynman Integrals, Monodromy and Calabi-Yau Varieties

Abstract:
It is well known that Feynman integrals satisfy linear differential equations with respect to their kinematic parameters. This provides an efficient method for their numerical evaluation, provided one can construct a basis of solutions to these differential equations and has a sufficient number of boundary conditions. In this talk, I explain how boundary conditions can be obtained from regularity properties of the Feynman integral and the monodromy of the associated differential equations. I show this using the family of banana integrals as an example. In this case, the associated differential equations also occur as Picard-Fuchs equations of families of Calabi-Yau varieties, and this makes the monodromy particularly simple.