The talk is a first order perturbation around my PhD defense and will consist of two different topics:

The topic of the first part is defect conformal field theories that arise as modifications of the well-known AdS5/CFT4 correspondence between type IIB superstring theory and N = 4 super-symmetric Yang-Mills theory. We review the supersymmetric D3-D5 probe brane intersection and then study two D3-D7 brane intersections in which supersymmetry is completely broken. We discuss how to obtain the mass spectrum of the field theories by diagonalizing the quadratic part of the action and how to derive the propagators, thereby allowing for perturbative computations of correlation functions. We show the results for one-point function of a scalar single-trace operator and compare the results to a computation on the string theory side of the correspondence. We point out connections of the one-point functions to integrability.

The second part deals with the special functions that arise as integrals over loop momenta in Feynman diagrams in the perturbative computation of scattering amplitudes. We review direct integration techniques that can be used to study both polylogarithmic and non-polylogarithmic integrals. To the latter class of integrals we discuss different ways to associate a geometry to the integral. We demonstrate these methods for the sunrise and the traintrack integral families.